Daily Papers

Language models have demonstrated remarkable performance in solving reasoning tasks; however, even the strongest models still occasionally make reasoning mistakes. Recently, there has been active research aimed at improving reasoning accuracy, particularly by using pretrained language models to "self-correct" their mistakes via multi-round prompting. In this paper, we follow this line of work but focus on understanding the usefulness of incorporating "error-correction" data directly into the pretraining stage. This data consists of erroneous solution steps immediately followed by their corrections. Using a synthetic math dataset, we show promising results: this type of pretrain data can help language models achieve higher reasoning accuracy directly (i.e., through simple auto-regression, without multi-round prompting) compared to pretraining on the same amount of error-free data. We also delve into many details, such as (1) how this approach differs from beam search, (2) how such data can be prepared, (3) whether masking is needed on the erroneous tokens, (4) the amount of error required, (5) whether such data can be deferred to the fine-tuning stage, and many others.

We discovered the underlying physics in Next-token Prediction (NTP). We identified the law of information conservation within NTP and proposed the First Law of Information Capacity (IC-1), demonstrating that the essence of intelligence emergence in auto-regressive models is fundamentally a process of information transfer. We also introduced Landauer's Principle into NTP, formulating the Second Law of Information Capacity (IC-2), which establishes the relationship between auto-regressive model training and energy consumption. Additionally, we presented several corollaries, which hold practical significance for production practices. Finally, we validated the compatibility and complementarity of our findings with existing theories.

Scaling laws describe the relationship between the size of language models and their capabilities. Unlike prior studies that evaluate a model's capability via loss or benchmarks, we estimate the number of knowledge bits a model stores. We focus on factual knowledge represented as tuples, such as (USA, capital, Washington D.C.) from a Wikipedia page. Through multiple controlled datasets, we establish that language models can and only can store 2 bits of knowledge per parameter, even when quantized to int8, and such knowledge can be flexibly extracted for downstream applications. Consequently, a 7B model can store 14B bits of knowledge, surpassing the English Wikipedia and textbooks combined based on our estimation. More broadly, we present 12 results on how (1) training duration, (2) model architecture, (3) quantization, (4) sparsity constraints such as MoE, and (5) data signal-to-noise ratio affect a model's knowledge storage capacity. Notable insights include: * The GPT-2 architecture, with rotary embedding, matches or even surpasses LLaMA/Mistral architectures in knowledge storage, particularly over shorter training durations. This arises because LLaMA/Mistral uses GatedMLP, which is less stable and harder to train. * Prepending training data with domain names (e.g., wikipedia.org) significantly increases a model's knowledge capacity. Language models can autonomously identify and prioritize domains rich in knowledge, optimizing their storage capacity.

Large language models (LLMs) can store a vast amount of world knowledge, often extractable via question-answering (e.g., "What is Abraham Lincoln's birthday?"). However, do they answer such questions based on exposure to similar questions during training (i.e., cheating), or by genuinely learning to extract knowledge from sources like Wikipedia? In this paper, we investigate this issue using a controlled biography dataset. We find a strong correlation between the model's ability to extract knowledge and various diversity measures of the training data. Essentially, for knowledge to be reliably extracted, it must be sufficiently augmented (e.g., through paraphrasing, sentence shuffling) during pretraining. Without such augmentation, knowledge may be memorized but not extractable, leading to 0% accuracy, regardless of subsequent instruction fine-tuning. To understand why this occurs, we employ (nearly) linear probing to demonstrate a strong connection between the observed correlation and how the model internally encodes knowledge -- whether it is linearly encoded in the hidden embeddings of entity names or distributed across other token embeddings in the training text. This paper provides several key recommendations for LLM pretraining in the industry: (1) rewrite the pretraining data -- using small, auxiliary models -- to provide knowledge augmentation, and (2) incorporate more instruction-finetuning data into the pretraining stage before it becomes too late.

Language models can store vast amounts of factual knowledge, but their ability to use this knowledge for logical reasoning remains questionable. This paper explores a language model's ability to manipulate its stored knowledge during inference. We focus on four manipulation types: retrieval (e.g., "What is person A's attribute X"), classification (e.g., "Is A's attribute X even or odd?"), comparison (e.g., "Is A greater than B in attribute X?") and inverse search (e.g., "Which person's attribute X equals T?") We observe that pre-trained language models like GPT2/3/4 excel in knowledge retrieval but struggle with simple classification or comparison tasks unless Chain of Thoughts (CoTs) are employed during both training and inference. They also perform poorly in inverse knowledge search, irrespective of the prompts. Our primary contribution is a synthetic dataset for a controlled experiment that confirms these inherent weaknesses: a language model cannot efficiently manipulate knowledge from pre-training data, even when such knowledge is perfectly stored and fully extractable in the models, and despite adequate instruct fine-tuning.

Avatars are important to create interactive and immersive experiences in virtual worlds. One challenge in animating these characters to mimic a user's motion is that commercial AR/VR products consist only of a headset and controllers, providing very limited sensor data of the user's pose. Another challenge is that an avatar might have a different skeleton structure than a human and the mapping between them is unclear. In this work we address both of these challenges. We introduce a method to retarget motions in real-time from sparse human sensor data to characters of various morphologies. Our method uses reinforcement learning to train a policy to control characters in a physics simulator. We only require human motion capture data for training, without relying on artist-generated animations for each avatar. This allows us to use large motion capture datasets to train general policies that can track unseen users from real and sparse data in real-time. We demonstrate the feasibility of our approach on three characters with different skeleton structure: a dinosaur, a mouse-like creature and a human. We show that the avatar poses often match the user surprisingly well, despite having no sensor information of the lower body available. We discuss and ablate the important components in our framework, specifically the kinematic retargeting step, the imitation, contact and action reward as well as our asymmetric actor-critic observations. We further explore the robustness of our method in a variety of settings including unbalancing, dancing and sports motions.

We design controlled experiments to study HOW generative language models, like GPT, learn context-free grammars (CFGs) -- diverse language systems with a tree-like structure capturing many aspects of natural languages, programs, and logics. CFGs are as hard as pushdown automata, and can be ambiguous so that verifying if a string satisfies the rules requires dynamic programming. We construct synthetic data and demonstrate that even for difficult (long and ambiguous) CFGs, pre-trained transformers can learn to generate sentences with near-perfect accuracy and impressive diversity. More importantly, we delve into the physical principles behind how transformers learns CFGs. We discover that the hidden states within the transformer implicitly and precisely encode the CFG structure (such as putting tree node information exactly on the subtree boundary), and learn to form "boundary to boundary" attentions resembling dynamic programming. We also cover some extension of CFGs as well as the robustness aspect of transformers against grammar mistakes. Overall, our research provides a comprehensive and empirical understanding of how transformers learn CFGs, and reveals the physical mechanisms utilized by transformers to capture the structure and rules of languages.

Recent advances in language models have demonstrated their capability to solve mathematical reasoning problems, achieving near-perfect accuracy on grade-school level math benchmarks like GSM8K. In this paper, we formally study how language models solve these problems. We design a series of controlled experiments to address several fundamental questions: (1) Can language models truly develop reasoning skills, or do they simply memorize templates? (2) What is the model's hidden (mental) reasoning process? (3) Do models solve math questions using skills similar to or different from humans? (4) Do models trained on GSM8K-like datasets develop reasoning skills beyond those necessary for solving GSM8K problems? (5) What mental process causes models to make reasoning mistakes? (6) How large or deep must a model be to effectively solve GSM8K-level math questions? Our study uncovers many hidden mechanisms by which language models solve mathematical questions, providing insights that extend beyond current understandings of LLMs.

Acquisition of large datasets for three-dimensional (3D) partial differential equations are usually very expensive. Physics-informed neural operator (PINO) eliminates the high costs associated with generation of training datasets, and shows great potential in a variety of partial differential equations. In this work, we employ physics-informed neural operator, encoding the large-eddy simulation (LES) equations directly into the neural operator for simulating three-dimensional incompressible turbulent flows. We develop the LESnets (Large-Eddy Simulation nets) by adding large-eddy simulation equations to two different data-driven models, including Fourier neural operator (FNO) and implicit Fourier neural operator (IFNO) without using label data. Notably, by leveraging only PDE constraints to learn the spatio-temporal dynamics problem, LESnets retains the computational efficiency of data-driven approaches while obviating the necessity for data. Meanwhile, using large-eddy simulation equations as PDE constraints makes it possible to efficiently predict complex turbulence at coarse grids. We investigate the performance of the LESnets with two standard three-dimensional turbulent flows: decaying homogeneous isotropic turbulence and temporally evolving turbulent mixing layer. In the numerical experiments, the LESnets model shows a similar or even better accuracy as compared to traditional large-eddy simulation and data-driven models of FNO and IFNO. Moreover, the well-trained LESnets is significantly faster than traditional LES, and has a similar efficiency as the data-driven FNO and IFNO models. Thus, physics-informed neural operators have a strong potential for 3D nonlinear engineering applications.

Physics-based inverse rendering aims to jointly optimize shape, materials, and lighting from captured 2D images. Here lighting is an important part of achieving faithful light transport simulation. While the environment map is commonly used as the lighting model in inverse rendering, we show that its distant lighting assumption leads to spatial invariant lighting, which can be an inaccurate approximation in real-world inverse rendering. We propose to use NeRF as a spatially varying environment lighting model and build an inverse rendering pipeline using NeRF as the non-distant environment emitter. By comparing our method with the environment map on real and synthetic datasets, we show that our NeRF-based emitter models the scene lighting more accurately and leads to more accurate inverse rendering. Project page and video: https://nerfemitterpbir.github.io/.

Magnetic navigation (MagNav) is a rising alternative to the Global Positioning System (GPS) and has proven useful for aircraft navigation. Traditional aircraft navigation systems, while effective, face limitations in precision and reliability in certain environments and against attacks. Airborne MagNav leverages the Earth's magnetic field to provide accurate positional information. However, external magnetic fields induced by aircraft electronics and Earth's large-scale magnetic fields disrupt the weaker signal of interest. We introduce a physics-informed approach using Tolles-Lawson coefficients for compensation and Liquid Time-Constant Networks (LTCs) to remove complex, noisy signals derived from the aircraft's magnetic sources. Using real flight data with magnetometer measurements and aircraft measurements, we observe up to a 64% reduction in aeromagnetic compensation error (RMSE nT), outperforming conventional models. This significant improvement underscores the potential of a physics-informed, machine learning approach for extracting clean, reliable, and accurate magnetic signals for MagNav positional estimation.

In this work, we present a novel physics-based data-driven framework for reduced-order modeling of laser ignition in a model rocket combustor based on parameterized neural ordinary differential equations (PNODE). Deep neural networks are embedded as functions of high-dimensional parameters of laser ignition to predict various terms in a 0D flow model including the heat source function, pre-exponential factors, and activation energy. Using the governing equations of a 0D flow model, our PNODE needs only a limited number of training samples and predicts trajectories of various quantities such as temperature, pressure, and mass fractions of species while satisfying physical constraints. We validate our physics-based PNODE on solution snapshots of high-fidelity Computational Fluid Dynamics (CFD) simulations of laser-induced ignition in a prototype rocket combustor. We compare the performance of our physics-based PNODE with that of kernel ridge regression and fully connected neural networks. Our results show that our physics-based PNODE provides solutions with lower mean absolute errors of average temperature over time, thus improving the prediction of successful laser ignition with high-dimensional parameters.

A faster than real time forecast system for solar wind and interplanetary magnetic field transients that is driven by hourly updated solar magnetograms is proposed to provide a continuous nowcast of the solar corona (<0.1AU) and 24-hours forecast of the solar wind at 1 AU by solving a full 3-D MHD model. This new model has been inspired by the concept of relativity of simultaneity used in the theory of special relativity. It is based on time transformation between two coordinate systems: the solar rest frame and a boosted system in which the current observations of the solar magnetic field and tomorrow's measurement of the solar wind at 1 AU are simultaneous. In this paper we derive the modified governing equations for both hydrodynamics (HD) and magnetohydrodynamics (MHD) and present a new numerical algorithm that only modifies the conserved quantities but preserves the original HD/MHD numerical flux. The proposed method enables an efficient numerical implementation, and thus a significantly longer forecast time than the traditional method.

We delve into the physics-informed neural reconstruction of smoke and obstacles through sparse-view RGB videos, tackling challenges arising from limited observation of complex dynamics. Existing physics-informed neural networks often emphasize short-term physics constraints, leaving the proper preservation of long-term conservation less explored. We introduce Neural Characteristic Trajectory Fields, a novel representation utilizing Eulerian neural fields to implicitly model Lagrangian fluid trajectories. This topology-free, auto-differentiable representation facilitates efficient flow map calculations between arbitrary frames as well as efficient velocity extraction via auto-differentiation. Consequently, it enables end-to-end supervision covering long-term conservation and short-term physics priors. Building on the representation, we propose physics-informed trajectory learning and integration into NeRF-based scene reconstruction. We enable advanced obstacle handling through self-supervised scene decomposition and seamless integrated boundary constraints. Our results showcase the ability to overcome challenges like occlusion uncertainty, density-color ambiguity, and static-dynamic entanglements. Code and sample tests are at https://github.com/19reborn/PICT_smoke.

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied data distribution are expected to adhere to specific governing equations. We present a framework that unifies generative modeling and partial differential equation fulfillment by introducing a first-principle-based loss term that enforces generated samples to fulfill the underlying physical constraints. Our approach reduces the residual error by up to two orders of magnitude compared to previous work in a fluid flow case study and outperforms task-specific frameworks in relevant metrics for structural topology optimization. We also present numerical evidence that our extended training objective acts as a natural regularization mechanism against overfitting. Our framework is simple to implement and versatile in its applicability for imposing equality and inequality constraints as well as auxiliary optimization objectives.

3D reconstruction of dynamic scenes is a long-standing problem in computer graphics and increasingly difficult the less information is available. Shape-from-Template (SfT) methods aim to reconstruct a template-based geometry from RGB images or video sequences, often leveraging just a single monocular camera without depth information, such as regular smartphone recordings. Unfortunately, existing reconstruction methods are either unphysical and noisy or slow in optimization. To solve this problem, we propose a novel SfT reconstruction algorithm for cloth using a pre-trained neural surrogate model that is fast to evaluate, stable, and produces smooth reconstructions due to a regularizing physics simulation. Differentiable rendering of the simulated mesh enables pixel-wise comparisons between the reconstruction and a target video sequence that can be used for a gradient-based optimization procedure to extract not only shape information but also physical parameters such as stretching, shearing, or bending stiffness of the cloth. This allows to retain a precise, stable, and smooth reconstructed geometry while reducing the runtime by a factor of 400-500 compared to phi-SfT, a state-of-the-art physics-based SfT approach.

Physics-Informed Neural Networks (PINNs) have emerged as a promising deep learning framework for approximating numerical solutions to partial differential equations (PDEs). However, conventional PINNs, relying on multilayer perceptrons (MLP), neglect the crucial temporal dependencies inherent in practical physics systems and thus fail to propagate the initial condition constraints globally and accurately capture the true solutions under various scenarios. In this paper, we introduce a novel Transformer-based framework, termed PINNsFormer, designed to address this limitation. PINNsFormer can accurately approximate PDE solutions by utilizing multi-head attention mechanisms to capture temporal dependencies. PINNsFormer transforms point-wise inputs into pseudo sequences and replaces point-wise PINNs loss with a sequential loss. Additionally, it incorporates a novel activation function, Wavelet, which anticipates Fourier decomposition through deep neural networks. Empirical results demonstrate that PINNsFormer achieves superior generalization ability and accuracy across various scenarios, including PINNs failure modes and high-dimensional PDEs. Moreover, PINNsFormer offers flexibility in integrating existing learning schemes for PINNs, further enhancing its performance.

Image distortion by atmospheric turbulence is a stochastic degradation, which is a critical problem in long-range optical imaging systems. A number of research has been conducted during the past decades, including model-based and emerging deep-learning solutions with the help of synthetic data. Although fast and physics-grounded simulation tools have been introduced to help the deep-learning models adapt to real-world turbulence conditions recently, the training of such models only relies on the synthetic data and ground truth pairs. This paper proposes the Physics-integrated Restoration Network (PiRN) to bring the physics-based simulator directly into the training process to help the network to disentangle the stochasticity from the degradation and the underlying image. Furthermore, to overcome the ``average effect" introduced by deterministic models and the domain gap between the synthetic and real-world degradation, we further introduce PiRN with Stochastic Refinement (PiRN-SR) to boost its perceptual quality. Overall, our PiRN and PiRN-SR improve the generalization to real-world unknown turbulence conditions and provide a state-of-the-art restoration in both pixel-wise accuracy and perceptual quality. Our codes are available at https://github.com/VITA-Group/PiRN.

Physics-informed Neural Networks (PINNs) have recently achieved remarkable progress in solving Partial Differential Equations (PDEs) in various fields by minimizing a weighted sum of PDE loss and boundary loss. However, there are several critical challenges in the training of PINNs, including the lack of theoretical frameworks and the imbalance between PDE loss and boundary loss. In this paper, we present an analysis of second-order non-homogeneous PDEs, which are classified into three categories and applicable to various common problems. We also characterize the connections between the training loss and actual error, guaranteeing convergence under mild conditions. The theoretical analysis inspires us to further propose MultiAdam, a scale-invariant optimizer that leverages gradient momentum to parameter-wisely balance the loss terms. Extensive experiment results on multiple problems from different physical domains demonstrate that our MultiAdam solver can improve the predictive accuracy by 1-2 orders of magnitude compared with strong baselines.

We present a physics-based inverse rendering method that learns the illumination, geometry, and materials of a scene from posed multi-view RGB images. To model the illumination of a scene, existing inverse rendering works either completely ignore the indirect illumination or model it by coarse approximations, leading to sub-optimal illumination, geometry, and material prediction of the scene. In this work, we propose a physics-based illumination model that first locates surface points through an efficient refined sphere tracing algorithm, then explicitly traces the incoming indirect lights at each surface point based on reflection. Then, we estimate each identified indirect light through an efficient neural network. Moreover, we utilize the Leibniz's integral rule to resolve non-differentiability in the proposed illumination model caused by boundary lights inspired by differentiable irradiance in computer graphics. As a result, the proposed differentiable illumination model can be learned end-to-end together with geometry and materials estimation. As a side product, our physics-based inverse rendering model also facilitates flexible and realistic material editing as well as relighting. Extensive experiments on synthetic and real-world datasets demonstrate that the proposed method performs favorably against existing inverse rendering methods on novel view synthesis and inverse rendering.

Physics-informed neural networks (PINNs) are emerging as popular mesh-free solvers for partial differential equations (PDEs). Recent extensions decompose the domain, applying different PINNs to solve the equation in each subdomain and aligning the solution at the interface of the subdomains. Hence, they can further alleviate the problem complexity, reduce the computational cost, and allow parallelization. However, the performance of the multi-domain PINNs is sensitive to the choice of the interface conditions for solution alignment. While quite a few conditions have been proposed, there is no suggestion about how to select the conditions according to specific problems. To address this gap, we propose META Learning of Interface Conditions (METALIC), a simple, efficient yet powerful approach to dynamically determine the optimal interface conditions for solving a family of parametric PDEs. Specifically, we develop two contextual multi-arm bandit models. The first one applies to the entire training procedure, and online updates a Gaussian process (GP) reward surrogate that given the PDE parameters and interface conditions predicts the solution error. The second one partitions the training into two stages, one is the stochastic phase and the other deterministic phase; we update a GP surrogate for each phase to enable different condition selections at the two stages so as to further bolster the flexibility and performance. We have shown the advantage of METALIC on four bench-mark PDE families.

Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints. These soft constraints are often considered to be the sources of the complexity in the training phase of PINNs. Here, we demonstrate that the challenge of training (i) persists even when the boundary conditions are strictly enforced, and (ii) is closely related to the Kolmogorov n-width associated with problems demonstrating transport, convection, traveling waves, or moving fronts. Given this realization, we describe the mechanism underlying the training schemes such as those used in eXtended PINNs (XPINN), curriculum regularization, and sequence-to-sequence learning. For an important category of PDEs, i.e., governed by non-linear convection-diffusion equation, we propose reformulating PINNs on a Lagrangian frame of reference, i.e., LPINNs, as a PDE-informed solution. A parallel architecture with two branches is proposed. One branch solves for the state variables on the characteristics, and the second branch solves for the low-dimensional characteristics curves. The proposed architecture conforms to the causality innate to the convection, and leverages the direction of travel of the information in the domain. Finally, we demonstrate that the loss landscapes of LPINNs are less sensitive to the so-called "complexity" of the problems, compared to those in the traditional PINNs in the Eulerian framework.

Enhancing the visibility in extreme low-light environments is a challenging task. Under nearly lightless condition, existing image denoising methods could easily break down due to significantly low SNR. In this paper, we systematically study the noise statistics in the imaging pipeline of CMOS photosensors, and formulate a comprehensive noise model that can accurately characterize the real noise structures. Our novel model considers the noise sources caused by digital camera electronics which are largely overlooked by existing methods yet have significant influence on raw measurement in the dark. It provides a way to decouple the intricate noise structure into different statistical distributions with physical interpretations. Moreover, our noise model can be used to synthesize realistic training data for learning-based low-light denoising algorithms. In this regard, although promising results have been shown recently with deep convolutional neural networks, the success heavily depends on abundant noisy clean image pairs for training, which are tremendously difficult to obtain in practice. Generalizing their trained models to images from new devices is also problematic. Extensive experiments on multiple low-light denoising datasets -- including a newly collected one in this work covering various devices -- show that a deep neural network trained with our proposed noise formation model can reach surprisingly-high accuracy. The results are on par with or sometimes even outperform training with paired real data, opening a new door to real-world extreme low-light photography.

Nonlinear model order reduction has opened the door to parameter optimization and uncertainty quantification in complex physics problems governed by nonlinear equations. In particular, the computational cost of solving these equations can be reduced by means of local reduced-order bases. This article examines the benefits of a physics-informed cluster analysis for the construction of cluster-specific reduced-order bases. We illustrate that the choice of the dissimilarity measure for clustering is fundamental and highly affects the performances of the local reduced-order bases. It is shown that clustering with an angle-based dissimilarity on simulation data efficiently decreases the intra-cluster Kolmogorov N-width. Additionally, an a priori efficiency criterion is introduced to assess the relevance of a ROM-net, a methodology for the reduction of nonlinear physics problems introduced in our previous work in [T. Daniel, F. Casenave, N. Akkari, D. Ryckelynck, Model order reduction assisted by deep neural networks (ROM-net), Advanced Modeling and Simulation in Engineering Sciences 7 (16), 2020]. This criterion also provides engineers with a very practical method for ROM-nets' hyperparameters calibration under constrained computational costs for the training phase. On five different physics problems, our physics-informed clustering strategy significantly outperforms classic strategies for the construction of local reduced-order bases in terms of projection errors.

We design a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. Although existing nonlinear manifold learning methods seem to be compelling tools to reduce the dimensionality of data characterized by a large Kolmogorov n-width, they typically lack a straightforward mapping from the latent space to the high-dimensional physical space. Moreover, the realized latent variables are often hard to interpret. Therefore, many of these methods are often dismissed in the reduced order modeling of dynamical systems governed by the partial differential equations (PDEs). Accordingly, we propose an auto-encoder type nonlinear dimensionality reduction algorithm. The unsupervised learning problem trains a diffeomorphic spatio-temporal grid, that registers the output sequence of the PDEs on a non-uniform parameter/time-varying grid, such that the Kolmogorov n-width of the mapped data on the learned grid is minimized. We demonstrate the efficacy and interpretability of our approach to separate convection/advection from diffusion/scaling on various manufactured and physical systems.

In recent years, there has been rapid development in 3D generation models, opening up new possibilities for applications such as simulating the dynamic movements of 3D objects and customizing their behaviors. However, current 3D generative models tend to focus only on surface features such as color and shape, neglecting the inherent physical properties that govern the behavior of objects in the real world. To accurately simulate physics-aligned dynamics, it is essential to predict the physical properties of materials and incorporate them into the behavior prediction process. Nonetheless, predicting the diverse materials of real-world objects is still challenging due to the complex nature of their physical attributes. In this paper, we propose Physics3D, a novel method for learning various physical properties of 3D objects through a video diffusion model. Our approach involves designing a highly generalizable physical simulation system based on a viscoelastic material model, which enables us to simulate a wide range of materials with high-fidelity capabilities. Moreover, we distill the physical priors from a video diffusion model that contains more understanding of realistic object materials. Extensive experiments demonstrate the effectiveness of our method with both elastic and plastic materials. Physics3D shows great potential for bridging the gap between the physical world and virtual neural space, providing a better integration and application of realistic physical principles in virtual environments. Project page: https://liuff19.github.io/Physics3D.

The image-to-image translation abilities of generative learning models have recently made significant progress in the estimation of complex (steered) mappings between image distributions. While appearance based tasks like image in-painting or style transfer have been studied at length, we propose to investigate the potential of generative models in the context of physical simulations. Providing a dataset of 300k image-pairs and baseline evaluations for three different physical simulation tasks, we propose a benchmark to investigate the following research questions: i) are generative models able to learn complex physical relations from input-output image pairs? ii) what speedups can be achieved by replacing differential equation based simulations? While baseline evaluations of different current models show the potential for high speedups (ii), these results also show strong limitations toward the physical correctness (i). This underlines the need for new methods to enforce physical correctness. Data, baseline models and evaluation code http://www.physics-gen.org.

Realistic object interactions are crucial for creating immersive virtual experiences, yet synthesizing realistic 3D object dynamics in response to novel interactions remains a significant challenge. Unlike unconditional or text-conditioned dynamics generation, action-conditioned dynamics requires perceiving the physical material properties of objects and grounding the 3D motion prediction on these properties, such as object stiffness. However, estimating physical material properties is an open problem due to the lack of material ground-truth data, as measuring these properties for real objects is highly difficult. We present PhysDreamer, a physics-based approach that endows static 3D objects with interactive dynamics by leveraging the object dynamics priors learned by video generation models. By distilling these priors, PhysDreamer enables the synthesis of realistic object responses to novel interactions, such as external forces or agent manipulations. We demonstrate our approach on diverse examples of elastic objects and evaluate the realism of the synthesized interactions through a user study. PhysDreamer takes a step towards more engaging and realistic virtual experiences by enabling static 3D objects to dynamically respond to interactive stimuli in a physically plausible manner. See our project page at https://physdreamer.github.io/.

We introduce PhysGaussian, a new method that seamlessly integrates physically grounded Newtonian dynamics within 3D Gaussians to achieve high-quality novel motion synthesis. Employing a custom Material Point Method (MPM), our approach enriches 3D Gaussian kernels with physically meaningful kinematic deformation and mechanical stress attributes, all evolved in line with continuum mechanics principles. A defining characteristic of our method is the seamless integration between physical simulation and visual rendering: both components utilize the same 3D Gaussian kernels as their discrete representations. This negates the necessity for triangle/tetrahedron meshing, marching cubes, "cage meshes," or any other geometry embedding, highlighting the principle of "what you see is what you simulate (WS^2)." Our method demonstrates exceptional versatility across a wide variety of materials--including elastic entities, metals, non-Newtonian fluids, and granular materials--showcasing its strong capabilities in creating diverse visual content with novel viewpoints and movements. Our project page is at: https://xpandora.github.io/PhysGaussian/

We investigate the emergence of intuitive physics understanding in general-purpose deep neural network models trained to predict masked regions in natural videos. Leveraging the violation-of-expectation framework, we find that video prediction models trained to predict outcomes in a learned representation space demonstrate an understanding of various intuitive physics properties, such as object permanence and shape consistency. In contrast, video prediction in pixel space and multimodal large language models, which reason through text, achieve performance closer to chance. Our comparisons of these architectures reveal that jointly learning an abstract representation space while predicting missing parts of sensory input, akin to predictive coding, is sufficient to acquire an understanding of intuitive physics, and that even models trained on one week of unique video achieve above chance performance. This challenges the idea that core knowledge -- a set of innate systems to help understand the world -- needs to be hardwired to develop an understanding of intuitive physics.

The approximation of Partial Differential Equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and flexibility in implementing various PDEs, PINNs often suffer from limited accuracy due to the spectral bias of Multi-Layer Perceptrons (MLPs), which struggle to effectively learn high-frequency and non-linear components. Recently, parametric mesh representations in combination with neural networks have been investigated as a promising approach to eliminate the inductive biases of neural networks. However, they usually require very high-resolution grids and a large number of collocation points to achieve high accuracy while avoiding overfitting issues. In addition, the fixed positions of the mesh parameters restrict their flexibility, making it challenging to accurately approximate complex PDEs. To overcome these limitations, we propose Physics-Informed Gaussians (PIGs), which combine feature embeddings using Gaussian functions with a lightweight neural network. Our approach uses trainable parameters for the mean and variance of each Gaussian, allowing for dynamic adjustment of their positions and shapes during training. This adaptability enables our model to optimally approximate PDE solutions, unlike models with fixed parameter positions. Furthermore, the proposed approach maintains the same optimization framework used in PINNs, allowing us to benefit from their excellent properties. Experimental results show the competitive performance of our model across various PDEs, demonstrating its potential as a robust tool for solving complex PDEs. Our project page is available at https://namgyukang.github.io/Physics-Informed-Gaussians/

We introduce Augmented Physics, a machine learning-integrated authoring tool designed for creating embedded interactive physics simulations from static textbook diagrams. Leveraging recent advancements in computer vision, such as Segment Anything and Multi-modal LLMs, our web-based system enables users to semi-automatically extract diagrams from physics textbooks and generate interactive simulations based on the extracted content. These interactive diagrams are seamlessly integrated into scanned textbook pages, facilitating interactive and personalized learning experiences across various physics concepts, such as optics, circuits, and kinematics. Drawing from an elicitation study with seven physics instructors, we explore four key augmentation strategies: 1) augmented experiments, 2) animated diagrams, 3) bi-directional binding, and 4) parameter visualization. We evaluate our system through technical evaluation, a usability study (N=12), and expert interviews (N=12). Study findings suggest that our system can facilitate more engaging and personalized learning experiences in physics education.

Generating videos with realistic and physically plausible motion is one of the main recent challenges in computer vision. While diffusion models are achieving compelling results in image generation, video diffusion models are limited by heavy training and huge models, resulting in videos that are still biased to the training dataset. In this work we propose MotionCraft, a new zero-shot video generator to craft physics-based and realistic videos. MotionCraft is able to warp the noise latent space of an image diffusion model, such as Stable Diffusion, by applying an optical flow derived from a physics simulation. We show that warping the noise latent space results in coherent application of the desired motion while allowing the model to generate missing elements consistent with the scene evolution, which would otherwise result in artefacts or missing content if the flow was applied in the pixel space. We compare our method with the state-of-the-art Text2Video-Zero reporting qualitative and quantitative improvements, demonstrating the effectiveness of our approach to generate videos with finely-prescribed complex motion dynamics. Project page: https://mezzelfo.github.io/MotionCraft/

This paper presents a modeling effort to explore the underlying physics of temperature evolution during additive friction stir deposition (AFSD) by a human-AI teaming approach. AFSD is an emerging solid-state additive manufacturing technology that deposits materials without melting. However, both process modeling and modeling of the AFSD tool are at an early stage. In this paper, a human-AI teaming approach is proposed to combine models based on first principles with AI. The resulting human-informed machine learning method, denoted as AFSD-Physics, can effectively learn the governing equations of temperature evolution at the tool and the build from in-process measurements. Experiments are designed and conducted to collect in-process measurements for the deposition of aluminum 7075 with a total of 30 layers. The acquired governing equations are physically interpretable models with low computational cost and high accuracy. Model predictions show good agreement with the measurements. Experimental validation with new process parameters demonstrates the model's generalizability and potential for use in tool temperature control and process optimization.

Near-field multiple-input multiple-output (MIMO) radar imaging systems have recently gained significant attention. In this paper, we develop novel non-iterative deep learning-based reconstruction methods for real-time near-field MIMO imaging. The goal is to achieve high image quality with low computational cost at compressive settings. The developed approaches have two stages. In the first approach, physics-based initial stage performs adjoint operation to back-project the measurements to the image-space, and deep neural network (DNN)-based second stage converts the 3D backprojected measurements to a magnitude-only reflectivity image. Since scene reflectivities often have random phase, DNN processes directly the magnitude of the adjoint result. As DNN, 3D U-Net is used to jointly exploit range and cross-range correlations. To comparatively evaluate the significance of exploiting physics in a learning-based approach, two additional approaches that replace the physics-based first stage with fully connected layers are also developed as purely learning-based methods. The performance is also analyzed by changing the DNN architecture for the second stage to include complex-valued processing (instead of magnitude-only processing), 2D convolution kernels (instead of 3D), and ResNet architecture (instead of U-Net). Moreover, we develop a synthesizer to generate large-scale dataset for training with 3D extended targets. We illustrate the performance through experimental data and extensive simulations. The results show the effectiveness of the developed physics-based learned reconstruction approach in terms of both run-time and image quality at highly compressive settings. Our source codes and dataset are made available at GitHub.

Scientific machine learning and the advent of the Physics-Informed Neural Network (PINN) show considerable potential in their capacity to identify solutions to complex differential equations. Over the past two years, much work has gone into the development of PINNs capable of solving the gravity field modeling problem -- i.e.\ learning a differentiable form of the gravitational potential from position and acceleration estimates. While the past PINN gravity models (PINN-GMs) have demonstrated advantages in model compactness, robustness to noise, and sample efficiency; there remain key modeling challenges which this paper aims to address. Specifically, this paper introduces the third generation of the Physics-Informed Neural Network Gravity Model (PINN-GM-III) which solves the problems of extrapolation error, bias towards low-altitude samples, numerical instability at high-altitudes, and compliant boundary conditions through numerous modifications to the model's design. The PINN-GM-III is tested by modeling a known heterogeneous density asteroid, and its performance is evaluated using seven core metrics which showcases its strengths against its predecessors and other analytic and numerical gravity models.

We introduce a benchmark to evaluate the capability of AI to solve problems in theoretical physics, focusing on high-energy theory and cosmology. The first iteration of our benchmark consists of 57 problems of varying difficulty, from undergraduate to research level. These problems are novel in the sense that they do not come from public problem collections. We evaluate our data set on various open and closed language models, including o3-mini, o1, DeepSeek-R1, GPT-4o and versions of Llama and Qwen. While we find impressive progress in model performance with the most recent models, our research-level difficulty problems are mostly unsolved. We address challenges of auto-verifiability and grading, and discuss common failure modes. While currently state-of-the art models are still of limited use for researchers, our results show that AI assisted theoretical physics research may become possible in the near future. We discuss the main obstacles towards this goal and possible strategies to overcome them. The public problems and solutions, results for various models, and updates to the data set and score distribution, are available on the website of the dataset tpbench.org.

Recently, the field of text-guided 3D scene generation has garnered significant attention. High-quality generation that aligns with physical realism and high controllability is crucial for practical 3D scene applications. However, existing methods face fundamental limitations: (i) difficulty capturing complex relationships between multiple objects described in the text, (ii) inability to generate physically plausible scene layouts, and (iii) lack of controllability and extensibility in compositional scenes. In this paper, we introduce LayoutDreamer, a framework that leverages 3D Gaussian Splatting (3DGS) to facilitate high-quality, physically consistent compositional scene generation guided by text. Specifically, given a text prompt, we convert it into a directed scene graph and adaptively adjust the density and layout of the initial compositional 3D Gaussians. Subsequently, dynamic camera adjustments are made based on the training focal point to ensure entity-level generation quality. Finally, by extracting directed dependencies from the scene graph, we tailor physical and layout energy to ensure both realism and flexibility. Comprehensive experiments demonstrate that LayoutDreamer outperforms other compositional scene generation quality and semantic alignment methods. Specifically, it achieves state-of-the-art (SOTA) performance in the multiple objects generation metric of T3Bench.

In physics, Lagrangians provide a systematic way to describe laws governing physical systems. In the context of particle physics, they encode the interactions and behavior of the fundamental building blocks of our universe. By treating Lagrangians as complex, rule-based constructs similar to linguistic expressions, we trained a transformer model -- proven to be effective in natural language tasks -- to predict the Lagrangian corresponding to a given list of particles. We report on the transformer's performance in constructing Lagrangians respecting the Standard Model SU(3)times SU(2)times U(1) gauge symmetries. The resulting model is shown to achieve high accuracies (over 90\%) with Lagrangians up to six matter fields, with the capacity to generalize beyond the training distribution, albeit within architectural constraints. We show through an analysis of input embeddings that the model has internalized concepts such as group representations and conjugation operations as it learned to generate Lagrangians. We make the model and training datasets available to the community. An interactive demonstration can be found at: https://huggingface.co/spaces/JoseEliel/generate-lagrangians.

The loss functions of many learning problems contain multiple additive terms that can disagree and yield conflicting update directions. For Physics-Informed Neural Networks (PINNs), loss terms on initial/boundary conditions and physics equations are particularly interesting as they are well-established as highly difficult tasks. To improve learning the challenging multi-objective task posed by PINNs, we propose the ConFIG method, which provides conflict-free updates by ensuring a positive dot product between the final update and each loss-specific gradient. It also maintains consistent optimization rates for all loss terms and dynamically adjusts gradient magnitudes based on conflict levels. We additionally leverage momentum to accelerate optimizations by alternating the back-propagation of different loss terms. We provide a mathematical proof showing the convergence of the ConFIG method, and it is evaluated across a range of challenging PINN scenarios. ConFIG consistently shows superior performance and runtime compared to baseline methods. We also test the proposed method in a classic multi-task benchmark, where the ConFIG method likewise exhibits a highly promising performance. Source code is available at https://tum-pbs.github.io/ConFIG

We introduce PICA, a novel representation for high-fidelity animatable clothed human avatars with physics-accurate dynamics, even for loose clothing. Previous neural rendering-based representations of animatable clothed humans typically employ a single model to represent both the clothing and the underlying body. While efficient, these approaches often fail to accurately represent complex garment dynamics, leading to incorrect deformations and noticeable rendering artifacts, especially for sliding or loose garments. Furthermore, previous works represent garment dynamics as pose-dependent deformations and facilitate novel pose animations in a data-driven manner. This often results in outcomes that do not faithfully represent the mechanics of motion and are prone to generating artifacts in out-of-distribution poses. To address these issues, we adopt two individual 3D Gaussian Splatting (3DGS) models with different deformation characteristics, modeling the human body and clothing separately. This distinction allows for better handling of their respective motion characteristics. With this representation, we integrate a graph neural network (GNN)-based clothed body physics simulation module to ensure an accurate representation of clothing dynamics. Our method, through its carefully designed features, achieves high-fidelity rendering of clothed human bodies in complex and novel driving poses, significantly outperforming previous methods under the same settings.

Imposing known physical constraints, such as conservation laws, during neural network training introduces an inductive bias that can improve accuracy, reliability, convergence, and data efficiency for modeling physical dynamics. While such constraints can be softly imposed via loss function penalties, recent advancements in differentiable physics and optimization improve performance by incorporating PDE-constrained optimization as individual layers in neural networks. This enables a stricter adherence to physical constraints. However, imposing hard constraints significantly increases computational and memory costs, especially for complex dynamical systems. This is because it requires solving an optimization problem over a large number of points in a mesh, representing spatial and temporal discretizations, which greatly increases the complexity of the constraint. To address this challenge, we develop a scalable approach to enforce hard physical constraints using Mixture-of-Experts (MoE), which can be used with any neural network architecture. Our approach imposes the constraint over smaller decomposed domains, each of which is solved by an "expert" through differentiable optimization. During training, each expert independently performs a localized backpropagation step by leveraging the implicit function theorem; the independence of each expert allows for parallelization across multiple GPUs. Compared to standard differentiable optimization, our scalable approach achieves greater accuracy in the neural PDE solver setting for predicting the dynamics of challenging non-linear systems. We also improve training stability and require significantly less computation time during both training and inference stages.

In the face of escalating climate changes, typhoon intensities and their ensuing damage have surged. Accurate trajectory prediction is crucial for effective damage control. Traditional physics-based models, while comprehensive, are computationally intensive and rely heavily on the expertise of forecasters. Contemporary data-driven methods often rely on reanalysis data, which can be considered to be the closest to the true representation of weather conditions. However, reanalysis data is not produced in real-time and requires time for adjustment because prediction models are calibrated with observational data. This reanalysis data, such as ERA5, falls short in challenging real-world situations. Optimal preparedness necessitates predictions at least 72 hours in advance, beyond the capabilities of standard physics models. In response to these constraints, we present an approach that harnesses real-time Unified Model (UM) data, sidestepping the limitations of reanalysis data. Our model provides predictions at 6-hour intervals for up to 72 hours in advance and outperforms both state-of-the-art data-driven methods and numerical weather prediction models. In line with our efforts to mitigate adversities inflicted by typhoons, we release our preprocessed PHYSICS TRACK dataset, which includes ERA5 reanalysis data, typhoon best-track, and UM forecast data.

Denoising diffusion models hold great promise for generating diverse and realistic human motions. However, existing motion diffusion models largely disregard the laws of physics in the diffusion process and often generate physically-implausible motions with pronounced artifacts such as floating, foot sliding, and ground penetration. This seriously impacts the quality of generated motions and limits their real-world application. To address this issue, we present a novel physics-guided motion diffusion model (PhysDiff), which incorporates physical constraints into the diffusion process. Specifically, we propose a physics-based motion projection module that uses motion imitation in a physics simulator to project the denoised motion of a diffusion step to a physically-plausible motion. The projected motion is further used in the next diffusion step to guide the denoising diffusion process. Intuitively, the use of physics in our model iteratively pulls the motion toward a physically-plausible space, which cannot be achieved by simple post-processing. Experiments on large-scale human motion datasets show that our approach achieves state-of-the-art motion quality and improves physical plausibility drastically (>78% for all datasets).

Differentiable physics enables efficient gradient-based optimizations of neural network (NN) controllers. However, existing work typically only delivers NN controllers with limited capability and generalizability. We present a practical learning framework that outputs unified NN controllers capable of tasks with significantly improved complexity and diversity. To systematically improve training robustness and efficiency, we investigated a suite of improvements over the baseline approach, including periodic activation functions, and tailored loss functions. In addition, we find our adoption of batching and an Adam optimizer effective in training complex locomotion tasks. We evaluate our framework on differentiable mass-spring and material point method (MPM) simulations, with challenging locomotion tasks and multiple robot designs. Experiments show that our learning framework, based on differentiable physics, delivers better results than reinforcement learning and converges much faster. We demonstrate that users can interactively control soft robot locomotion and switch among multiple goals with specified velocity, height, and direction instructions using a unified NN controller trained in our system. Code is available at https://github.com/erizmr/Complex-locomotion-skill-learning-via-differentiable-physics.

Deep neural networks have enabled improved image quality and fast inference times for various inverse problems, including accelerated magnetic resonance imaging (MRI) reconstruction. However, such models require a large number of fully-sampled ground truth datasets, which are difficult to curate, and are sensitive to distribution drifts. In this work, we propose applying physics-driven data augmentations for consistency training that leverage our domain knowledge of the forward MRI data acquisition process and MRI physics to achieve improved label efficiency and robustness to clinically-relevant distribution drifts. Our approach, termed VORTEX, (1) demonstrates strong improvements over supervised baselines with and without data augmentation in robustness to signal-to-noise ratio change and motion corruption in data-limited regimes; (2) considerably outperforms state-of-the-art purely image-based data augmentation techniques and self-supervised reconstruction methods on both in-distribution and out-of-distribution data; and (3) enables composing heterogeneous image-based and physics-driven data augmentations. Our code is available at https://github.com/ad12/meddlr.

We present PhysGen, a novel image-to-video generation method that converts a single image and an input condition (e.g., force and torque applied to an object in the image) to produce a realistic, physically plausible, and temporally consistent video. Our key insight is to integrate model-based physical simulation with a data-driven video generation process, enabling plausible image-space dynamics. At the heart of our system are three core components: (i) an image understanding module that effectively captures the geometry, materials, and physical parameters of the image; (ii) an image-space dynamics simulation model that utilizes rigid-body physics and inferred parameters to simulate realistic behaviors; and (iii) an image-based rendering and refinement module that leverages generative video diffusion to produce realistic video footage featuring the simulated motion. The resulting videos are realistic in both physics and appearance and are even precisely controllable, showcasing superior results over existing data-driven image-to-video generation works through quantitative comparison and comprehensive user study. PhysGen's resulting videos can be used for various downstream applications, such as turning an image into a realistic animation or allowing users to interact with the image and create various dynamics. Project page: https://stevenlsw.github.io/physgen/

Modeling and rendering photorealistic avatars is of crucial importance in many applications. Existing methods that build a 3D avatar from visual observations, however, struggle to reconstruct clothed humans. We introduce PhysAvatar, a novel framework that combines inverse rendering with inverse physics to automatically estimate the shape and appearance of a human from multi-view video data along with the physical parameters of the fabric of their clothes. For this purpose, we adopt a mesh-aligned 4D Gaussian technique for spatio-temporal mesh tracking as well as a physically based inverse renderer to estimate the intrinsic material properties. PhysAvatar integrates a physics simulator to estimate the physical parameters of the garments using gradient-based optimization in a principled manner. These novel capabilities enable PhysAvatar to create high-quality novel-view renderings of avatars dressed in loose-fitting clothes under motions and lighting conditions not seen in the training data. This marks a significant advancement towards modeling photorealistic digital humans using physically based inverse rendering with physics in the loop. Our project website is at: https://qingqing-zhao.github.io/PhysAvatar

We present a novel approach to synthesize dexterous motions for physically simulated hands in tasks that require coordination between the control of two hands with high temporal precision. Instead of directly learning a joint policy to control two hands, our approach performs bimanual control through cooperative learning where each hand is treated as an individual agent. The individual policies for each hand are first trained separately, and then synchronized through latent space manipulation in a centralized environment to serve as a joint policy for two-hand control. By doing so, we avoid directly performing policy learning in the joint state-action space of two hands with higher dimensions, greatly improving the overall training efficiency. We demonstrate the effectiveness of our proposed approach in the challenging guitar-playing task. The virtual guitarist trained by our approach can synthesize motions from unstructured reference data of general guitar-playing practice motions, and accurately play diverse rhythms with complex chord pressing and string picking patterns based on the input guitar tabs that do not exist in the references. Along with this paper, we provide the motion capture data that we collected as the reference for policy training. Code is available at: https://pei-xu.github.io/guitar.

Generating animation of physics-based characters with intuitive control has long been a desirable task with numerous applications. However, generating physically simulated animations that reflect high-level human instructions remains a difficult problem due to the complexity of physical environments and the richness of human language. In this paper, we present InsActor, a principled generative framework that leverages recent advancements in diffusion-based human motion models to produce instruction-driven animations of physics-based characters. Our framework empowers InsActor to capture complex relationships between high-level human instructions and character motions by employing diffusion policies for flexibly conditioned motion planning. To overcome invalid states and infeasible state transitions in planned motions, InsActor discovers low-level skills and maps plans to latent skill sequences in a compact latent space. Extensive experiments demonstrate that InsActor achieves state-of-the-art results on various tasks, including instruction-driven motion generation and instruction-driven waypoint heading. Notably, the ability of InsActor to generate physically simulated animations using high-level human instructions makes it a valuable tool, particularly in executing long-horizon tasks with a rich set of instructions.

Crafting a single, versatile physics-based controller that can breathe life into interactive characters across a wide spectrum of scenarios represents an exciting frontier in character animation. An ideal controller should support diverse control modalities, such as sparse target keyframes, text instructions, and scene information. While previous works have proposed physically simulated, scene-aware control models, these systems have predominantly focused on developing controllers that each specializes in a narrow set of tasks and control modalities. This work presents MaskedMimic, a novel approach that formulates physics-based character control as a general motion inpainting problem. Our key insight is to train a single unified model to synthesize motions from partial (masked) motion descriptions, such as masked keyframes, objects, text descriptions, or any combination thereof. This is achieved by leveraging motion tracking data and designing a scalable training method that can effectively utilize diverse motion descriptions to produce coherent animations. Through this process, our approach learns a physics-based controller that provides an intuitive control interface without requiring tedious reward engineering for all behaviors of interest. The resulting controller supports a wide range of control modalities and enables seamless transitions between disparate tasks. By unifying character control through motion inpainting, MaskedMimic creates versatile virtual characters. These characters can dynamically adapt to complex scenes and compose diverse motions on demand, enabling more interactive and immersive experiences.

Large language models demonstrate remarkable capabilities across various domains, especially mathematics and logic reasoning. However, current evaluations overlook physics-based reasoning - a complex task requiring physics theorems and constraints. We present PhysReason, a 1,200-problem benchmark comprising knowledge-based (25%) and reasoning-based (75%) problems, where the latter are divided into three difficulty levels (easy, medium, hard). Notably, problems require an average of 8.1 solution steps, with hard requiring 15.6, reflecting the complexity of physics-based reasoning. We propose the Physics Solution Auto Scoring Framework, incorporating efficient answer-level and comprehensive step-level evaluations. Top-performing models like Deepseek-R1, Gemini-2.0-Flash-Thinking, and o3-mini-high achieve less than 60% on answer-level evaluation, with performance dropping from knowledge questions (75.11%) to hard problems (31.95%). Through step-level evaluation, we identified four key bottlenecks: Physics Theorem Application, Physics Process Understanding, Calculation, and Physics Condition Analysis. These findings position PhysReason as a novel and comprehensive benchmark for evaluating physics-based reasoning capabilities in large language models. Our code and data will be published at https:/dxzxy12138.github.io/PhysReason.

Human motion generation plays a vital role in applications such as digital humans and humanoid robot control. However, most existing approaches disregard physics constraints, leading to the frequent production of physically implausible motions with pronounced artifacts such as floating and foot sliding. In this paper, we propose Morph, a Motion-free physics optimization framework, comprising a Motion Generator and a Motion Physics Refinement module, for enhancing physical plausibility without relying on costly real-world motion data. Specifically, the Motion Generator is responsible for providing large-scale synthetic motion data, while the Motion Physics Refinement Module utilizes these synthetic data to train a motion imitator within a physics simulator, enforcing physical constraints to project the noisy motions into a physically-plausible space. These physically refined motions, in turn, are used to fine-tune the Motion Generator, further enhancing its capability. Experiments on both text-to-motion and music-to-dance generation tasks demonstrate that our framework achieves state-of-the-art motion generation quality while improving physical plausibility drastically.

Air quality prediction and modelling plays a pivotal role in public health and environment management, for individuals and authorities to make informed decisions. Although traditional data-driven models have shown promise in this domain, their long-term prediction accuracy can be limited, especially in scenarios with sparse or incomplete data and they often rely on black-box deep learning structures that lack solid physical foundation leading to reduced transparency and interpretability in predictions. To address these limitations, this paper presents a novel approach named Physics guided Neural Network for Air Quality Prediction (AirPhyNet). Specifically, we leverage two well-established physics principles of air particle movement (diffusion and advection) by representing them as differential equation networks. Then, we utilize a graph structure to integrate physics knowledge into a neural network architecture and exploit latent representations to capture spatio-temporal relationships within the air quality data. Experiments on two real-world benchmark datasets demonstrate that AirPhyNet outperforms state-of-the-art models for different testing scenarios including different lead time (24h, 48h, 72h), sparse data and sudden change prediction, achieving reduction in prediction errors up to 10%. Moreover, a case study further validates that our model captures underlying physical processes of particle movement and generates accurate predictions with real physical meaning.

Accurate prediction of climate in the subseasonal-to-seasonal scale is crucial for disaster readiness, reduced economic risk, and improved policy-making amidst climate change. Yet, S2S prediction remains challenging due to the chaotic nature of the system. At present, existing benchmarks for weather and climate applications, tend to (1) have shorter forecasting range of up-to 14 days, (2) do not include a wide range of operational baseline forecasts, and (3) lack physics-based constraints for explainability. Thus, we propose ChaosBench, a large-scale, multi-channel, physics-based benchmark for S2S prediction. ChaosBench has over 460K frames of real-world observations and simulations, each with 60 variable-channels and spanning for up-to 45 years. We also propose several physics-based, in addition to vision-based metrics, that enables for a more physically-consistent model. Furthermore, we include a diverse set of physics-based forecasts from 4 national weather agencies as baselines to our data-driven counterpart. We establish two tasks that vary in complexity: full and sparse dynamics prediction. Our benchmark is one of the first to perform large-scale evaluation on existing models including PanguWeather, FourCastNetV2, GraphCast, and ClimaX, and finds methods originally developed for weather-scale applications fails on S2S task. We release our benchmark code and datasets at https://leap-stc.github.io/ChaosBench.

Modern climate projections lack adequate spatial and temporal resolution due to computational constraints. A consequence is inaccurate and imprecise predictions of critical processes such as storms. Hybrid methods that combine physics with machine learning (ML) have introduced a new generation of higher fidelity climate simulators that can sidestep Moore's Law by outsourcing compute-hungry, short, high-resolution simulations to ML emulators. However, this hybrid ML-physics simulation approach requires domain-specific treatment and has been inaccessible to ML experts because of lack of training data and relevant, easy-to-use workflows. We present ClimSim, the largest-ever dataset designed for hybrid ML-physics research. It comprises multi-scale climate simulations, developed by a consortium of climate scientists and ML researchers. It consists of 5.7 billion pairs of multivariate input and output vectors that isolate the influence of locally-nested, high-resolution, high-fidelity physics on a host climate simulator's macro-scale physical state. The dataset is global in coverage, spans multiple years at high sampling frequency, and is designed such that resulting emulators are compatible with downstream coupling into operational climate simulators. We implement a range of deterministic and stochastic regression baselines to highlight the ML challenges and their scoring. The data (https://huggingface.co/datasets/LEAP/ClimSim_high-res, https://huggingface.co/datasets/LEAP/ClimSim_low-res, and https://huggingface.co/datasets/LEAP/ClimSim_low-res_aqua-planet) and code (https://leap-stc.github.io/ClimSim) are released openly to support the development of hybrid ML-physics and high-fidelity climate simulations for the benefit of science and society.

Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021).

In an industrial group like Safran, numerical simulations of physical phenomena are integral to most design processes. At Safran's corporate research center, we enhance these processes by developing fast and reliable surrogate models for various physics. We focus here on two technologies developed in recent years. The first is a physical reduced-order modeling method for non-linear structural mechanics and thermal analysis, used for calculating the lifespan of high-pressure turbine blades and performing heat analysis of high-pressure compressors. The second technology involves learning physics simulations with non-parameterized geometrical variability using classical machine learning tools, such as Gaussian process regression. Finally, we present our contributions to the open-source and open-data community.

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and require large amounts of {\em labeled} training data. We propose the Deep Generative Neural Operator (DGNO), a physics-aware framework that addresses these challenges by leveraging a deep, generative, probabilistic model in combination with a set of lower-dimensional, latent variables that simultaneously encode PDE-inputs and PDE-outputs. This formulation can make use of unlabeled data and significantly improves inverse problem-solving, particularly for discontinuous or discrete-valued input functions. DGNO enforces physics constraints without labeled data by incorporating as virtual observables, weak-form residuals based on compactly supported radial basis functions (CSRBFs). These relax regularity constraints and eliminate higher-order derivatives from the objective function. We also introduce MultiONet, a novel neural operator architecture, which is a more expressive generalization of the popular DeepONet that significantly enhances the approximating power of the proposed model. These innovations make DGNO particularly effective for challenging forward and inverse, PDE-based problems, such as those involving multi-phase media. Numerical experiments demonstrate that DGNO achieves higher accuracy across multiple benchmarks while exhibiting robustness to noise and strong generalization to out-of-distribution cases. Its adaptability, and the ability to handle sparse, noisy data while providing probabilistic estimates, make DGNO a powerful tool for scientific and engineering applications.

Text-to-3D asset generation has achieved significant optimization under the supervision of 2D diffusion priors. However, when dealing with compositional scenes, existing methods encounter several challenges: 1). failure to ensure that composite scene layouts comply with physical laws; 2). difficulty in accurately capturing the assets and relationships described in complex scene descriptions; 3). limited autonomous asset generation capabilities among layout approaches leveraging large language models (LLMs). To avoid these compromises, we propose a novel framework for compositional scene generation, PhiP-G, which seamlessly integrates generation techniques with layout guidance based on a world model. Leveraging LLM-based agents, PhiP-G analyzes the complex scene description to generate a scene graph, and integrating a multimodal 2D generation agent and a 3D Gaussian generation method for targeted assets creation. For the stage of layout, PhiP-G employs a physical pool with adhesion capabilities and a visual supervision agent, forming a world model for layout prediction and planning. Extensive experiments demonstrate that PhiP-G significantly enhances the generation quality and physical rationality of the compositional scenes. Notably, PhiP-G attains state-of-the-art (SOTA) performance in CLIP scores, achieves parity with the leading methods in generation quality as measured by the T^3Bench, and improves efficiency by 24x.

Large Language Models (LLMs) have demonstrated strong capabilities in text-based tasks but struggle with the complex reasoning required for physics problems, particularly in advanced arithmetic and conceptual understanding. While some research has explored ways to enhance LLMs in physics education using techniques such as prompt engineering and Retrieval Augmentation Generation (RAG), not enough effort has been made in addressing their limitations in physics reasoning. This paper presents a novel approach to improving LLM performance on physics questions using Reinforcement Learning with Human and Artificial Intelligence Feedback (RLHAIF). We evaluate several reinforcement learning methods, including Proximal Policy Optimization (PPO), Direct Preference Optimization (DPO), and Remax optimization. These methods are chosen to investigate RL policy performance with different settings on the PhyQA dataset, which includes challenging physics problems from high school textbooks. Our RLHAIF model, tested on leading LLMs like LLaMA2 and Mistral, achieved superior results, notably with the MISTRAL-PPO model, demonstrating marked improvements in reasoning and accuracy. It achieved high scores, with a 58.67 METEOR score and a 0.74 Reasoning score, making it a strong example for future physics reasoning research in this area.

Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the AMG method, a Multi-Graph neural operator approach designed for efficiently solving PDEs on Arbitrary geometries. AMG leverages advanced graph-based techniques and dynamic attention mechanisms within a novel GraphFormer architecture, enabling precise management of diverse spatial domains and complex data interdependencies. By constructing multi-scale graphs to handle variable feature frequencies and a physics graph to encapsulate inherent physical properties, AMG significantly outperforms previous methods, which are typically limited to uniform grids. We present a comprehensive evaluation of AMG across six benchmarks, demonstrating its consistent superiority over existing state-of-the-art models. Our findings highlight the transformative potential of tailored graph neural operators in surmounting the challenges faced by conventional PDE solvers. Our code and datasets are available on https://github.com/lizhihao2022/AMG.

4D content generation focuses on creating dynamic 3D objects that change over time. Existing methods primarily rely on pre-trained video diffusion models, utilizing sampling processes or reference videos. However, these approaches face significant challenges. Firstly, the generated 4D content often fails to adhere to real-world physics since video diffusion models do not incorporate physical priors. Secondly, the extensive sampling process and the large number of parameters in diffusion models result in exceedingly time-consuming generation processes. To address these issues, we introduce Phy124, a novel, fast, and physics-driven method for controllable 4D content generation from a single image. Phy124 integrates physical simulation directly into the 4D generation process, ensuring that the resulting 4D content adheres to natural physical laws. Phy124 also eliminates the use of diffusion models during the 4D dynamics generation phase, significantly speeding up the process. Phy124 allows for the control of 4D dynamics, including movement speed and direction, by manipulating external forces. Extensive experiments demonstrate that Phy124 generates high-fidelity 4D content with significantly reduced inference times, achieving stateof-the-art performance. The code and generated 4D content are available at the provided link: https://anonymous.4open.science/r/BBF2/.

Driven by advancements in sensing and computing, deep reinforcement learning (DRL)-based methods have demonstrated significant potential in effectively tackling distribution system restoration (DSR) challenges under uncertain operational scenarios. However, the data-intensive nature of DRL poses obstacles in achieving satisfactory DSR solutions for large-scale, complex distribution systems. Inspired by the transformative impact of emerging foundation models, including large language models (LLMs), across various domains, this paper explores an innovative approach harnessing LLMs' powerful computing capabilities to address scalability challenges inherent in conventional DRL methods for solving DSR. To our knowledge, this study represents the first exploration of foundation models, including LLMs, in revolutionizing conventional DRL applications in power system operations. Our contributions are twofold: 1) introducing a novel LLM-powered Physics-Informed Decision Transformer (PIDT) framework that leverages LLMs to transform conventional DRL methods for DSR operations, and 2) conducting comparative studies to assess the performance of the proposed LLM-powered PIDT framework at its initial development stage for solving DSR problems. While our primary focus in this paper is on DSR operations, the proposed PIDT framework can be generalized to optimize sequential decision-making across various power system operations.

Given the existence of various forward and inverse problems in combustion studies and applications that necessitate distinct methods for resolution, a framework to solve them in a unified way is critically needed. A promising approach is the integration of machine learning methods with governing equations of combustion systems, which exhibits superior generality and few-shot learning ability compared to purely data-driven methods. In this work, the FlamePINN-1D framework is proposed to solve the forward and inverse problems of 1D laminar flames based on physics-informed neural networks. Three cases with increasing complexity have been tested: Case 1 are freely-propagating premixed (FPP) flames with simplified physical models, while Case 2 and Case 3 are FPP and counterflow premixed (CFP) flames with detailed models, respectively. For forward problems, FlamePINN-1D aims to solve the flame fields and infer the unknown eigenvalues (such as laminar flame speeds) under the constraints of governing equations and boundary conditions. For inverse problems, FlamePINN-1D aims to reconstruct the continuous fields and infer the unknown parameters (such as transport and chemical kinetics parameters) from noisy sparse observations of the flame. Our results strongly validate these capabilities of FlamePINN-1D across various flames and working conditions. Compared to traditional methods, FlamePINN-1D is differentiable and mesh-free, exhibits no discretization errors, and is easier to implement for inverse problems. The inverse problem results also indicate the possibility of optimizing chemical mechanisms from measurements of laboratory 1D flames. Furthermore, some proposed strategies, such as hard constraints and thin-layer normalization, are proven to be essential for the robust learning of FlamePINN-1D. The code for this paper is partially available at https://github.com/CAME-THU/FlamePINN-1D.

Scene representations using 3D Gaussian primitives have produced excellent results in modeling the appearance of static and dynamic 3D scenes. Many graphics applications, however, demand the ability to manipulate both the appearance and the physical properties of objects. We introduce Feature Splatting, an approach that unifies physics-based dynamic scene synthesis with rich semantics from vision language foundation models that are grounded by natural language. Our first contribution is a way to distill high-quality, object-centric vision-language features into 3D Gaussians, that enables semi-automatic scene decomposition using text queries. Our second contribution is a way to synthesize physics-based dynamics from an otherwise static scene using a particle-based simulator, in which material properties are assigned automatically via text queries. We ablate key techniques used in this pipeline, to illustrate the challenge and opportunities in using feature-carrying 3D Gaussians as a unified format for appearance, geometry, material properties and semantics grounded on natural language. Project website: https://feature-splatting.github.io/

We introduce DIFFTACTILE, a physics-based differentiable tactile simulation system designed to enhance robotic manipulation with dense and physically accurate tactile feedback. In contrast to prior tactile simulators which primarily focus on manipulating rigid bodies and often rely on simplified approximations to model stress and deformations of materials in contact, DIFFTACTILE emphasizes physics-based contact modeling with high fidelity, supporting simulations of diverse contact modes and interactions with objects possessing a wide range of material properties. Our system incorporates several key components, including a Finite Element Method (FEM)-based soft body model for simulating the sensing elastomer, a multi-material simulator for modeling diverse object types (such as elastic, elastoplastic, cables) under manipulation, a penalty-based contact model for handling contact dynamics. The differentiable nature of our system facilitates gradient-based optimization for both 1) refining physical properties in simulation using real-world data, hence narrowing the sim-to-real gap and 2) efficient learning of tactile-assisted grasping and contact-rich manipulation skills. Additionally, we introduce a method to infer the optical response of our tactile sensor to contact using an efficient pixel-based neural module. We anticipate that DIFFTACTILE will serve as a useful platform for studying contact-rich manipulations, leveraging the benefits of dense tactile feedback and differentiable physics. Code and supplementary materials are available at the project website https://difftactile.github.io/.

We introduce a co-designed approach for human portrait relighting that combines a physics-guided architecture with a pre-training framework. Drawing on the Cook-Torrance reflectance model, we have meticulously configured the architecture design to precisely simulate light-surface interactions. Furthermore, to overcome the limitation of scarce high-quality lightstage data, we have developed a self-supervised pre-training strategy. This novel combination of accurate physical modeling and expanded training dataset establishes a new benchmark in relighting realism.

Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power. Data-driven methods based on large-scale machine learning promise high adaptivity by integrating long-range dependencies more directly and efficiently. In this work, we focus on fluid dynamics and address the shortcomings of a large part of the literature, which are based on fixed support for computations and predictions in the form of regular or irregular grids. We propose a novel setup to perform predictions in a continuous spatial and temporal domain while being trained on sparse observations. We formulate the task as a double observation problem and propose a solution with two interlinked dynamical systems defined on, respectively, the sparse positions and the continuous domain, which allows to forecast and interpolate a solution from the initial condition. Our practical implementation involves recurrent GNNs and a spatio-temporal attention observer capable of interpolating the solution at arbitrary locations. Our model not only generalizes to new initial conditions (as standard auto-regressive models do) but also performs evaluation at arbitrary space and time locations. We evaluate on three standard datasets in fluid dynamics and compare to strong baselines, which are outperformed both in classical settings and in the extended new task requiring continuous predictions.

While molecular pre-training has shown great potential in enhancing drug discovery, the lack of a solid physical interpretation in current methods raises concerns about whether the learned representation truly captures the underlying explanatory factors in observed data, ultimately resulting in limited generalization and robustness. Although denoising methods offer a physical interpretation, their accuracy is often compromised by ad-hoc noise design, leading to inaccurate learned force fields. To address this limitation, this paper proposes a new method for molecular pre-training, called sliced denoising (SliDe), which is based on the classical mechanical intramolecular potential theory. SliDe utilizes a novel noise strategy that perturbs bond lengths, angles, and torsion angles to achieve better sampling over conformations. Additionally, it introduces a random slicing approach that circumvents the computationally expensive calculation of the Jacobian matrix, which is otherwise essential for estimating the force field. By aligning with physical principles, SliDe shows a 42\% improvement in the accuracy of estimated force fields compared to current state-of-the-art denoising methods, and thus outperforms traditional baselines on various molecular property prediction tasks.

Neural networks have shown great potential in accelerating the solution of partial differential equations (PDEs). Recently, there has been a growing interest in introducing physics constraints into training neural PDE solvers to reduce the use of costly data and improve the generalization ability. However, these physics constraints, based on certain finite dimensional approximations over the function space, must resolve the smallest scaled physics to ensure the accuracy and stability of the simulation, resulting in high computational costs from large input, output, and neural networks. This paper proposes a general acceleration methodology called NeuralStagger by spatially and temporally decomposing the original learning tasks into several coarser-resolution subtasks. We define a coarse-resolution neural solver for each subtask, which requires fewer computational resources, and jointly train them with the vanilla physics-constrained loss by simply arranging their outputs to reconstruct the original solution. Due to the perfect parallelism between them, the solution is achieved as fast as a coarse-resolution neural solver. In addition, the trained solvers bring the flexibility of simulating with multiple levels of resolution. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations, which leads to an additional 10sim100times speed-up. Moreover, the experiment also shows that the learned model could be well used for optimal control.

Despite the success of physics-informed neural networks (PINNs) in approximating partial differential equations (PDEs), PINNs can sometimes fail to converge to the correct solution in problems involving complicated PDEs. This is reflected in several recent studies on characterizing the "failure modes" of PINNs, although a thorough understanding of the connection between PINN failure modes and sampling strategies is missing. In this paper, we provide a novel perspective of failure modes of PINNs by hypothesizing that training PINNs relies on successful "propagation" of solution from initial and/or boundary condition points to interior points. We show that PINNs with poor sampling strategies can get stuck at trivial solutions if there are propagation failures, characterized by highly imbalanced PDE residual fields. To mitigate propagation failures, we propose a novel Retain-Resample-Release sampling (R3) algorithm that can incrementally accumulate collocation points in regions of high PDE residuals with little to no computational overhead. We provide an extension of R3 sampling to respect the principle of causality while solving time-dependent PDEs. We theoretically analyze the behavior of R3 sampling and empirically demonstrate its efficacy and efficiency in comparison with baselines on a variety of PDE problems.

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this work we attribute this shortcoming to the inability of existing PINNs formulations to respect the spatio-temporal causal structure that is inherent to the evolution of physical systems. We argue that this is a fundamental limitation and a key source of error that can ultimately steer PINN models to converge towards erroneous solutions. We address this pathology by proposing a simple re-formulation of PINNs loss functions that can explicitly account for physical causality during model training. We demonstrate that this simple modification alone is enough to introduce significant accuracy improvements, as well as a practical quantitative mechanism for assessing the convergence of a PINNs model. We provide state-of-the-art numerical results across a series of benchmarks for which existing PINNs formulations fail, including the chaotic Lorenz system, the Kuramoto-Sivashinsky equation in the chaotic regime, and the Navier-Stokes equations in the turbulent regime. To the best of our knowledge, this is the first time that PINNs have been successful in simulating such systems, introducing new opportunities for their applicability to problems of industrial complexity.

The specialized language and complex concepts in physics pose significant challenges for information extraction through Natural Language Processing (NLP). Central to effective NLP applications is the text embedding model, which converts text into dense vector representations for efficient information retrieval and semantic analysis. In this work, we introduce PhysBERT, the first physics-specific text embedding model. Pre-trained on a curated corpus of 1.2 million arXiv physics papers and fine-tuned with supervised data, PhysBERT outperforms leading general-purpose models on physics-specific tasks including the effectiveness in fine-tuning for specific physics subdomains.

This work introduces a highly efficient implementation of the transformer architecture on a Field-Programmable Gate Array (FPGA) by using the hls4ml tool. Given the demonstrated effectiveness of transformer models in addressing a wide range of problems, their application in experimental triggers within particle physics becomes a subject of significant interest. In this work, we have implemented critical components of a transformer model, such as multi-head attention and softmax layers. To evaluate the effectiveness of our implementation, we have focused on a particle physics jet flavor tagging problem, employing a public dataset. We recorded latency under 2 mus on the Xilinx UltraScale+ FPGA, which is compatible with hardware trigger requirements at the CERN Large Hadron Collider experiments.

In this paper, we aim to model 3D scene dynamics from multi-view videos. Unlike the majority of existing works which usually focus on the common task of novel view synthesis within the training time period, we propose to simultaneously learn the geometry, appearance, and physical velocity of 3D scenes only from video frames, such that multiple desirable applications can be supported, including future frame extrapolation, unsupervised 3D semantic scene decomposition, and dynamic motion transfer. Our method consists of three major components, 1) the keyframe dynamic radiance field, 2) the interframe velocity field, and 3) a joint keyframe and interframe optimization module which is the core of our framework to effectively train both networks. To validate our method, we further introduce two dynamic 3D datasets: 1) Dynamic Object dataset, and 2) Dynamic Indoor Scene dataset. We conduct extensive experiments on multiple datasets, demonstrating the superior performance of our method over all baselines, particularly in the critical tasks of future frame extrapolation and unsupervised 3D semantic scene decomposition.

Brain tumor growth is unique to each glioma patient and extends beyond what is visible in imaging scans, infiltrating surrounding brain tissue. Understanding these hidden patient-specific progressions is essential for effective therapies. Current treatment plans for brain tumors, such as radiotherapy, typically involve delineating a uniform margin around the visible tumor on pre-treatment scans to target this invisible tumor growth. This "one size fits all" approach is derived from population studies and often fails to account for the nuances of individual patient conditions. We present the GliODIL framework, which infers the full spatial distribution of tumor cell concentration from available multi-modal imaging, leveraging a Fisher-Kolmogorov type physics model to describe tumor growth. This is achieved through the newly introduced method of Optimizing the Discrete Loss (ODIL), where both data and physics-based constraints are softly assimilated into the solution. Our test dataset comprises 152 glioblastoma patients with pre-treatment imaging and post-treatment follow-ups for tumor recurrence monitoring. By blending data-driven techniques with physics-based constraints, GliODIL enhances recurrence prediction in radiotherapy planning, challenging traditional uniform margins and strict adherence to the Fisher-Kolmogorov partial differential equation (PDE) model, which is adapted for complex cases.

Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each presents its unique limitations and generally balances training cost, numerical accuracy, and ease of applicability to different problem setups. To address these limitations, we introduce several methods to apply latent diffusion models to physics simulation. Firstly, we introduce a mesh autoencoder to compress arbitrarily discretized PDE data, allowing for efficient diffusion training across various physics. Furthermore, we investigate full spatio-temporal solution generation to mitigate autoregressive error accumulation. Lastly, we investigate conditioning on initial physical quantities, as well as conditioning solely on a text prompt to introduce text2PDE generation. We show that language can be a compact, interpretable, and accurate modality for generating physics simulations, paving the way for more usable and accessible PDE solvers. Through experiments on both uniform and structured grids, we show that the proposed approach is competitive with current neural PDE solvers in both accuracy and efficiency, with promising scaling behavior up to sim3 billion parameters. By introducing a scalable, accurate, and usable physics simulator, we hope to bring neural PDE solvers closer to practical use.

AI for partial differential equations (PDEs) has garnered significant attention, particularly with the emergence of Physics-informed neural networks (PINNs). The recent advent of Kolmogorov-Arnold Network (KAN) indicates that there is potential to revisit and enhance the previously MLP-based PINNs. Compared to MLPs, KANs offer interpretability and require fewer parameters. PDEs can be described in various forms, such as strong form, energy form, and inverse form. While mathematically equivalent, these forms are not computationally equivalent, making the exploration of different PDE formulations significant in computational physics. Thus, we propose different PDE forms based on KAN instead of MLP, termed Kolmogorov-Arnold-Informed Neural Network (KINN). We systematically compare MLP and KAN in various numerical examples of PDEs, including multi-scale, singularity, stress concentration, nonlinear hyperelasticity, heterogeneous, and complex geometry problems. Our results demonstrate that KINN significantly outperforms MLP in terms of accuracy and convergence speed for numerous PDEs in computational solid mechanics, except for the complex geometry problem. This highlights KINN's potential for more efficient and accurate PDE solutions in AI for PDEs.

Accurately measuring the cycle lifetime of commercial lithium-ion batteries is crucial for performance and technology development. We introduce a novel hybrid approach combining a physics-based equation with a self-attention model to predict the cycle lifetimes of commercial lithium iron phosphate graphite cells via early-cycle data. After fitting capacity loss curves to this physics-based equation, we then use a self-attention layer to reconstruct entire battery capacity loss curves. Our model exhibits comparable performances to existing models while predicting more information: the entire capacity loss curve instead of cycle life. This provides more robustness and interpretability: our model does not need to be retrained for a different notion of end-of-life and is backed by physical intuition.

In this work, we aim to teach robots to manipulate various thin-shell materials. Prior works studying thin-shell object manipulation mostly rely on heuristic policies or learn policies from real-world video demonstrations, and only focus on limited material types and tasks (e.g., cloth unfolding). However, these approaches face significant challenges when extended to a wider variety of thin-shell materials and a diverse range of tasks. While virtual simulations are shown to be effective in diverse robot skill learning and evaluation, prior thin-shell simulation environments only support a subset of thin-shell materials, which also limits their supported range of tasks. We introduce ThinShellLab - a fully differentiable simulation platform tailored for robotic interactions with diverse thin-shell materials possessing varying material properties, enabling flexible thin-shell manipulation skill learning and evaluation. Our experiments suggest that manipulating thin-shell objects presents several unique challenges: 1) thin-shell manipulation relies heavily on frictional forces due to the objects' co-dimensional nature, 2) the materials being manipulated are highly sensitive to minimal variations in interaction actions, and 3) the constant and frequent alteration in contact pairs makes trajectory optimization methods susceptible to local optima, and neither standard reinforcement learning algorithms nor trajectory optimization methods (either gradient-based or gradient-free) are able to solve the tasks alone. To overcome these challenges, we present an optimization scheme that couples sampling-based trajectory optimization and gradient-based optimization, boosting both learning efficiency and converged performance across various proposed tasks. In addition, the differentiable nature of our platform facilitates a smooth sim-to-real transition.

A digital twin is a virtual replica of a real-world physical phenomena that uses mathematical modeling to characterize and simulate its defining features. By constructing digital twins for disease processes, we can perform in-silico simulations that mimic patients' health conditions and counterfactual outcomes under hypothetical interventions in a virtual setting. This eliminates the need for invasive procedures or uncertain treatment decisions. In this paper, we propose a method to identify digital twin model parameters using only noninvasive patient health data. We approach the digital twin modeling as a composite inverse problem, and observe that its structure resembles pretraining and finetuning in self-supervised learning (SSL). Leveraging this, we introduce a physics-informed SSL algorithm that initially pretrains a neural network on the pretext task of solving the physical model equations. Subsequently, the model is trained to reconstruct low-dimensional health measurements from noninvasive modalities while being constrained by the physical equations learned in pretraining. We apply our method to identify digital twins of cardiac hemodynamics using noninvasive echocardiogram videos, and demonstrate its utility in unsupervised disease detection and in-silico clinical trials.

In this paper, we investigate the behavior of gradient descent algorithms in physics-informed machine learning methods like PINNs, which minimize residuals connected to partial differential equations (PDEs). Our key result is that the difficulty in training these models is closely related to the conditioning of a specific differential operator. This operator, in turn, is associated to the Hermitian square of the differential operator of the underlying PDE. If this operator is ill-conditioned, it results in slow or infeasible training. Therefore, preconditioning this operator is crucial. We employ both rigorous mathematical analysis and empirical evaluations to investigate various strategies, explaining how they better condition this critical operator, and consequently improve training.

We present a universal motion representation that encompasses a comprehensive range of motor skills for physics-based humanoid control. Due to the high-dimensionality of humanoid control as well as the inherent difficulties in reinforcement learning, prior methods have focused on learning skill embeddings for a narrow range of movement styles (e.g. locomotion, game characters) from specialized motion datasets. This limited scope hampers its applicability in complex tasks. Our work closes this gap, significantly increasing the coverage of motion representation space. To achieve this, we first learn a motion imitator that can imitate all of human motion from a large, unstructured motion dataset. We then create our motion representation by distilling skills directly from the imitator. This is achieved using an encoder-decoder structure with a variational information bottleneck. Additionally, we jointly learn a prior conditioned on proprioception (humanoid's own pose and velocities) to improve model expressiveness and sampling efficiency for downstream tasks. Sampling from the prior, we can generate long, stable, and diverse human motions. Using this latent space for hierarchical RL, we show that our policies solve tasks using natural and realistic human behavior. We demonstrate the effectiveness of our motion representation by solving generative tasks (e.g. strike, terrain traversal) and motion tracking using VR controllers.

Combinatorial inverse problems in high energy physics span enormous algorithmic challenges. This work presents a new deep learning driven clustering algorithm that utilizes a space-time non-local trainable graph constructor, a graph neural network, and a set transformer. The model is trained with loss functions at the graph node, edge and object level, including contrastive learning and meta-supervision. The algorithm can be applied to problems such as charged particle tracking, calorimetry, pile-up discrimination, jet physics, and beyond. We showcase the effectiveness of this cutting-edge AI approach through particle tracking simulations. The code is available online.

This paper addresses a novel task of anticipating 3D human-object interactions (HOIs). Most existing research on HOI synthesis lacks comprehensive whole-body interactions with dynamic objects, e.g., often limited to manipulating small or static objects. Our task is significantly more challenging, as it requires modeling dynamic objects with various shapes, capturing whole-body motion, and ensuring physically valid interactions. To this end, we propose InterDiff, a framework comprising two key steps: (i) interaction diffusion, where we leverage a diffusion model to encode the distribution of future human-object interactions; (ii) interaction correction, where we introduce a physics-informed predictor to correct denoised HOIs in a diffusion step. Our key insight is to inject prior knowledge that the interactions under reference with respect to contact points follow a simple pattern and are easily predictable. Experiments on multiple human-object interaction datasets demonstrate the effectiveness of our method for this task, capable of producing realistic, vivid, and remarkably long-term 3D HOI predictions.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

We discuss why AI is hard and why physics is simple. We discuss how physical intuition and the approach of theoretical physics can be brought to bear on the field of artificial intelligence and specifically machine learning. We suggest that the underlying project of machine learning and the underlying project of physics are strongly coupled through the principle of sparsity, and we call upon theoretical physicists to work on AI as physicists. As a first step in that direction, we discuss an upcoming book on the principles of deep learning theory that attempts to realize this approach.