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| [//]: # (Logo:) | |
| <div align="center"> | |
| https://user-images.githubusercontent.com/7593028/188328887-1b6cda72-2f41-439e-ae23-75dd3489bc24.mp4 | |
| # PySR: High-Performance Symbolic Regression in Python | |
| </div> | |
| PySR uses evolutionary algorithms to search for symbolic expressions which optimize a particular objective. | |
| <div align="center"> | |
| | **Docs** | **colab** | **pip** | **conda** | **Stats** | | |
| |---|---|---|---|---| | |
| |[](https://astroautomata.com/PySR/)|[](https://colab.research.google.com/github/MilesCranmer/PySR/blob/master/examples/pysr_demo.ipynb)|[](https://badge.fury.io/py/pysr)|[](https://anaconda.org/conda-forge/pysr)|<div align="center">pip: [](https://badge.fury.io/py/pysr)<br>conda: [](https://anaconda.org/conda-forge/pysr)</div>| | |
| </div> | |
| (pronounced like *py* as in python, and then *sur* as in surface) | |
| If you find PySR useful, please cite it using the citation information given in [CITATION.md](https://github.com/MilesCranmer/PySR/blob/master/CITATION.md). | |
| If you've finished a project with PySR, please submit a PR to showcase your work on the [Research Showcase page](https://astroautomata.com/PySR/papers)! | |
| <div align="center"> | |
| ### Test status | |
| | **Linux** | **Windows** | **macOS (intel)** | | |
| |---|---|---| | |
| |[](https://github.com/MilesCranmer/PySR/actions/workflows/CI.yml)|[](https://github.com/MilesCranmer/PySR/actions/workflows/CI_Windows.yml)|[](https://github.com/MilesCranmer/PySR/actions/workflows/CI_mac.yml)| | |
| | **Docker** | **Conda** | **Coverage** | | |
| |[](https://github.com/MilesCranmer/PySR/actions/workflows/CI_docker.yml)|[](https://github.com/MilesCranmer/PySR/actions/workflows/CI_conda_forge.yml)|[](https://coveralls.io/github/MilesCranmer/PySR)| | |
| </div> | |
| PySR is built on an extremely optimized pure-Julia backend: [SymbolicRegression.jl](https://github.com/MilesCranmer/SymbolicRegression.jl). | |
| Symbolic regression is a very interpretable machine learning algorithm | |
| for low-dimensional problems: these tools search equation space | |
| to find algebraic relations that approximate a dataset. | |
| One can also | |
| extend these approaches to higher-dimensional | |
| spaces by using a neural network as proxy, as explained in | |
| [2006.11287](https://arxiv.org/abs/2006.11287), where we apply | |
| it to N-body problems. Here, one essentially uses | |
| symbolic regression to convert a neural net | |
| to an analytic equation. Thus, these tools simultaneously present | |
| an explicit and powerful way to interpret deep models. | |
| *Backstory:* | |
| Previously, we have used | |
| [eureqa](https://www.creativemachineslab.com/eureqa.html), | |
| which is a very efficient and user-friendly tool. However, | |
| eureqa is GUI-only, doesn't allow for user-defined | |
| operators, has no distributed capabilities, | |
| and has become proprietary (and recently been merged into an online | |
| service). Thus, the goal | |
| of this package is to have an open-source symbolic regression tool | |
| as efficient as eureqa, while also exposing a configurable | |
| python interface. | |
| # Installation | |
| <div align="center"> | |
| | pip - **recommended** <br> (works everywhere) | conda <br>(Linux and Intel-based macOS) | | |
| |---|---| | |
| | 1. [Install Julia](https://julialang.org/downloads/)<br>2. Then, run: `pip install -U pysr`<br>3. Finally, to install Julia packages:<br>`python -c 'import pysr; pysr.install()'` | `conda install -c conda-forge pysr` | | |
| </div> | |
| Common issues tend to be related to Python not finding Julia. | |
| To debug this, try running `python -c 'import os; print(os.environ["PATH"])'`. | |
| If none of these folders contain your Julia binary, then you need to add Julia's `bin` folder to your `PATH` environment variable. | |
| **Running PySR on macOS with an M1 processor:** you should use the pip version, and make sure to get the Julia binary for ARM/M-series processors. | |
| # Introduction | |
| Let's create a PySR example. First, let's import | |
| numpy to generate some test data: | |
| ```python | |
| import numpy as np | |
| X = 2 * np.random.randn(100, 5) | |
| y = 2.5382 * np.cos(X[:, 3]) + X[:, 0] ** 2 - 0.5 | |
| ``` | |
| We have created a dataset with 100 datapoints, with 5 features each. | |
| The relation we wish to model is $2.5382 \cos(x_3) + x_0^2 - 0.5$. | |
| Now, let's create a PySR model and train it. | |
| PySR's main interface is in the style of scikit-learn: | |
| ```python | |
| from pysr import PySRRegressor | |
| model = PySRRegressor( | |
| model_selection="best", # Result is mix of simplicity+accuracy | |
| niterations=40, | |
| binary_operators=["+", "*"], | |
| unary_operators=[ | |
| "cos", | |
| "exp", | |
| "sin", | |
| "inv(x) = 1/x", | |
| # ^ Custom operator (julia syntax) | |
| ], | |
| extra_sympy_mappings={"inv": lambda x: 1 / x}, | |
| # ^ Define operator for SymPy as well | |
| loss="loss(x, y) = (x - y)^2", | |
| # ^ Custom loss function (julia syntax) | |
| ) | |
| ``` | |
| This will set up the model for 40 iterations of the search code, which contains hundreds of thousands of mutations and equation evaluations. | |
| Let's train this model on our dataset: | |
| ```python | |
| model.fit(X, y) | |
| ``` | |
| Internally, this launches a Julia process which will do a multithreaded search for equations to fit the dataset. | |
| Equations will be printed during training, and once you are satisfied, you may | |
| quit early by hitting 'q' and then \<enter\>. | |
| After the model has been fit, you can run `model.predict(X)` | |
| to see the predictions on a given dataset. | |
| You may run: | |
| ```python | |
| print(model) | |
| ``` | |
| to print the learned equations: | |
| ```python | |
| PySRRegressor.equations_ = [ | |
| pick score equation loss complexity | |
| 0 0.000000 4.4324794 42.354317 1 | |
| 1 1.255691 (x0 * x0) 3.437307 3 | |
| 2 0.011629 ((x0 * x0) + -0.28087974) 3.358285 5 | |
| 3 0.897855 ((x0 * x0) + cos(x3)) 1.368308 6 | |
| 4 0.857018 ((x0 * x0) + (cos(x3) * 2.4566472)) 0.246483 8 | |
| 5 >>>> inf (((cos(x3) + -0.19699033) * 2.5382123) + (x0 *... 0.000000 10 | |
| ] | |
| ``` | |
| This arrow in the `pick` column indicates which equation is currently selected by your | |
| `model_selection` strategy for prediction. | |
| (You may change `model_selection` after `.fit(X, y)` as well.) | |
| `model.equations_` is a pandas DataFrame containing all equations, including callable format | |
| (`lambda_format`), | |
| SymPy format (`sympy_format` - which you can also get with `model.sympy()`), and even JAX and PyTorch format | |
| (both of which are differentiable - which you can get with `model.jax()` and `model.pytorch()`). | |
| Note that `PySRRegressor` stores the state of the last search, and will restart from where you left off the next time you call `.fit()`, assuming you have set `warm_start=True`. | |
| This will cause problems if significant changes are made to the search parameters (like changing the operators). You can run `model.reset()` to reset the state. | |
| You will notice that PySR will save two files: `hall_of_fame...csv` and `hall_of_fame...pkl`. | |
| The csv file is a list of equations and their losses, and the pkl file is a saved state of the model. | |
| You may load the model from the `pkl` file with: | |
| ```python | |
| model = PySRRegressor.from_file("hall_of_fame.2022-08-10_100832.281.pkl") | |
| ``` | |
| There are several other useful features such as denoising (e.g., `denoising=True`), | |
| feature selection (e.g., `select_k_features=3`). | |
| For examples of these and other features, see the [examples page](https://astroautomata.com/PySR/examples). | |
| For a detailed look at more options, see the [options page](https://astroautomata.com/PySR/options). | |
| You can also see the full API at [this page](https://astroautomata.com/PySR/api). | |
| ## Detailed Example | |
| The following code makes use of as many PySR features as possible. | |
| Note that is just a demonstration of features and you should not use this example as-is. | |
| For details on what each parameter does, check out the [API page](https://astroautomata.com/PySR/api/). | |
| ```python | |
| model = PySRRegressor( | |
| procs=4, | |
| populations=8, | |
| # ^ 2 populations per core, so one is always running. | |
| population_size=50, | |
| # ^ Slightly larger populations, for greater diversity. | |
| ncyclesperiteration=500, | |
| # ^ Generations between migrations. | |
| niterations=10000000, # Run forever | |
| early_stop_condition=( | |
| "stop_if(loss, complexity) = loss < 1e-6 && complexity < 10" | |
| # Stop early if we find a good and simple equation | |
| ), | |
| timeout_in_seconds=60 * 60 * 24, | |
| # ^ Alternatively, stop after 24 hours have passed. | |
| maxsize=50, | |
| # ^ Allow greater complexity. | |
| maxdepth=10, | |
| # ^ But, avoid deep nesting. | |
| binary_operators=["*", "+", "-", "/"], | |
| unary_operators=["square", "cube", "exp", "cos2(x)=cos(x)^2"], | |
| constraints={ | |
| "/": (-1, 9), | |
| "square": 9, | |
| "cube": 9, | |
| "exp": 9, | |
| }, | |
| # ^ Limit the complexity within each argument. | |
| # "inv": (-1, 9) states that the numerator has no constraint, | |
| # but the denominator has a max complexity of 9. | |
| # "exp": 9 simply states that `exp` can only have | |
| # an expression of complexity 9 as input. | |
| nested_constraints={ | |
| "square": {"square": 1, "cube": 1, "exp": 0}, | |
| "cube": {"square": 1, "cube": 1, "exp": 0}, | |
| "exp": {"square": 1, "cube": 1, "exp": 0}, | |
| }, | |
| # ^ Nesting constraints on operators. For example, | |
| # "square(exp(x))" is not allowed, since "square": {"exp": 0}. | |
| complexity_of_operators={"/": 2, "exp": 3}, | |
| # ^ Custom complexity of particular operators. | |
| complexity_of_constants=2, | |
| # ^ Punish constants more than variables | |
| select_k_features=4, | |
| # ^ Train on only the 4 most important features | |
| progress=True, | |
| # ^ Can set to false if printing to a file. | |
| weight_randomize=0.1, | |
| # ^ Randomize the tree much more frequently | |
| cluster_manager=None, | |
| # ^ Can be set to, e.g., "slurm", to run a slurm | |
| # cluster. Just launch one script from the head node. | |
| precision=64, | |
| # ^ Higher precision calculations. | |
| warm_start=True, | |
| # ^ Start from where left off. | |
| turbo=True, | |
| # ^ Faster evaluation (experimental) | |
| julia_project=None, | |
| # ^ Can set to the path of a folder containing the | |
| # "SymbolicRegression.jl" repo, for custom modifications. | |
| update=False, | |
| # ^ Don't update Julia packages | |
| extra_sympy_mappings={"cos2": lambda x: sympy.cos(x)**2}, | |
| # extra_torch_mappings={sympy.cos: torch.cos}, | |
| # ^ Not needed as cos already defined, but this | |
| # is how you define custom torch operators. | |
| # extra_jax_mappings={sympy.cos: "jnp.cos"}, | |
| # ^ For JAX, one passes a string. | |
| ) | |
| ``` | |
| # Docker | |
| You can also test out PySR in Docker, without | |
| installing it locally, by running the following command in | |
| the root directory of this repo: | |
| ```bash | |
| docker build --pull --rm -f "Dockerfile" -t pysr "." | |
| ``` | |
| This builds an image called `pysr`. | |
| You can then run this with: | |
| ```bash | |
| docker run -it --rm -v "$PWD:/data" pysr ipython | |
| ``` | |
| which will link the current directory to the container's `/data` directory | |
| and then launch ipython. | |
| If you have issues building (for example, on Apple Silicon), | |
| you can emulate another architecture by including `--platform linux/amd64`, | |
| before the `build` and `run` commands. | |