Installation

PySR uses both Julia and Python, so you need to have both installed.

Install Julia - see downloads, and then instructions for mac and linux. (Don't use the conda-forge version; it doesn't seem to work properly.)

You can install PySR with:

pip3 install pysr
python3 -c 'import pysr; pysr.install()'

The second line will install and update the required Julia packages, including PyCall.jl.

Most common issues at this stage are solved by tweaking the Julia package server. to use up-to-date packages.

Introduction

Let's create a PySR example. First, let's import numpy to generate some test data:

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:

from pysr import PySRRegressor
model = PySRRegressor(
    niterations=5,
    populations=8,
    binary_operators=["+", "*"],
    unary_operators=[
        "cos",
        "exp",
        "sin",
        "inv(x) = 1/x",  # Custom operator (julia syntax)
    ],
    model_selection="best",
    loss="loss(x, y) = (x - y)^2",  # Custom loss function (julia syntax)
)

This will set up the model for 5 iterations of the search code, which contains hundreds of thousands of mutations and equation evaluations.

Let's train this model on our dataset:

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:

print(model)

to print the learned equations:

PySRRegressor.equations = [
   pick      score                                           Equation           MSE  Complexity
0         0.000000                                          3.5082064  2.710828e+01           1
1         0.964260                                          (x0 * x0)  3.940544e+00           3
2         0.030096                          (-0.47978288 + (x0 * x0))  3.710349e+00           5
3         0.840770                              ((x0 * x0) + cos(x3))  1.600564e+00           6
4         0.928380                ((x0 * x0) + (2.5313091 * cos(x3)))  2.499724e-01           8
5  >>>>  13.956461  ((-0.49999997 + (x0 * x0)) + (2.5382001 * cos(...  1.885665e-13          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), and even JAX and PyTorch format (both of which are differentiable).

Note that PySRRegressor stores the state of the last search, and will restart from where you left off the next time you call .fit(). 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.

There are several other useful features such as denoising (e.g., denoising=True), feature selection (e.g., select_k_features=3). For a summary of features and options, see this docs page. You can see the full API at this page.

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:

docker build --pull --rm -f "Dockerfile" -t pysr "."

This builds an image called pysr. If you have issues building (for example, on Apple Silicon), you can emulate an architecture that works by including: --platform linux/amd64. You can then run this with:

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.