MilesCranmer / PySR

High-Performance Symbolic Regression in Python

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PySR: High-Performance Symbolic Regression in Python

PySR is built on an extremely optimized pure-Julia backend, and uses regularized evolution, simulated annealing, and gradient-free optimization to search for equations that fit your data.

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(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 If you've finished a project with PySR, please submit a PR to showcase your work on the Research Showcase page!

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Check out SymbolicRegression.jl for the pure-Julia backend of this package.

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, 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.


Previously, we have used eureqa, 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.


pip conda
1. Install Julia manually (see downloads)
2. pip install pysr
3. python -c 'import pysr; pysr.install()'
1. conda install -c conda-forge pysr
2. python -c 'import pysr; pysr.install()'

This last step will install and update the required Julia packages, including PyCall.jl.

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.


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(
    binary_operators=["+", "*"],
        "inv(x) = 1/x",  # Custom operator (julia syntax)
    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:, 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:


to print the learned equations:

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(). 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 examples of these and other features, see the examples page. For a detailed look at more options, see the options page. You can also see the full API at this page.


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.

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High-Performance Symbolic Regression in Python

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