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[//]: # (Logo:)
<img src="https://raw.githubusercontent.com/MilesCranmer/PySR/master/docs/images/pysr_logo.svg" width="400" />
# 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.
| **Docs** | **pip** | **conda** | **Stats** |
|---|---|---|---|
|[](https://astroautomata.com/PySR/)|[](https://badge.fury.io/py/pysr)|[](https://anaconda.org/conda-forge/pysr)|[](https://badge.fury.io/py/pysr)|
(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 let me know and I may showcase your work here!
### 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)|
Check out [SymbolicRegression.jl](https://github.com/MilesCranmer/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](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
| pip | conda |
|---|---|
| 1. Install Julia manually (see [downloads](https://julialang.org/downloads/))<br>2. `pip install pysr`<br>3. `python -c 'import pysr; pysr.install()'` | 1. `conda install -c conda-forge pysr`<br>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.
# 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(
niterations=5,
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:
```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()`. 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](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).
# 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`. 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:
```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.
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