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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** |
|---|---|
|[](https://astroautomata.com/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)** | **Docker** | **Coverage** |
|---|---|---|---|---|
|[](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)|[](https://github.com/MilesCranmer/PySR/actions/workflows/CI_docker.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
PySR uses both Julia and Python, so you need to have both installed.
Install Julia - see [downloads](https://julialang.org/downloads/), and
then instructions for [mac](https://julialang.org/downloads/platform/#macos)
and [linux](https://julialang.org/downloads/platform/#linux_and_freebsd).
(Don't use the `conda-forge` version; it doesn't seem to work properly.)
You can install PySR with:
```bash
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](https://github.com/MilesCranmer/PySR/issues/27).
to use up-to-date packages.
# 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,
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:
```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 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](https://pysr.readthedocs.io/en/latest/docs/options/).
You can see the full API at [this page](https://pysr.readthedocs.io/en/latest/docs/api-documentation/).
# 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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