<h1><img align="left" height="171" src="https://raw.githubusercontent.com/MilesCranmer/PySR_Docs/master/images/pysr-logo.png" alt="">PySR<br><sub><sub>Symbolic Regression in Python and Julia</sub></sub><br><sub><sub><a href="https://pysr.ai/">Docs</a> × <a href="https://pysr.ai/examples">Examples</a> × <a href="https://pysr.ai/api">API</a> × <a href="https://github.com/astroautomata/PySR/discussions">Forum</a> × <a href="#ai-agent-skill">Agents</a></sub></sub><br><sub><a href="https://pypi.org/project/pysr/"><img src="https://img.shields.io/pypi/v/pysr" alt="PyPI"></a> <a href="https://anaconda.org/conda-forge/pysr"><img src="https://img.shields.io/conda/vn/conda-forge/pysr" alt="conda-forge"></a> <a href="https://arxiv.org/abs/2305.01582"><img src="https://img.shields.io/badge/arXiv-2305.01582-b31b1b" alt="arXiv"></a></sub><br clear="all"></h1>
```bash
pip install pysr
```
If you find PySR useful, please cite the paper [arXiv:2305.01582](https://arxiv.org/abs/2305.01582).
If you've finished a project with PySR, please submit a PR to showcase your work on the [research showcase page](https://pysr.ai/papers)!
**Contents**:
- [Why PySR?](#why-pysr)
- [Installation](#installation)
- [Quickstart](#quickstart)
- [→ Documentation](https://pysr.ai)
- [Contributors](#contributors-)
## Why PySR?
PySR is an open-source tool for *Symbolic Regression*: a machine learning
task where the goal is to find an interpretable symbolic expression that optimizes some objective.
Over a period of several years, PySR has been engineered from the ground up
to be (1) as high-performance as possible,
(2) as configurable as possible, and (3) easy to use.
PySR is developed alongside the Julia library [SymbolicRegression.jl](https://github.com/astroautomata/SymbolicRegression.jl),
which forms the powerful search engine of PySR.
The details of these algorithms are described in the [PySR paper](https://arxiv.org/abs/2305.01582).
Symbolic regression works best on low-dimensional datasets, but
one can also extend these approaches to higher-dimensional
spaces by using "*Symbolic Distillation*" of Neural Networks, 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 neural networks.
## Installation
You can install PySR with pip or conda:
```bash
pip install pysr
```
```bash
conda install -c conda-forge pysr
```
Julia dependencies will be installed at first import.
### AI Agent Skill
Install the [PySR skill](skills/pysr/SKILL.md) to provide your coding
agents guidance using PySR as part of a larger agentic loop:
```bash
npx skills add astroautomata/PySR
```
Add `--global` to install the skill globally.
<details>
<summary>
### Docker
</summary>
You can also use the `Dockerfile` to install PySR in a docker container
1. Clone this repo.
2. Within the repo's directory, build the docker container:
```bash
docker build -t pysr .
```
3. You can then start the container with an IPython execution with:
```bash
docker run -it --rm pysr ipython
```
For more details, see the [docker section](#docker).
</details>
<details>
<summary>
### Apptainer
</summary>
If you are using PySR on a cluster where you do not have root access,
you can use [Apptainer](https://apptainer.org/) to build a container
instead of Docker. The `Apptainer.def` file is analogous to the `Dockerfile`,
and can be built with:
```bash
apptainer build --notest pysr.sif Apptainer.def
```
and launched with
```bash
apptainer run pysr.sif
```
</details>
<details>
<summary>
### Troubleshooting
</summary>
One issue you might run into can result in a hard crash at import with
a message like "`GLIBCXX_...` not found". This is due to another one of the Python dependencies
loading an incorrect `libstdc++` library. To fix this, you should modify your
`LD_LIBRARY_PATH` variable to reference the Julia libraries. For example, if the Julia
version of `libstdc++.so` is located in `$HOME/.julia/juliaup/julia-1.10.0+0.x64.linux.gnu/lib/julia/`
(which likely differs on your system!), you could add:
```
export LD_LIBRARY_PATH=$HOME/.julia/juliaup/julia-1.10.0+0.x64.linux.gnu/lib/julia/:$LD_LIBRARY_PATH
```
to your `.bashrc` or `.zshrc` file.
</details>
## Quickstart
You might wish to try the interactive tutorial [here](https://colab.research.google.com/github/astroautomata/PySR/blob/master/examples/pysr_demo.ipynb), which uses the notebook in `examples/pysr_demo.ipynb`.
In practice, I highly recommend using IPython rather than Jupyter, as the printing is much nicer.
Below is a quick demo here which you can paste into a Python runtime.
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(
maxsize=20,
niterations=40, # < Increase me for better results
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
elementwise_loss="loss(prediction, target) = (prediction - target)^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 using the automatically-selected expression,
or, for example, `model.predict(X, 3)` to see the predictions of the 3rd equation.
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., `denoise=True`),
feature selection (e.g., `select_k_features=3`).
For examples of these and other features, see the [examples page](https://pysr.ai/examples).
For a detailed look at more options, see the [options page](https://pysr.ai/options).
You can also see the full API at [this page](https://pysr.ai/api).
There are also tips for tuning PySR on [this page](https://pysr.ai/tuning).
### 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://pysr.ai/api).
```python
model = PySRRegressor(
populations=8,
# ^ Assuming we have 4 cores, this means 2 populations per core, so one is always running.
population_size=50,
# ^ Slightly larger populations, for greater diversity.
ncycles_per_iteration=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)
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 -t pysr .
```
This builds an image called `pysr` for your system's architecture,
which also contains IPython. You can select a specific version
of Python and Julia with:
```bash
docker build -t pysr --build-arg JLVERSION=1.10.0 --build-arg PYVERSION=3.11.6 .
```
You can then run with this dockerfile using:
```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 your system's architecture,
you can emulate another architecture by including `--platform linux/amd64`,
before the `build` and `run` commands.
<div align="center">
### Contributors ✨
</div>
We are eager to welcome new contributors! Check out our contributors [guide](https://github.com/astroautomata/PySR/blob/master/CONTRIBUTORS.md) for tips 🚀.
If you have an idea for a new feature, don't hesitate to share it on the [issues](https://github.com/astroautomata/PySR/issues) or [discussions](https://github.com/astroautomata/PySR/discussions) page.
<!-- ALL-CONTRIBUTORS-LIST:START - Do not remove or modify this section -->
<!-- prettier-ignore-start -->
<!-- markdownlint-disable -->
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<td align="center" valign="top" width="12.5%"><a href="https://github.com/WilliamBC-SL"><img src="https://avatars.githubusercontent.com/u/118170949?v=4?s=50" width="50px;" alt="William Booth-Clibborn"/><br /><sub><b>William Booth-Clibborn</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://raulpl.github.io/about"><img src="https://avatars.githubusercontent.com/u/3116652?v=4?s=50" width="50px;" alt="Raúl Peralta Lozada"/><br /><sub><b>Raúl Peralta Lozada</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://www.linkedin.com/in/hvaara/"><img src="https://avatars.githubusercontent.com/u/1535968?v=4?s=50" width="50px;" alt="Roy Hvaara"/><br /><sub><b>Roy Hvaara</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/VishalJ99"><img src="https://avatars.githubusercontent.com/u/51826812?v=4?s=50" width="50px;" alt="Vishal Jain"/><br /><sub><b>Vishal Jain</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/spaette"><img src="https://avatars.githubusercontent.com/u/111918424?v=4?s=50" width="50px;" alt="spaette"/><br /><sub><b>spaette</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="http://www.yxliu.group"><img src="https://avatars.githubusercontent.com/u/1089344?v=4?s=50" width="50px;" alt="Yi-Xin Liu"/><br /><sub><b>Yi-Xin Liu</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/spinnau"><img src="https://avatars.githubusercontent.com/u/2995937?v=4?s=50" width="50px;" alt="spinnau"/><br /><sub><b>spinnau</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/sunxd3"><img src="https://avatars.githubusercontent.com/u/5433119?v=4?s=50" width="50px;" alt="Xianda Sun"/><br /><sub><b>Xianda Sun</b></sub></a></td>
</tr>
<tr>
<td align="center" valign="top" width="12.5%"><a href="https://jaywadekar.github.io/"><img src="https://avatars.githubusercontent.com/u/5493388?v=4?s=50" width="50px;" alt="Jay Wadekar"/><br /><sub><b>Jay Wadekar</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/ablaom"><img src="https://avatars.githubusercontent.com/u/30517088?v=4?s=50" width="50px;" alt="Anthony Blaom, PhD"/><br /><sub><b>Anthony Blaom, PhD</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/Jgmedina95"><img src="https://avatars.githubusercontent.com/u/97254349?v=4?s=50" width="50px;" alt="Jgmedina95"/><br /><sub><b>Jgmedina95</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/mcabbott"><img src="https://avatars.githubusercontent.com/u/32575566?v=4?s=50" width="50px;" alt="Michael Abbott"/><br /><sub><b>Michael Abbott</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/oscardssmith"><img src="https://avatars.githubusercontent.com/u/11729272?v=4?s=50" width="50px;" alt="Oscar Smith"/><br /><sub><b>Oscar Smith</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://ericphanson.com/"><img src="https://avatars.githubusercontent.com/u/5846501?v=4?s=50" width="50px;" alt="Eric Hanson"/><br /><sub><b>Eric Hanson</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/henriquebecker91"><img src="https://avatars.githubusercontent.com/u/14113435?v=4?s=50" width="50px;" alt="Henrique Becker"/><br /><sub><b>Henrique Becker</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/qwertyjl"><img src="https://avatars.githubusercontent.com/u/110912592?v=4?s=50" width="50px;" alt="qwertyjl"/><br /><sub><b>qwertyjl</b></sub></a></td>
</tr>
<tr>
<td align="center" valign="top" width="12.5%"><a href="https://huijzer.xyz/"><img src="https://avatars.githubusercontent.com/u/20724914?v=4?s=50" width="50px;" alt="Rik Huijzer"/><br /><sub><b>Rik Huijzer</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/GCaptainNemo"><img src="https://avatars.githubusercontent.com/u/43086239?v=4?s=50" width="50px;" alt="Hongyu Wang"/><br /><sub><b>Hongyu Wang</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/ZehaoJin"><img src="https://avatars.githubusercontent.com/u/50961376?v=4?s=50" width="50px;" alt="Zehao Jin"/><br /><sub><b>Zehao Jin</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/tmengel"><img src="https://avatars.githubusercontent.com/u/38924390?v=4?s=50" width="50px;" alt="Tanner Mengel"/><br /><sub><b>Tanner Mengel</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/agrundner24"><img src="https://avatars.githubusercontent.com/u/38557656?v=4?s=50" width="50px;" alt="Arthur Grundner"/><br /><sub><b>Arthur Grundner</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/sjwetzel"><img src="https://avatars.githubusercontent.com/u/24393721?v=4?s=50" width="50px;" alt="sjwetzel"/><br /><sub><b>sjwetzel</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://sauravmaheshkar.github.io/"><img src="https://avatars.githubusercontent.com/u/61241031?v=4?s=50" width="50px;" alt="Saurav Maheshkar"/><br /><sub><b>Saurav Maheshkar</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/chris-soelistyo"><img src="https://avatars.githubusercontent.com/u/68875981?v=4?s=50" width="50px;" alt="chris-soelistyo"/><br /><sub><b>chris-soelistyo</b></sub></a></td>
</tr>
<tr>
<td align="center" valign="top" width="12.5%"><a href="https://ilyaorson.gitlab.io"><img src="https://avatars.githubusercontent.com/u/12092488?v=4?s=50" width="50px;" alt="Ilya Orson "/><br /><sub><b>Ilya Orson </b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://hftsoi.github.io"><img src="https://avatars.githubusercontent.com/u/51976330?v=4?s=50" width="50px;" alt="Ho Fung Tsoi"/><br /><sub><b>Ho Fung Tsoi</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/LionessOfCintra"><img src="https://avatars.githubusercontent.com/u/92221853?v=4?s=50" width="50px;" alt="LionessOfCintra"/><br /><sub><b>LionessOfCintra</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/manuel-morales-a"><img src="https://avatars.githubusercontent.com/u/64017590?v=4?s=50" width="50px;" alt="Manuel Morales "/><br /><sub><b>Manuel Morales </b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://paulomontero.github.io"><img src="https://avatars.githubusercontent.com/u/23636178?v=4?s=50" width="50px;" alt="Paulo Montero Camacho"/><br /><sub><b>Paulo Montero Camacho</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/luna026"><img src="https://avatars.githubusercontent.com/u/88938665?v=4?s=50" width="50px;" alt="Writu Dasgupta"/><br /><sub><b>Writu Dasgupta</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/anubhavkamal"><img src="https://avatars.githubusercontent.com/u/23038512?v=4?s=50" width="50px;" alt="Anubhav Kamal"/><br /><sub><b>Anubhav Kamal</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/anthony-sun"><img src="https://avatars.githubusercontent.com/u/115842064?v=4?s=50" width="50px;" alt="anthony-sun"/><br /><sub><b>anthony-sun</b></sub></a></td>
</tr>
<tr>
<td align="center" valign="top" width="12.5%"><a href="https://nithouson.github.io"><img src="https://avatars.githubusercontent.com/u/26868834?v=4?s=50" width="50px;" alt="Hao Guo"/><br /><sub><b>Hao Guo</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/TrailblazerH"><img src="https://avatars.githubusercontent.com/u/177746076?v=4?s=50" width="50px;" alt="Trailblazer"/><br /><sub><b>Trailblazer</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/christospliakos"><img src="https://avatars.githubusercontent.com/u/64842094?v=4?s=50" width="50px;" alt="Christos Pliakos"/><br /><sub><b>Christos Pliakos</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/zouzaxd"><img src="https://avatars.githubusercontent.com/u/103605983?v=4?s=50" width="50px;" alt="Sousa Neto"/><br /><sub><b>Sousa Neto</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/LeoVoltolini"><img src="https://avatars.githubusercontent.com/u/94749527?v=4?s=50" width="50px;" alt="Leonardo Voltolini"/><br /><sub><b>Leonardo Voltolini</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/con13375"><img src="https://avatars.githubusercontent.com/u/19805622?v=4?s=50" width="50px;" alt="Daniel Eduardo Conde Villatoro"/><br /><sub><b>Daniel Eduardo Conde Villatoro</b></sub></a></td>
<td align="center" valign="top" width="12.5%"><a href="https://github.com/sambeckers"><img src="https://avatars.githubusercontent.com/u/127021792?v=4?s=50" width="50px;" alt="Sam Beckers"/><br /><sub><b>Sam Beckers</b></sub></a></td>
</tr>
</tbody>
</table>
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