RamonYeung / PhySO

Physical Symbolic Optimization

$\Phi$-SO : Physical Symbolic Optimization

The physical symbolic regression ( $\Phi$-SO ) package physo is a symbolic regression package that fully leverages physical units constraints. For more details see: [Tenachi et al 2023].

demo_light.mp4

Installation

Virtual environment

The package has been tested on Unix and OSX. To install the package it is recommend to first create a conda virtual environment:

conda create -n PhySO python=3.8

And activate it:

conda activate PhySO

Dependencies

From the repository root:

Installing essential dependencies :

conda install --file requirements.txt

Installing optional dependencies (for advanced debugging in tree representation) :

conda install --file requirements_display1.txt

pip install -r requirements_display2.txt

Side note regarding CUDA acceleration:

$\Phi$-SO supports CUDA but it should be noted that since the bottleneck of the code is free constant optimization, using CUDA (even on a very high-end GPU) does not improve performances over a CPU and can actually hinder performances.

Installing $\Phi$-SO

Installing physo (from the repository root):

pip install -e .

Testing install

Import test:

python3
>>> import physo

This should result in physo being successfully imported.

Unit tests:

From the repository root:

python -m unittest discover -p "*UnitTest.py"

This should result in all tests being successfully passed (except for program_display_UnitTest tests if optional dependencies were not installed).

Getting started

Symbolic regression with default hyperparameters

[Coming soon] In the meantime you can have a look at our demo folder ! :)

Symbolic regression

[Coming soon]

Custom symbolic optimization task

[Coming soon]

Using custom functions

[Coming soon]

Open training loop

[Coming soon]

About performances

The main performance bottleneck of physo is free constant optimization, therefore, performances are almost linearly dependent on the number of free constant optimization steps and on the number of trial expressions per epoch (ie. the batch size).

In addition, it should be noted that generating monitoring plots takes ~3s, therefore we suggest making monitoring plots every >10 epochs for low time / epoch cases.

Summary of expected performances with physo:

Time / epoch	Batch size	# free const	free const opti steps	Example	Device
~20s	10k	2	15	eg: demo_damped_harmonic_oscillator	CPU: Mac M1 RAM: 16 Go
~30s	10k	2	15	eg: demo_damped_harmonic_oscillator	CPU: Intel W-2155 10c/20t RAM: 128 Go
~250s	10k	2	15	eg: demo_damped_harmonic_oscillator	GPU: Nvidia GV100 VRAM : 32 Go
~3s	1k	2	15	eg: demo_mechanical_energy	CPU: Mac M1 RAM: 16 Go
~3s	1k	2	15	eg: demo_mechanical_energy	CPU: Intel W-2155 10c/20t RAM: 128 Go
~4s	1k	2	15	eg: demo_mechanical_energy	GPU: Nvidia GV100 VRAM : 32 Go

Please note that using a CPU typically results in higher performances than when using a GPU.

Uninstalling

Uninstalling the package.

conda deactivate
conda env remove -n PhySO

Citing this work

@ARTICLE{2023arXiv230303192T,
       author = {{Tenachi}, Wassim and {Ibata}, Rodrigo and {Diakogiannis}, Foivos I.},
        title = "{Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws}",
      journal = {arXiv e-prints},
     keywords = {Astrophysics - Instrumentation and Methods for Astrophysics, Computer Science - Machine Learning, Physics - Computational Physics},
         year = 2023,
        month = mar,
          eid = {arXiv:2303.03192},
        pages = {arXiv:2303.03192},
          doi = {10.48550/arXiv.2303.03192},
archivePrefix = {arXiv},
       eprint = {2303.03192},
 primaryClass = {astro-ph.IM},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2023arXiv230303192T},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}