SymbolicPhysicsLearner

source code and examples for Symbolic physics learner: Discovering governing equations via Monte Carlo tree search.

Dependencies

requirements.txt

Baseline Models

The following packages are not included in the requirements list. Please install at your interest.

base GP model: pip install gplearn https://gplearn.readthedocs.io/en/stable/
SINDy: pip install pysindy https://pysindy.readthedocs.io/en/latest/
Deep Symbolic Regression: refer to dso

Datasets

symbolic regression data

To generate training and testing datasets for Nguyen's benchmark problems, run

python regression_task/make_datasets.py --task=nguyen-1

dropping ball experiment data

source data is from https://github.com/briandesilva/discovery-of-physics-from-data

To proces the data into the input of SPL model, run

python physics_task/make_datasets_balldrop.py

Lorenz dataset

Lorenz experimental dataset is simulted by MATLAB ode113 function.

double pendulum dataset

Double Pendulum dataset is from camera-recorded experiments provided by https://developer.ibm.com/exchanges/data/all/double-pendulum-chaotic/

Check more details about its pre-processing from dynamics_task/dp_makedata.ipynb

Run Model

symbolic regression job

Job configurations for Nguyen's benchmark problems are already included. To run experiments with Symbolic Physics Learner, use

import sys
import numpy as np
sys.path.append(r'../')
from spl_train import run_spl

output_folder = 'results_dump/' ## directory to save discovered results
save_eqs = True                ## if true, discovered equations are saved to "output_folder" dir

task = 'nguyen-1'
all_eqs, success_rate, all_times = run_spl(task, 
                                           num_run=100, 
                                           transplant_step=10000)
                                           
if save_eqs:
    output_file = open(output_folder + task + '.txt', 'w')
    for eq in all_eqs:
        output_file.write(eq + '\n')
    output_file.close()

print('success rate :', "{:.0%}".format(success_rate))
print('average discovery time is', np.round(np.mean(all_times), 3), 'seconds')

To use base-GP model or Deep Symbolic Regression model, please check run_gp.py and run_dsr.py.

physics discovery job

refer to examples in physics_task/balldrop_tasks.ipynb

nonlinear dynamics discovery job

refer to examples in dynamics_task/spl double pendulum.ipynb and dynamics_task/spl lorenz.ipynb

Citing the paper

@inproceedings{
sun2023symbolic,
title={Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search},
author={Fangzheng Sun and Yang Liu and Jian-Xun Wang and Hao Sun},
booktitle={The Eleventh International Conference on Learning Representations },
year={2023},
url={https://openreview.net/forum?id=ZTK3SefE8_Z}
}

toontran / SymbolicPhysicsLearner