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.

1. base GP model: pip install gplearn https://gplearn.readthedocs.io/en/stable/
2. SINDy: pip install pysindy https://pysindy.readthedocs.io/en/latest/
3. 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}
}