Discovering Symbolic Models from Deep Learning with Inductive Biases
This repository is the official implementation of Discovering Symbolic Models from Deep Learning with Inductive Biases.
Miles Cranmer, Alvaro Sanchez-Gonzalez, Peter Battaglia, Rui Xu, Kyle Cranmer, David Spergel, Shirley Ho
Check out our Blog, Paper, Video, and Interactive Demo.
Requirements
For model:
- pytorch
- pytorch-geometric
- numpy
Symbolic regression:
- PySR, our new open-source Eureqa alternative
For simulations:
Training
To train an example model from the paper, try out the demo.
Full model definitions are given in models.py. Data is generated from simulate.py.
Results
We train on simulations produced by the following equations:
giving us time series:
We recorded performance for each model:
and also measured how well each model's messages
correlated with a linear combination of forces:
Finally, we trained on a dark matter simulation and extracted the following equations
from the message function:
