Learning Symbolic Physics with Graph Networks

TL;DR

This paper presents a graph network approach that incorporates physical inductive biases to learn interpretable models of physical interactions, successfully recovering known laws and generalizing to larger systems.

Contribution

It introduces a method to embed physical principles into graph networks, enabling symbolic recovery of physical laws and improved zero-shot generalization.

Findings

Recovered Newton's law of gravitation without prior knowledge

Achieved better generalization to larger systems

Learned message representations equivalent to true force vectors

Abstract

We introduce an approach for imposing physically motivated inductive biases on graph networks to learn interpretable representations and improved zero-shot generalization. Our experiments show that our graph network models, which implement this inductive bias, can learn message representations equivalent to the true force vector when trained on n-body gravitational and spring-like simulations. We use symbolic regression to fit explicit algebraic equations to our trained model's message function and recover the symbolic form of Newton's law of gravitation without prior knowledge. We also show that our model generalizes better at inference time to systems with more bodies than had been experienced during training. Our approach is extensible, in principle, to any unknown interaction law learned by a graph network, and offers a valuable technique for interpreting and inferring explicit causal theories about the world from implicit knowledge captured by deep learning.