  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.
