Lagrangian Neural Network with Differentiable Symmetries and Relational Inductive Bias

TL;DR

This paper introduces a Lagrangian neural network that preserves translational and rotational symmetries, ensuring conservation laws and enabling generalization to systems of arbitrary size, with improved interpretability.

Contribution

The authors develop a momentum conserving Lagrangian neural network that explicitly incorporates symmetries, enhancing physical accuracy and interpretability over prior models.

Findings

Successfully conserves energy and momentum in tested systems.

Generalizes to systems of arbitrary size.

Provides physical insights into multi-particle interactions.

Abstract

Realistic models of physical world rely on differentiable symmetries that, in turn, correspond to conservation laws. Recent works on Lagrangian and Hamiltonian neural networks show that the underlying symmetries of a system can be easily learned by a neural network when provided with an appropriate inductive bias. However, these models still suffer from issues such as inability to generalize to arbitrary system sizes, poor interpretability, and most importantly, inability to learn translational and rotational symmetries, which lead to the conservation laws of linear and angular momentum, respectively. Here, we present a momentum conserving Lagrangian neural network (MCLNN) that learns the Lagrangian of a system, while also preserving the translational and rotational symmetries. We test our approach on linear and non-linear spring systems, and a gravitational system, demonstrating the energy and momentum conservation. We also show that the model developed can generalize to systems of any arbitrary size. Finally, we discuss the interpretability of the MCLNN, which directly provides physical insights into the interactions of multi-particle systems.