Modular Neural Ordinary Differential Equations

TL;DR

This paper introduces Modular Neural ODEs, a flexible and interpretable architecture that learns force components separately, improving performance and incorporating physical priors in modeling differential equations.

Contribution

It proposes a modular approach to Neural ODEs that enhances interpretability, flexibility, and the ability to incorporate physical priors, addressing limitations of previous models.

Findings

Better performance in dynamics modeling

Enhanced interpretability of learned models

Flexible incorporation of physical priors

Abstract

The laws of physics have been written in the language of dif-ferential equations for centuries. Neural Ordinary Differen-tial Equations (NODEs) are a new machine learning architecture which allows these differential equations to be learned from a dataset. These have been applied to classical dynamics simulations in the form of Lagrangian Neural Net-works (LNNs) and Second Order Neural Differential Equations (SONODEs). However, they either cannot represent the most general equations of motion or lack interpretability. In this paper, we propose Modular Neural ODEs, where each force component is learned with separate modules. We show how physical priors can be easily incorporated into these models. Through a number of experiments, we demonstrate these result in better performance, are more interpretable, and add flexibility due to their modularity.