ModLaNets: Learning Generalisable Dynamics via Modularity and Physical Inductive Bias

TL;DR

ModLaNets introduces a modular neural network framework with physical inductive bias that efficiently learns and generalizes dynamical systems across different complexities, outperforming existing models in data efficiency and accuracy.

Contribution

The paper presents ModLaNets, a novel modular neural network framework that leverages physical laws to improve generalization and reusability in learning dynamical systems.

Findings

Achieves superior data efficiency and accuracy on double-pendulum and three-body systems.

Enables extension to multi-pendulum and multi-body systems with reusability.

Outperforms existing physics-informed neural networks in learning complex dynamics.

Abstract

Deep learning models are able to approximate one specific dynamical system but struggle at learning generalisable dynamics, where dynamical systems obey the same laws of physics but contain different numbers of elements (e.g., double- and triple-pendulum systems). To relieve this issue, we proposed the Modular Lagrangian Network (ModLaNet), a structural neural network framework with modularity and physical inductive bias. This framework models the energy of each element using modularity and then construct the target dynamical system via Lagrangian mechanics. Modularity is beneficial for reusing trained networks and reducing the scale of networks and datasets. As a result, our framework can learn from the dynamics of simpler systems and extend to more complex ones, which is not feasible using other relevant physics-informed neural networks. We examine our framework for modelling double-pendulum or three-body systems with small training datasets, where our models achieve the best data efficiency and accuracy performance compared with counterparts. We also reorganise our models as extensions to model multi-pendulum and multi-body systems, demonstrating the intriguing reusable feature of our framework.