Deepmechanics

TL;DR

This paper benchmarks physics-informed deep learning models on various dynamical systems, revealing challenges in stability and robustness, especially for chaotic and non-conservative systems, and highlights the need for further research.

Contribution

It systematically evaluates Hamiltonian, Lagrangian, and Symplectic neural networks across diverse physical systems using the DeepChem framework, providing insights into their stability and robustness.

Findings

All models struggle with chaotic and non-conservative systems.

Models have difficulty maintaining stability over long trajectories.

Further research is needed to improve robustness of physics-informed models.

Abstract

Physics-informed deep learning models have emerged as powerful tools for learning dynamical systems. These models directly encode physical principles into network architectures. However, systematic benchmarking of these approaches across diverse physical phenomena remains limited, particularly in conservative and dissipative systems. In addition, benchmarking that has been done thus far does not integrate out full trajectories to check stability. In this work, we benchmark three prominent physics-informed architectures such as Hamiltonian Neural Networks (HNN), Lagrangian Neural Networks (LNN), and Symplectic Recurrent Neural Networks (SRNN) using the DeepChem framework, an open-source scientific machine learning library. We evaluate these models on six dynamical systems spanning classical conservative mechanics (mass-spring system, simple pendulum, double pendulum, and three-body problem, spring-pendulum) and non-conservative systems with contact (bouncing ball). We evaluate models by computing error on predicted trajectories and evaluate error both quantitatively and qualitatively. We find that all benchmarked models struggle to maintain stability for chaotic or nonconservative systems. Our results suggest that more research is needed for physics-informed deep learning models to learn robust models of classical mechanical systems.