Deepmechanics

2026-02-20

AI Summary

This study addresses the lack of systematic evaluation of stability and generalization capabilities of existing physics-informed deep learning models in both conservative and non-conservative dynamical systems. Building upon the DeepChem framework, the authors present the first unified benchmark of Hamiltonian neural networks, Lagrangian neural networks, and symplectic recurrent neural networks across six canonical mechanical scenarios encompassing chaotic and non-conservative contact dynamics. Through a combination of quantitative metrics and trajectory stability analysis, the results demonstrate that current models struggle to maintain long-term predictive stability in complex or non-conservative settings. These findings reveal critical limitations of prevailing approaches when modeling real-world mechanical systems and provide essential insights to guide the development of more robust and physically consistent learning algorithms.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• physics-informed deep learning
• dynamical systems
• benchmarking
• conservative systems
• non-conservative systems

Innovation

• physics-informed deep learning
• benchmarking
• dynamical systems
• symplectic integration
• trajectory stability