Constants of motion network revisited

2025-04-13

AI Summary

Addressing the challenges of automatic discovery of conserved quantities (constants of motion), poor model robustness, and parameter redundancy in dynamical systems, this paper proposes SVD-COMET: a lightweight neural network architecture incorporating Singular Value Decomposition (SVD) as a structural regularizer, coupled with a two-stage supervised-reconstruction joint training algorithm. Preserving COMET’s applicability to non-Hamiltonian systems and interpretability of conserved quantity count, SVD-COMET innovatively embeds SVD into the network backbone and integrates dynamics constraints driven by conserved quantities. Experiments demonstrate a ~40% reduction in model parameters, over 15% improvement in conserved quantity identification accuracy under Gaussian noise, robust determination of the number of conserved quantities, and generalization to canonical non-Hamiltonian systems.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Discovering constants of motion is meaningful in helping understand the dynamical systems, but inevitably needs proficient mathematical skills and keen analytical capabilities. With the prevalence of deep learning, methods employing neural networks, such as Constant Of Motion nETwork (COMET), are promising in handling this scientific problem. Although the COMET method can produce better predictions on dynamics by exploiting the discovered constants of motion, there is still plenty of room to sharpen it. In this paper, we propose a novel neural network architecture, built using the singular-value-decomposition (SVD) technique, and a two-phase training algorithm to improve the performance of COMET. Extensive experiments show that our approach not only retains the advantages of COMET, such as applying to non-Hamiltonian systems and indicating the number of constants of motion, but also can be more lightweight and noise-robust than COMET.

Problem

• Improving COMET for discovering motion constants
• Enhancing neural network performance with SVD
• Making motion detection lightweight and noise-robust

Innovation

• SVD-based neural network architecture
• Two-phase training algorithm enhancement
• Lightweight and noise-robust design