A general physics-constrained method for the modelling of equation's closure terms with sparse data

2025/04/30 by Tian Chen, Shengping Liu, Chen, Tian +5
Computer Science · Materials Science · Physics and Astronomy · #Advanced Multi-Objective Optimization Algorithms #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Machine Learning in Materials Science #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2505.03783

openalex publication_date 2025/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Accurate modeling of closure terms is a critical challenge in engineering and scientific research, particularly when data is sparse (scarse or incomplete), making widely applicable models difficult to develop. This study proposes a novel approach for constructing closure models in such challenging scenarios. We introduce a Series-Parallel Multi-Network Architecture that integrates Physics-Informed Neural Networks (PINNs) to incorporate physical constraints and heterogeneous data from multiple initial and boundary conditions, while employing dedicated subnetworks to independently model unknown closure terms, enhancing generalizability across diverse problems. These closure models are integrated into an accurate Partial Differential Equation (PDE) solver, enabling robust solutions to complex predictive simulations in engineering applications.

Citations

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• A hands-on introduction to Physics-Informed Neural Networks for solving partial differential equations with benchmark tests taken from astrophysics and plasma physics