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

TL;DR

This paper introduces a physics-constrained neural network approach for modeling closure terms in PDEs using sparse data, improving generalizability and accuracy in engineering simulations.

Contribution

It presents a Series-Parallel Multi-Network Architecture that combines PINNs with dedicated subnetworks to model closure terms from limited data, enhancing flexibility and physical consistency.

Findings

Effective modeling of closure terms with sparse data.

Improved PDE solver accuracy in engineering applications.

Enhanced generalizability across diverse problems.

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.