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

• URL: http://arxiv.org/abs/2505.03783v1
• Date: Wed, 30 Apr 2025 14:41:18 GMT
• Title: A general physics-constrained method for the modelling of equation's closure terms with sparse data
• Authors: Tian Chen, Shengping Liu, Li Liu, Heng Yong,
• Abstract summary: We introduce a Series-Parallel Multi-Network Architecture that integrates physical constraints and heterogeneous data from multiple initial and boundary conditions.<n>We employ dedicatedworks to independently model unknown closure terms, enhancing generalizability across diverse problems.<n>These closure models are integrated into an accurate Partial Differential Equation (PDE) solver, enabling robust solutions to complex predictive simulations in engineering applications.
• Score: 8.927683811459543
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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