A general physics-constrained method for the modelling of equation's closure terms with sparse data
This addresses the problem of developing widely applicable closure models for engineers and scientists dealing with sparse data, representing a novel method for a known bottleneck.
The study tackled the challenge of modeling closure terms in engineering and scientific research with sparse data by proposing a Series-Parallel Multi-Network Architecture that integrates Physics-Informed Neural Networks, resulting in enhanced generalizability and robust solutions for predictive simulations.
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.