用物理约束提升稀疏数据下闭合项建模的准确性
A general physics-constrained method for the modelling of equation's closure terms with sparse data
- 构建串联并联多网络架构，融合物理规律与多组边界条件数据
- 在稀疏数据下实现对闭合项的精准建模，支持复杂工程模拟求解
- 适合需要高泛化能力的物理系统建模，如流体、热传导等
准确建模闭合项是工程与科研中的关键挑战，尤其在数据稀疏或不完整的情况下，难以构建通用模型。本研究提出一种新方法，用于在困难场景下构建闭合项模型。我们引入串联-并联多网络架构，结合物理信息神经网络（PINNs）融入物理约束，并利用多组初始与边界条件的异构数据，同时通过专用子网络独立建模未知闭合项，提升模型在不同问题间的泛化能力。该闭合项模型被集成至高精度偏微分方程（PDE）求解器中，可实现复杂工程预测模拟的鲁棒求解。
原文摘要 · Abstract (English)
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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