Hybrid coupling with numerics-informed neural networks and the overlapping Schwarz alternating method

2026-09-15

AI Summary

研究使用数值信息神经网络与重叠Schwarz交替方法结合经典全阶模型，解决二维对流扩散方程在高Peclet数下的模拟问题。

Abstract

We develop a hybrid modeling framework for coupling pre-trained numerics-informed neural networks (NINNs) with classical full order models (FOMs) using the overlapping Schwarz alternating method. We consider the two-dimensional advection-diffusion equation in the advection-dominated, Peclet-number 10^6 regime. We first demonstrate that, unlike the corresponding physics-informed neural network (PINN), a monolithic NINN can be accurately trained on our model problem without domain decomposition. We then employ overlapping multiplicative Schwarz as a deployment mechanism for coupling a pre-trained, subdomain-local NINN with a neighboring FOM, with the NINN weights held fixed throughout the Schwarz iteration. We consider two training approaches for the subdomain-local NINNs: a top-down approach, in which boundary data are obtained from a coupled Schwarz solve on the full domain with a FOM on each subdomain (FOM-FOM Schwarz), and a bottom-up approach, in which boundary traces are generated synthetically on the NINN subdomain without requiring any full-domain solves. The resulting hybrid NINN-FOM solutions agree closely with the corresponding FOM-FOM Schwarz solutions, with the top-down and bottom-up training approaches yielding comparable accuracy.

Problem

• Hybrid coupling
• Numerics-informed neural networks
• Overlapping Schwarz alternating method
• Advection-diffusion equation

Innovation

• numerics-informed neural networks
• overlapping Schwarz alternating method
• hybrid modeling framework