Hybrid method couples neural networks with classical models for fluid flow
Hybrid coupling with numerics-informed neural networks and the overlapping Schwarz alternating method
Machine Learning
Summary
This paper addresses how to combine two types of computer models to solve a complex physics problem involving fluid flow and heat transfer. The authors show that special neural networks trained with numerical data can work accurately on their own for this problem. They then develop a way to link these neural networks with traditional physics-based models using a mathematical method called Schwarz iteration. This hybrid approach produces results very close to using only traditional models, but with more flexibility in training and deploying parts of the model.
What this means in practice
- •For computational fluid dynamics engineers: Integrate neural-network-based submodels with classical solvers to speed up large-scale simulation of fluid flows with strong advection effects.
- •For simulation software developers: Develop hybrid solver frameworks that incorporate pre-trained neural networks on subregions for improved modularity without sacrificing accuracy.
Authors
George Chumbipuma, Irina Tezaur, Alejandro Diaz, Beatrice Riviere
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.