Interface learning in fluid dynamics: statistical inference of closures within micro-macro coupling models

TL;DR

This paper introduces a data-driven, neural network-based approach to learn interface closure relations in micro-macro fluid dynamics models, improving the coupling accuracy between different solver scales in complex reaction-diffusion systems.

Contribution

It presents a novel statistical inference method to learn interface closures, addressing the micro-macro coupling challenge in fluid dynamics simulations.

Findings

Effective neural network-based closure model demonstrated in bifidelity simulations.

Improved accuracy in micro-macro solver coupling for reaction-diffusion systems.

Framework applicable where analytical micro-macro relations are unavailable.

Abstract

Many complex multiphysics systems in fluid dynamics involve using solvers with varied levels of approximations in different regions of the computational domain to resolve multiple spatiotemporal scales present in the flow. The accuracy of the solution is governed by how the information is exchanged between these solvers at the interface and several methods have been devised for such coupling problems. In this article, we construct a data-driven model by spatially coupling a microscale lattice Boltzmann method (LBM) solver and macroscale finite difference method (FDM) solver for reaction-diffusion systems. The coupling between the micro-macro solvers has one to many mapping at the interface leading to the interface closure problem, and we propose a statistical inference method based on neural networks to learn this closure relation. The performance of the proposed framework in a bifidelity setting partitioned between the FDM and LBM domain shows its promise for complex systems where analytical relations between micro-macro solvers are not available.