Accurate and Efficient Data‐Driven Partitioned Scheme for Coupled Heterogeneous Numerical Models

ABSTRACT

Heterogeneous numerical models (HNMs) combine conventional discretization modules such as finite elements with nonconventional data‐driven and reduced‐order modules. HNMs can improve computational efficiency and enable simulations of multi‐physics systems in which one or more constituent components lack first‐principles descriptions and must be solved by a data‐driven method. A natural choice for solving HNMs is partitioned solvers that are minimally intrusive and only require exchange of interface information between the modules. In this article, we formulate and demonstrate a partitioned solution of a coupled HNM for a model transmission problem in which each subdomain can be solved by equation‐free and/or equation‐based modules. Specifically we consider HNMs combining Dynamic Mode Decomposition (DMD) [1] modules with other DMD modules or conventional Finite Elements. The subdomains are decoupled by specifying the interface flux exchanged between them as a Neumann boundary condition for the modules. At each time step, this flux is estimated by a dynamic flux surrogate that is learned offline from a combination of flux and state training data. We test the partitioned HNM approach using single‐ and multi‐material configurations of the model problem. Numerical results show that the dynamic flux surrogate approach enables accurate, stable, and efficient solution of the coupled problem.