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Many complex multiphysics systems in fluid dynamics involve using solverswith varied levels of approximations in different regions of the computationaldomain to resolve multiple spatiotemporal scales present in the flow. Theaccuracy of the solution is governed by how the information is exchangedbetween these solvers at the interface and several methods have been devisedfor such coupling problems. In this article, we construct a data-driven modelby spatially coupling a microscale lattice Boltzmann method (LBM) solver andmacroscale finite difference method (FDM) solver for reaction-diffusionsystems. The coupling between the micro-macro solvers has one to many mappingat the interface leading to the interface closure problem, and we propose astatistical inference method based on neural networks to learn this closurerelation. The performance of the proposed framework in a bifidelity settingpartitioned between the FDM and LBM domain shows its promise for complexsystems where analytical relations between micro-macro solvers are notavailable.

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