Train small, model big: Scalable physics simulators via reduced order modeling and domain decomposition.

Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and time-consuming. An alternative, the pilot-scale model, relies on high-fidelity numerical simulations, but even these simulations can be computationally prohibitive at larger scales. To overcome these limitations, we propose a scalable, physics-constrained reduced order model (ROM) method. The ROM identifies critical physics modes from small-scale unit components, projecting governing equations onto these modes to create a reduced model that retains essential physics details. We also employ Discontinuous Galerkin Domain Decomposition (DG-DD) to apply ROM to unit components and interfaces, enabling the construction of large-scale global systems without data at such large scales. This method is demonstrated on the Poisson and Stokes flow equations, showing that it can solve equations about 15–40 times faster with only ∼ 1% relative error. Furthermore, ROM takes one order of magnitude less memory than the full order model, enabling larger scale predictions at a given memory limitation. • Developed a novel component reduced order model. • Identifies important physics modes from small-scale sample data. • Constructs the large-scale reduced order model only with small-scale data. • Provides efficient and robust predictions at large scales. • Demonstrated on Poisson, Stokes and advection-diffusion equation. [ABSTRACT FROM AUTHOR]