A multifidelity deep operator network approach to closure for multiscale systems

Projection-based reduced order models (PROMs) have shown promise in representing the behavior of multiscale systems using a small set generalized (or latent) variables. Despite their success, PROMs can be susceptible to inaccuracies, even instabilities, due improper accounting interaction between resolved and unresolved scales system (known as closure problem). In current work, we interpret multifidelity problem use deep operator network (DeepONet) framework address it. addition, enhance stability accuracy multifidelity-based closure, employ recently developed “in-the-loop” training approach from literature on coupling physics machine learning models. The resulting is tested shock advection for one-dimensional viscous Burgers equation vortex merging two-dimensional Navier–Stokes equations. numerical experiments show significant improvement predictive ability closure-corrected PROM over un-corrected one both interpolative extrapolative regimes.