An evolve-then-correct reduced order model for hidden fluid dynamics

TL;DR

This paper introduces an evolve-then-correct reduced order modeling approach that combines intrusive Galerkin methods with neural network emulators to accurately predict hidden fluid dynamics in real-time, even under uncertainty.

Contribution

It presents a novel hybrid modeling framework that integrates intrusive and nonintrusive techniques, including basis interpolation on a Grassmannian manifold, for improved reduced order modeling of complex fluid systems.

Findings

Achieves highly accurate predictions of vortex dynamics.

Demonstrates effectiveness under modeling uncertainty.

Enables real-time simulations without full process models.

Abstract

In this paper, we put forth an evolve-then-correct reduced order modeling approach that combines intrusive and nonintrusive models to take hidden physical processes into account. Specifically, we split the underlying dynamics into known and unknown components. In the known part, we first utilize an intrusive Galerkin method projected on a set of basis functions obtained by proper orthogonal decomposition. We then formulate a recurrent neural network emulator based on the assumption that observed data is a manifestation of all relevant processes. We further enhance our approach by using an orthonormality conforming basis interpolation approach on a Grassmannian manifold to address off-design conditions. The proposed framework is illustrated here with the application of two-dimensional co-rotating vortex simulations under modeling uncertainty. The results demonstrate highly accurate predictions underlining the effectiveness of the evolve-then-correct approach toward realtime simulations, where the full process model is not known a priori.