Forward sensitivity approach for estimating eddy viscosity closures in nonlinear model reduction

TL;DR

This paper introduces a variational forward sensitivity method to estimate eddy viscosity in nonlinear reduced order models, improving their accuracy using sparse observational data, with applications to turbulence and shock modeling.

Contribution

It presents a novel FSM-based variational approach for eddy viscosity estimation in reduced order models, enhancing data assimilation and model correction capabilities.

Findings

Successfully estimates eddy viscosity with sparse noisy data.

Improves reduced order model predictions for turbulence and shock scenarios.

Framework suitable for real-time digital twin applications.

Abstract

In this paper, we propose a variational approach to estimate eddy viscosity using forward sensitivity method (FSM) for closure modeling in nonlinear reduced order models. FSM is a data assimilation technique that blends model's predictions with noisy observations to correct initial state and/or model parameters. We apply this approach on a projection based reduced order model (ROM) of the one-dimensional viscous Burgers equation with a square wave defining a moving shock, and the two-dimensional vorticity transport equation formulating a decay of Kraichnan turbulence. We investigate the capability of the approach to approximate an optimal value for eddy viscosity with different measurement configurations. Specifically, we show that our approach can sufficiently assimilate information either through full field or sparse noisy measurements to estimate eddy viscosity closure to cure standard Galerkin reduced order model (GROM) predictions. Therefore, our approach provides a modular framework to correct forecasting error from a sparse observational network on a latent space. We highlight that the proposed GROM-FSM framework is promising for emerging digital twin applications, where real-time sensor measurements can be used to update and optimize surrogate model's parameters.