Data-driven Closure Strategies for Parametrized Reduced Order Models via Deep Operator Networks

TL;DR

This paper introduces a data-driven closure strategy for parametric reduced order models using deep operator networks, significantly enhancing accuracy in complex fluid flow simulations.

Contribution

It extends existing closure models to a parametric setting with deep operator networks, improving ROM accuracy across diverse flow scenarios.

Findings

Enhanced pressure and velocity accuracy in test cases

Deep operator networks effectively model closure terms

Significant improvement over standard POD-Galerkin methods

Abstract

In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in standard reduced-order approaches are not taken into account. In particular, in this work we focus on a Proper Orthogonal Decomposition (POD)-based formulation and our goal is to build a closure or correction model, aimed to re-introduce the contribution of the discarded modes. The approach has been investigated in previous works, and the goal of this manuscript is to extend the model to a parametric setting making use of machine learning procedures, and, in particular, of deep operator networks. More in detail, we model the closure terms through a deep operator network taking as input the reduced variables and the parameters of the problem. We tested the methods on three test cases with different behaviors: the periodic turbulent flow past a circular cylinder, the unsteady turbulent flow in a channel-driven cavity, and the geometrically-parametrized backstep flow. The performance of the machine learning-enhanced ROM is deeply studied in different modal regimes, and considerably improved the pressure and velocity accuracy with respect to the standard POD-Galerkin approach.