Memory embedded non-intrusive reduced order modeling of non-ergodic flows

TL;DR

This paper introduces a novel non-intrusive reduced order modeling approach combining POD, LSTM, and PID to accurately and efficiently model complex, non-ergodic convective flows, enabling near real-time predictions.

Contribution

It presents a new non-intrusive modeling framework integrating LSTM and PID with POD for improved accuracy in complex flow systems.

Findings

Outperforms traditional POD-Galerkin methods in accuracy.

Enables near real-time prediction of unsteady flows.

Effective for convection-dominated systems like Burgers, Navier-Stokes, and Boussinesq equations.

Abstract

Generating a digital twin of any complex system requires modeling and computational approaches that are efficient, accurate, and modular. Traditional reduced order modeling techniques are targeted at only the first two but the novel non-intrusive approach presented in this study is an attempt at taking all three into account effectively compared to their traditional counterparts. Based on dimensionality reduction using proper orthogonal decomposition (POD), we introduce a long short-term memory (LSTM) neural network architecture together with a principal interval decomposition (PID) framework as an enabler to account for localized modal deformation, which is a key element in accurate reduced order modeling of convective flows. Our applications for convection dominated systems governed by Burgers, Navier-Stokes, and Boussinesq equations demonstrate that the proposed approach yields significantly more accurate predictions than the POD-Galerkin method, and could be a key enabler towards near real-time predictions of unsteady flows.