Leveraging reduced-order models for state estimation using deep learning

TL;DR

This paper introduces a neural network-based approach for state estimation in fluid flows that overcomes limitations of linear models by capturing nonlinear relationships, improving accuracy and flexibility.

Contribution

It presents a novel neural network framework for nonlinear state estimation that is compatible with various reduced-order models, enhancing estimation performance.

Findings

Outperforms linear estimation methods in a 2D separated flow model

Flexible framework applicable to different ROM types

Demonstrates improved accuracy over traditional linear approaches

Abstract

State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When desired, the full state can be recovered via the ROM). Current methods in this category nearly always use a linear model to relate the sensor data to the reduced state, which often leads to restrictions on sensor locations and has inherent limitations in representing the generally nonlinear relationship between the measurements and reduced state. We propose an alternative methodology where a neural network architecture is used to learn this nonlinear relationship. Neural network is a natural choice for this estimation problem, as a physical interpretation of the reduced state-sensor measurement relationship is rarely obvious. The proposed estimation framework is agnostic to the ROM employed, and can be incorporated into any choice of ROMs derived on a linear subspace (e.g., proper orthogonal decomposition) or a nonlinear manifold. The proposed approach is demonstrated on a two-dimensional model problem of separated flow around a flat plate, and is found to outperform common linear estimation alternatives.