Identifying key differences between linear stochastic estimation and neural networks for fluid flow regressions

TL;DR

This paper compares linear stochastic estimation and neural networks in fluid flow regression tasks, showing neural networks generally outperform linear methods due to their nonlinear capabilities and analyzing their robustness and internal responses.

Contribution

It provides a fundamental comparison between LSE and various neural networks in fluid flow regression, highlighting the advantages of nonlinear models and analyzing their robustness.

Findings

Neural networks outperform linear methods in fluid flow regressions.

Nonlinear activation functions improve estimation accuracy.

Neural networks show greater robustness to noisy perturbations.

Abstract

Neural networks (NNs) and linear stochastic estimation (LSE) have widely been utilized as powerful tools for fluid-flow regressions. We investigate fundamental differences between them considering two canonical fluid-flow problems: 1. the estimation of high-order proper orthogonal decomposition coefficients from low-order their counterparts for a flow around a two-dimensional cylinder, and 2. the state estimation from wall characteristics in a turbulent channel flow. In the first problem, we compare the performance of LSE to that of a multi-layer perceptron (MLP). With the channel flow example, we capitalize on a convolutional neural network (CNN) as a nonlinear model which can handle high-dimensional fluid flows. For both cases, the nonlinear NNs outperform the linear methods thanks to nonlinear activation functions. We also perform error-curve analyses regarding the estimation error and the response of weights inside models. Our analysis visualizes the robustness against noisy perturbation on the error-curve domain while revealing the fundamental difference of the covered tools for fluid-flow regressions.