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

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.

11 pages, 9 figures

References in corpus (3)

• Evolutional Deep Neural Network
• Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regression
• Robust training approach of neural networks for fluid flow state estimations

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• Multi-fidelity prediction of fluid flow and temperature field based on transfer learning using Fourier Neural Operator
• Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regression
• Three-dimensional generative adversarial networks for turbulent flow estimation from wall measurements
• Robust training approach of neural networks for fluid flow state estimations
• Reconstructing three-dimensional bluff body wake from sectional flow fields with convolutional neural networks
• Projection-based multifidelity linear regression for data-scarce applications