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

Area of Science:

• Fluid dynamics
• Machine learning
• Scientific computing

Background:

• Neural networks (NNs) and linear stochastic estimation (LSE) are established methods for fluid-flow regression tasks.
• Understanding their fundamental differences is crucial for selecting appropriate models in fluid dynamics.

Purpose of the Study:

• To investigate and compare the performance of NNs and LSE in canonical fluid-flow regression problems.
• To highlight the advantages of nonlinear NNs over linear methods in complex flow scenarios.

Main Methods:

• Comparison of a multi-layer perceptron (MLP) against LSE for estimating proper orthogonal decomposition coefficients in a 2D cylinder flow.
• Application of a convolutional neural network (CNN) for state estimation in a turbulent channel flow, handling high-dimensional data.

Main Results:

• Nonlinear NNs consistently outperformed linear LSE methods across both fluid-flow problems.
• Error-curve analyses demonstrated the robustness of NNs against noisy perturbations.
• Fundamental differences in model behavior and predictive capabilities were identified.

Conclusions:

• Nonlinear neural networks offer superior performance for fluid-flow regressions compared to linear stochastic estimation.
• The nonlinear activation functions in NNs are key to their enhanced accuracy and robustness in complex fluid dynamics applications.