Generalization techniques of neural networks for fluid flow estimation

TL;DR

This paper explores methods to improve the interpretability, data augmentation, and generalization of neural networks applied to fluid flow estimation, demonstrating their effectiveness on various fluid dynamics problems.

Contribution

It introduces visualization and interpretability techniques, data augmentation strategies, and assesses generalizability, advancing neural network applications in fluid flow estimation.

Findings

Visualization methods reveal neural network decision processes.

Limited training data can be sufficient with proper augmentation.

Flow patterns are well reconstructed across different configurations.

Abstract

We demonstrate several techniques to encourage practical uses of neural networks for fluid flow estimation. In the present paper, three perspectives which are remaining challenges for applications of machine learning to fluid dynamics are considered: 1. interpretability of machine-learned results, 2. bulking out of training data, and 3. generalizability of neural networks. For the interpretability, we first demonstrate two methods to observe the internal procedure of neural networks, i.e., visualization of hidden layers and application of gradient-weighted class activation mapping (Grad-CAM), applied to canonical fluid flow estimation problems -- $(1)$ drag coefficient estimation of a cylinder wake and $(2)$ velocity estimation from particle images. It is exemplified that both approaches can successfully tell us evidences of the great capability of machine learning-based estimations. We then utilize some techniques to bulk out training data for super-resolution analysis and temporal prediction for cylinder wake and NOAA sea surface temperature data to demonstrate that sufficient training of neural networks with limited amount of training data can be achieved for fluid flow problems. The generalizability of machine learning model is also discussed by accounting for the perspectives of inter/extrapolation of training data, considering super-resolution of wakes behind two parallel cylinders. We find that various flow patterns generated by complex interaction between two cylinders can be reconstructed well, even for the test configurations regarding the distance factor. The present paper can be a significant step toward practical uses of neural networks for both laminar and turbulent flow problems.