# Nonlinear mode decomposition with convolutional neural networks for fluid dynamics

## TL;DR

This paper introduces a nonlinear mode decomposition method using convolutional neural network autoencoders to visualize and analyze fluid flow fields more effectively than traditional linear methods like POD.

## Contribution

The paper proposes the MD-CNN-AE, a novel nonlinear mode decomposition approach that improves flow field visualization and captures complex flow features with lower reconstruction errors.

## Key findings

- MD-CNN-AE with nonlinear activation outperforms POD in reconstruction accuracy.
- Nonlinear MD-CNN-AE modes contain multiple orthogonal bases, unlike linear methods.
- Potential for reduced-dimensional feature extraction while maintaining interpretability.

## Abstract

We present a new nonlinear mode decomposition method to visualize the decomposed flow fields, named the mode decomposing convolutional neural network autoencoder (MD-CNN-AE). The proposed method is applied to a flow around a circular cylinder at $Re_D=100$ as a test case. The flow attributes are mapped into two modes in the latent space and then these two modes are visualized in the physical space. Because the MD-CNN-AEs with nonlinear activation functions show lower reconstruction errors than the proper orthogonal decomposition (POD), the nonlinearity contained in the activation function is considered the key to improve the capability of the model. It is found by applying POD to each field decomposed using the MD-CNN-AE with hyperbolic tangent activation that a single nonlinear MD-CNN-AE mode contains multiple orthogonal bases, in contrast to the linear methods, i.e., POD and the MD-CNN-AE with linear activation. We further assess the proposed MD-CNN-AE by applying it to a transient process of a circular cylinder wake in order to examine its capability for flows containing high-order spatial modes. The present results suggest a great potential for the nonlinear MD-CNN-AE to be used for feature extraction of flow fields in lower dimension than POD, while retaining interpretable relationships with the conventional POD modes.