Nonlinear mode decomposition with convolutional neural networks for fluid dynamics

Abstract

We present a new nonlinear mode decomposition method to visualize the decomposed flow fields, named the mode decomposing convolutional neural network (MD-CNN). 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. Since the MD-CNNs 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 with hyperbolic tangent activation that a single nonlinear MD-CNN mode contains multiple orthogonal bases, in contrast to the linear methods, i.e., POD and MD-CNN with linear activation. The present results suggest a great potential for the nonlinear MD-CNN to be used for feature extraction of flow fields in lower dimension than POD, while retaining interpretable relationships with the conventional POD modes.

Image-based flow decomposition using empirical wavelet transform

“…The POD modes are arranged according to their energy, which is a meaningful indication of importance. However, highly nonlinear or travelling wave problems may require a large number of POD modes to cover the majority of the energy (Murata, Fukami & Fukagata 2020). On the other hand, a single correct way to rank DMD modes is absent, though the growth rate and amplitude provide means of measurement.…”

Neural Networks-Based Aerodynamic Data Modeling: A Comprehensive Review

“…In the work of Wang et al [133] and Omata et al [134], a deep convolutional autoencoder was used for dimensionality reduction in unsteady flow fields. Murata et al [135] proposed the mode decomposing convolutional neural network autoencoder (MD-CNN-AE) to visualize the decomposed flow fields. The results suggest a great potential for the nonlinear MD-CNN-AE to be used for feature extraction of flow fields in lower dimension.…”

The Structure of Urban Flows

“…For instance, recent work by Amor et al [140] has revealed the potential of using dynamic mode decomposition (DMD) to understand the complex physics of the wake in a wall-mounted square cylinder. Other approaches based on convolutional networks and autoencoders [141][142][143], combined with an adequate modelling of the temporal dynamics [144,145], may pave the way to more reliable flow predictions in urban environments.…”