Wavelet-Powered Neural Networks for Turbulence

Arvind T. Mohan, Daniel Livescu, Michael Chertkov

Keywords: Wavelets, Convolutional LSTM, turbulence

TL;DR: We propose an approach to learn high dimensional multiscale physics by using wavelet basis for dimensionality reduction, which is more interpretable and orders of magnitude cheaper than autoencoders.

Abstract: One of the fundamental driving phenomena for applications in engineering, earth sciences and climate is fluid turbulence. Modeling these flows and explaining its associated spatio-temporal phenomena are notoriously difficult tasks. Navier-Stokes (NS) equations describe all the details of the fluid motions, but require accounting for unfeasibly many degrees of freedom in the regime of developed turbulence. Model reduction and surrogate modeling of turbulence is a general methodology aiming to circumvent this curse of dimensionality. Originally driven by phenomenological considerations, multiple attempts to model-reduce NS equations got a new boost recently with Deep Learning (DL), trained on the ground truth data, e.g. extracted from high-fidelity Direct Numerical Simulations (DNS). However, early attempts of building NNs to model turbulence has also revealed its lack of interpretability as the most significant shortcoming. In this paper we address the key challenge of devising reduced but, at least partially, interpretable model. We take advantage of the balance between strong mathematical foundations and the physical interpretability of wavelet theory to build a spatio-temporally reduced dynamical map which fuses wavelet based spatial decomposition with spatio-temporal modeling based on Convolutional Long Short Term Memory (C-LSTM) architecture. It is shown that the wavelet-based NN makes progress in scaling to large flows, by reducing computational costs and GPU memory requirements.