From Deep to Physics-Informed Learning of Turbulence: Diagnostics

TL;DR

This paper evaluates deep learning neural networks trained on turbulence simulations, highlighting their strengths in capturing turbulence features and identifying limitations, while proposing methods to improve their accuracy in reproducing turbulence geometry.

Contribution

It demonstrates the effectiveness of dynamic neural network schemes over static ones in modeling turbulence and suggests pathways for enhancing turbulence geometry reproduction.

Findings

Static DL fails to reproduce small-scale intermittency.

Dynamic NN schemes improve turbulence geometry accuracy.

Neural networks show promise in accelerating turbulence simulations.

Abstract

We describe tests validating progress made toward acceleration and automation of hydrodynamic codes in the regime of developed turbulence by three Deep Learning (DL) Neural Network (NN) schemes trained on Direct Numerical Simulations of turbulence. Even the bare DL solutions, which do not take into account any physics of turbulence explicitly, are impressively good overall when it comes to qualitative description of important features of turbulence. However, the early tests have also uncovered some caveats of the DL approaches. We observe that the static DL scheme, implementing Convolutional GAN and trained on spatial snapshots of turbulence, fails to reproduce intermittency of turbulent fluctuations at small scales and details of the turbulence geometry at large scales. We show that the dynamic NN schemes, namely LAT-NET and Compressed Convolutional LSTM, trained on a temporal sequence of turbulence snapshots are capable to correct for the caveats of the static NN. We suggest a path forward towards improving reproducibility of the large-scale geometry of turbulence with NN.