Automated Dissipation Control for Turbulence Simulation with Shell Models

TL;DR

This paper explores using machine learning to model small-scale turbulence in fluid dynamics through a simplified shell model, aiming to reproduce statistical properties and address challenges in integrating ML with differential equations.

Contribution

It introduces a novel ML approach for turbulence modeling using the GOY shell model, focusing on reconstructing turbulence statistics rather than traditional supervised learning.

Findings

Encouraging results in reproducing turbulence scaling laws

Highlights potential pitfalls in combining ML with differential equations

Demonstrates feasibility of physics-constrained ML in turbulence simulation

Abstract

The application of machine learning (ML) techniques, especially neural networks, has seen tremendous success at processing images and language. This is because we often lack formal models to understand visual and audio input, so here neural networks can unfold their abilities as they can model solely from data. In the field of physics we typically have models that describe natural processes reasonably well on a formal level. Nonetheless, in recent years, ML has also proven useful in these realms, be it by speeding up numerical simulations or by improving accuracy. One important and so far unsolved problem in classical physics is understanding turbulent fluid motion. In this work we construct a strongly simplified representation of turbulence by using the Gledzer-Ohkitani-Yamada (GOY) shell model. With this system we intend to investigate the potential of ML-supported and physics-constrained small-scale turbulence modelling. Instead of standard supervised learning we propose an approach that aims to reconstruct statistical properties of turbulence such as the self-similar inertial-range scaling, where we could achieve encouraging experimental results. Furthermore we discuss pitfalls when combining machine learning with differential equations.