# Automated Dissipation Control for Turbulence Simulation with Shell Models

arXiv: https://arxiv.org/abs/2201.02485 · HTML: https://mlsanity.com/paper/2201.02485/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 49 references that are in the map.
- First posted on arXiv 7 Jan 2022.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [From Deep to Physics-Informed Learning of Turbulence: Diagnostics](https://mlsanity.com/paper/1810.07785/) (2018)
- [Deep learning at scale for subgrid modeling in turbulent flows](https://mlsanity.com/paper/1910.00928/) (2019)

## Abstract (arXiv)

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.