# Accurate deep learning sub-grid scale models for large eddy simulations

arXiv: https://arxiv.org/abs/2307.10060 · HTML: https://mlsanity.com/paper/2307.10060/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 66 references that are in the map.
- First posted on arXiv 19 Jul 2023.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizons](https://mlsanity.com/paper/2202.06988/) (2022)
- [Continual Object Detection: A review of definitions, strategies, and challenges](https://mlsanity.com/paper/2205.15445/) (2022)
- [A fast accurate fine-grain object detection model based on YOLOv4 deep neural network](https://mlsanity.com/paper/2111.00298/) (2021)
- [A Novel Semi-supervised Meta Learning Method for Subject-transfer Brain-computer Interface](https://mlsanity.com/paper/2209.03785/) (2022)

## Built on by (most cited first, 1 of 1)

- [Online Calibration of Deep Learning Sub-Models for Hybrid Numerical Modeling Systems](https://mlsanity.com/paper/2311.10665/) (2023)

## Abstract (arXiv)

We present two families of sub-grid scale (SGS) turbulence models developed for large-eddy simulation (LES) purposes. Their development required the formulation of physics-informed robust and efficient Deep Learning (DL) algorithms which, unlike state-of-the-art analytical modeling techniques can produce high-order complex non-linear relations between inputs and outputs. Explicit filtering of data from direct simulations of the canonical channel flow at two friction Reynolds numbers Reτ≈ 395 and 590 provided accurate data for training and testing. The two sets of models use different network architectures. One of the architectures uses tensor basis neural networks (TBNN) and embeds the simplified analytical model form of the general effective-viscosity hypothesis, thus incorporating the Galilean, rotational and reflectional invariances. The other architecture is that of a relatively simple network, that is able to incorporate the Galilean invariance only. However, this simpler architecture has better feature extraction capacity owing to its ability to establish relations between and extract information from cross-components of the integrity basis tensors and the SGS stresses. Both sets of models are used to predict the SGS stresses for feature datasets generated with different filter widths, and at different Reynolds numbers. It is shown that due to the simpler model's better feature learning capabilities, it outperforms the invariance embedded model in statistical performance metrics. In a priori tests, both sets of models provide similar levels of dissipation and backscatter. Based on the test results, both sets of models should be usable in a posteriori actual LESs.