# Toward Discretization-Consistent Closure Schemes for Large Eddy Simulation Using Reinforcement Learning

arXiv: https://arxiv.org/abs/2309.06260 · HTML: https://mlsanity.com/paper/2309.06260/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 83 references that are in the map.
- First posted on arXiv 12 Sep 2023.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Transfer Learning in Deep Reinforcement Learning: A Survey](https://mlsanity.com/paper/2009.07888/) (2020)
- [Meta-Reinforcement Learning of Structured Exploration Strategies](https://mlsanity.com/paper/1802.07245/) (2018)
- [Scientific multi-agent reinforcement learning for wall-models of turbulent flows](https://mlsanity.com/paper/2106.11144/) (2021)
- [Deep Neural Networks for Data-Driven Turbulence Models](https://mlsanity.com/paper/1806.04482/) (2018)
- [Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulations](https://mlsanity.com/paper/2206.11038/) (2022)
- [A Neural Network based Shock Detection and Localization Approach for Discontinuous Galerkin Methods](https://mlsanity.com/paper/2001.08201/) (2020)
- [FLEXI: A high order discontinuous Galerkin framework for hyperbolic-parabolic conservation laws](https://mlsanity.com/paper/1910.02858/) (2019)
- [Deep Reinforcement Learning for Computational Fluid Dynamics on HPC Systems](https://mlsanity.com/paper/2205.06502/) (2022)
- [A large eddy simulation method for DGSEM using non-linearly optimized relaxation filters](https://mlsanity.com/paper/1905.13450/) (2019)

## Built on by (most cited first, 5 of 5)

- [PICT -- A Differentiable, GPU-Accelerated Multi-Block PISO Solver for Simulation-Coupled Learning Tasks in Fluid Dynamics](https://mlsanity.com/paper/2505.16992/) (2025)
- [A Status Quo Investigation of Large Language Models towards Cost-Effective CFD Automation with OpenFOAMGPT: ChatGPT vs. Qwen vs. Deepseek](https://mlsanity.com/paper/2504.02888/) (2025)
- [A reinforcement learning strategy to automate and accelerate h/p-multigrid solvers](https://mlsanity.com/paper/2407.15872/) (2024)
- [Reinforcement learning for anisotropic p-adaptation and error estimation in high-order solvers](https://mlsanity.com/paper/2407.19000/) (2024)
- [Invariant Control Strategies for Active Flow Control using Graph Neural Networks](https://mlsanity.com/paper/2503.22775/) (2025)

## Abstract (arXiv)

This study proposes a novel method for developing discretization-consistent closure schemes for implicitly filtered Large Eddy Simulation (LES). Here, the induced filter kernel, and thus the closure terms, are determined by the properties of the grid and the discretization operator, leading to additional computational subgrid terms that are generally unknown in a priori analysis. In this work, the task of adapting the coefficients of LES closure models is thus framed as a Markov decision process and solved in an a posteriori manner with Reinforcement Learning (RL). This optimization framework is applied to both explicit and implicit closure models. The explicit model is based on an element-local eddy viscosity model. The optimized model is found to adapt its induced viscosity within discontinuous Galerkin (DG) methods to homogenize the dissipation within an element by adding more viscosity near its center. For the implicit modeling, RL is applied to identify an optimal blending strategy for a hybrid DG and Finite Volume (FV) scheme. The resulting optimized discretization yields more accurate results in LES than either the pure DG or FV method and renders itself as a viable modeling ansatz that could initiate a novel class of high-order schemes for compressible turbulence by combining turbulence modeling with shock capturing in a single framework. All newly derived models achieve accurate results that either match or outperform traditional models for different discretizations and resolutions. Overall, the results demonstrate that the proposed RL optimization can provide discretization-consistent closures that could reduce the uncertainty in implicitly filtered LES.