Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulations

Over the last years, supervised learning (SL) has established itself as the state-of-the-art for data-driven turbulence modeling. In the SL paradigm, models are trained based on a dataset, which is typically computed a priori from a high-fidelity solution by applying the respective filter function, which separates the resolved and the unresolved flow scales. For implicitly filtered large eddy simulation (LES), this approach is infeasible, since here, the employed discretization itself acts as an implicit filter function. As a consequence, the exact filter form is generally not known and thus, the corresponding closure terms cannot be computed even if the full solution is available. The reinforcement learning (RL) paradigm can be used to avoid this inconsistency by training not on a previously obtained training dataset, but instead by interacting directly with the dynamical LES environment itself. This allows to incorporate the potentially complex implicit LES filter into the training process by design. In this work, we apply a reinforcement learning framework to find an optimal eddy-viscosity for implicitly filtered large eddy simulations of forced homogeneous isotropic turbulence. For this, we formulate the task of turbulence modeling as an RL task with a policy network based on convolutional neural networks that adapts the eddy-viscosity in LES dynamically in space and time based on the local flow state only. We demonstrate that the trained models can provide long-term stable simulations and that they outperform established analytical models in terms of accuracy. In addition, the models generalize well to other resolutions and discretizations. We thus demonstrate that RL can provide a framework for consistent, accurate and stable turbulence modeling especially for implicitly filtered LES.

Deep Reinforcement Learning for Computational Fluid Dynamics on HPC Systems

Reinforcement learning (RL) is highly suitable for devising control strategies in the context of dynamical systems. A prominent instance of such a dynamical system is the system of equations governing fluid dynamics. Recent research results indicate that RL-augmented computational fluid dynamics (CFD) solvers can exceed the current state of the art, for example in the field of turbulence modeling. However, while in supervised learning, the training data can be generated a priori in an offline manner, RL requires constant run-time interaction and data exchange with the CFD solver during training. In order to leverage the potential of RL-enhanced CFD, the interaction between the CFD solver and the RL algorithm thus have to be implemented efficiently on high-performance computing (HPC) hardware. To this end, we present Relexi as a scalable RL framework that bridges the gap between machine learning workflows and modern CFD solvers on HPC systems providing both components with its specialized hardware. Relexi is built with modularity in mind and allows easy integration of various HPC solvers by means of the in-memory data transfer provided by the SmartSim library. Here, we demonstrate that the Relexi framework can scale up to hundreds of parallel environment on thousands of cores. This allows to leverage modern HPC resources to either enable larger problems or faster turnaround times. Finally, we demonstrate the potential of an RL-augmented CFD solver by finding a control strategy for optimal eddy viscosity selection in large eddy simulations.