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.
翻译:过去几年来, 监督学习( SL) 已经确立自己为数据驱动的动荡模型的离析状态。 在 SL 模式中, 模型的培训以数据集为基础, 通常通过应用相应的过滤功能, 将溶解的和未解决的流缩尺度区分开来, 通常通过应用相应的过滤功能, 以先验的方式从高纤维解决方案中先验地计算出。 对于隐含过滤的大型 Eddy 模拟( LES) 来说, 这种方法是行不通的, 因为在此过程中, 使用的离散本身是一个隐含过滤功能。 因此, 精确的过滤形式通常不为人所知, 因此, 即使有了完整的解决方案, 也无法计算相应的关闭条件。 强化学习( RL) 模式通常会被用来避免这种不一致, 而不是在先前获得的培训数据集中先验, 而是通过直接与动态的 LES 环境本身进行互动。 这可以将潜在复杂的隐含的 LES 过滤器纳入设计过程。 在这项工作中, 我们应用一个强化学习框架来找到一个最佳的, 用于隐含的 adddricent- admical adal admodal adal adal adal adal adliver modeal deal model model model model model model model lade ex laves lax lavestal 。 因此, lax lax lax lax lax 。