Collaborative Research: CDS&E: Generalizable RANS Turbulence Models through Scientific Multi-Agent Reinforcement Learning

可靠的、可预测的湍流计算模拟对于从航空航天、汽车到发电等领域的关键技术的进步至关重要。然而，由于湍流模型的不可靠性，目前可用的模拟的效用受到限制，有时甚至严重限制。最常见的湍流计算旨在模拟平均或平均速度，并模拟湍流的影响，因为在许多应用中，这是主要感兴趣的量。然而，人们普遍认为，已部署的湍流模型对于技术感兴趣的复杂流动具有有限的可靠性。这一挑战的核心原因是缺乏普遍适用的结束条款。这个项目通过制定湍流模型来解决这个缺点，以解释湍流特征的更一般的描述。这将产生普遍适用的模型，包括复杂的湍流。它还将带来许多重要领域的技术进步，包括航空、推进、发电和风能，这些领域目前因缺乏可靠的复杂湍流模型而受到阻碍。通过开发可靠的、可预测的、广泛适用的湍流模型，该项目将对这些领域产生深远的影响，并有可能实现对我们国家和社会重要的技术的突破性改进。该项目的目标是发展可靠的雷诺平均纳维-斯托克斯模型，推广到复杂的湍流。该方法是基于这样一个假设，即当前的湍流模型没有保留足够丰富的湍流统计状态的表示。提出了一组表征湍流各向异性和非均匀性的结构张量，作为充分的统计湍流状态空间的候选。这些结构张量的演化方程必须包含标量不变量的未知标量函数。这些函数将使用科学的多智能体强化学习从湍流统计数据中学习。所需的数据将从直接的数值模拟和实验中获得。这个过程产生的模型将在各种复杂的湍流中进行测试。可靠的雷诺平均湍流模型的潜在影响很难夸大，因为它们将大大增加计算流体动力学作为科学和工程工具的价值。此外，在该项目下培训的两名研究生将开发复杂系统的数学和数据信息模型，这将有助于培养解决我国和世界面临的各种复杂问题所需的高技能劳动力。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Reliable, predictive computational simulations of turbulent flows are essential for the advancement of key technologies in sectors ranging from aerospace and automotive to power generation. However, the utility of currently available simulations is limited, sometimes severely, by the unreliability of turbulence models. The most common computations of turbulence are intended to simulate only the mean or average velocity, with the effects of turbulence modeled, because in many applications this is the primary quantity of interest. However, the deployed models of turbulence are widely recognized as having limited reliability for complex flows of technological interest. The core reason for this challenge is the lack of universally applicable closure terms. This project addresses this shortcoming by formulating turbulence models to account for a more general description of the characteristics of the turbulence. This will yield models that are generally applicable, including complex turbulent flows. It will also yield technological advances in many important domains, including aeronautics, propulsion, power generation and wind energy that are presently hindered by the lack of reliable models of complex, turbulent flows. By developing reliable, predictive, and broadly applicable turbulence models, this project will have profound impacts on these fields, with the potential of enabling ground-breaking improvements in technologies important to our country and society.The objective of the project is to develop reliable Reynolds averaged Navier-Stokes models that generalize to complex turbulent flows. The approach is based on the hypothesis that current turbulence models do not retain a sufficiently rich representation of the statistical state of turbulence. A set of structure tensors that characterize the anisotropy and inhomogeneity of turbulence are proposed as a candidate for a sufficient statistical turbulence state space. Evolution equations for these structure tensors will be developed which will necessarily include unknown scalar functions of scalar invariants. These functions will be learned from turbulence statistical data using scientific multi-agent reinforcement learning. The required data will be obtained from direct numerical simulations and experiments. Models resulting from this process will be tested on a variety of complex turbulent flows. The potential impact of reliable Reynolds averaged turbulence models is hard to over-state, as they would greatly increase the value of computational fluid dynamics as a tool of science and engineering. In addition, the training of two graduate students under this project in the development of mathematical and data-informed models for complex systems will contribute to the highly skilled workforce required to address a broad class of complex problems facing our country and the world.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.