MLTURB: A new understanding of turbulence via a machine-learnt dynamical systems theory

大尺度湍流是一个复杂的非线性问题，具有重要的科学和社会意义。湍流计算通常依赖于“亚网格”模型，用于较小的耗散运动尺度。然而，精确的模拟和预测的大规模flowsof最重要的工业和地球物理学的重要性，需要一个子网格，其中涵盖了更大范围的规模-因此，必须编码更多的湍流动力学。因此，有迫切需要的答案，长期存在的问题，在强湍流流体中的能量传递机制的动力学。这项建议的重点是建立这种新的理解，重点是在发挥作用的湍流能量级联和罕见的，小规模的间歇性突发事件，这是与极端的本地值的阻力或热传递的动力学过程。新的方法是植根于动力系统理论建立around精确的，不稳定的解决方案的控制方程。这种方法在过渡/弱湍流流动中具有变革性，但到目前为止，由于与识别和收敛不稳定解相关的困难，因此在工业相关的参数范围内应用具有挑战性。这些局限性通过一种新的方法来克服，该方法使用新颖的机器学习算法和可微分编程-通过与Google的加速科学团队合作提供必要的计算能力和专业知识。这些工具由基于Koopman算子的鲁棒低阶建模框架补充，它将被用作理解不稳定解中所包含的动力学的工具，（以及它们周围的相空间），并探测更强烈的湍流，以建立主导机制，并准确评估未来亚网格尺度模型中需要哪些动态过程。

Turbulence at very large scales is a complex, nonlinear problem of fundamental scientific andsocietal importance. Turbulent computations often rely on a "subgrid" model for the smaller,dissipative scales of motion. However, accurate simulation and prediction in the large-scale flowsof paramount industrial and geophysical importance requires a subgrid which covers a greaterrange of scales - and hence must encode more of the turbulent dynamics. There is, therefore, apressing need for answers to long-standing questions on the dynamics of energy transfermechanisms in strongly turbulent fluids. This proposal is focused on establishing this newunderstanding, focusing on both the dynamical processes at play in the turbulent energy cascadeand the rare, small-scale intermittent bursting events which are associated with extreme localvalues of drag or heat transfer. The new methodology is rooted in dynamical systems theory builtaround exact, unstable solutions of the governing equations. This approach has beentransformative in transitional/weakly turbulent flows, but has so far proved challenging to apply inparameter regimes of industrial relevance, due to the difficulties associated with identifying andconverging the unstable solutions. These limitations are overcome here via a new approach usingnovel machine learning algorithms and differentiable programming - with the necessary computepower and expertise provided through a collaboration with Google's Accelerated Sciences team.These tools are complemented by a robust low-order modelling framework based on the Koopmanoperator, which will be used both as both a tool to understand the dynamics encapsulated in theunstable solutions (and around them in phase space) and also to probe even more stronglyturbulent flows to establish the dominant mechanisms and assess exactly which dynamicalprocesses are required in the subgrid scale models of the future.