流体动力学中的机器学习解释：壁面剪切流中的再层化事件的解释
Interpreted machine learning in fluid dynamics: Explaining relaminarisation events in wall-bounded shear flows
摘要：
机器学习（ML）在流体动力学中变得越来越流行。强大的机器学习算法，如神经网络或集成方法，是出了名的难以解释。在这里，我们介绍了新颖的Shapley加法运算（SHAP）算法（Lundberg & Lee，2017），这是一种博弈论方法，可以在流体动力学的背景下解释给定ML模型的输出。我们给出了关于SHAP作为一种可解释的AI方法的概念证明，该方法为流体动力学提供了有用的和人类可解释的见解。为了表明SHAP提供的特征重要性排名可以物理解释，我们首先考虑从一个已建立的低维模型的基础上的自持过程（SSP）在壁有界剪切流的数据，其中每个数据功能有一个明确的物理和动力学解释的近壁动态，即流向涡，条纹和线性条纹不稳定性的已知代表性特征。SHAP始终确定只有层流剖面、流向涡和特定条纹不稳定性在预测中起主要作用。我们表明，该方法可以应用于更大的流体动力学数据集的SHAP评价平面Couette流在一个最小的流动单元专注于相关的条纹和它们的不稳定性的预测再分层事件。在这里，我们发现，预测是基于代理条纹调制对应的线性条纹不稳定性内的SSP。也就是说，SHAP分析表明，自我维持循环的破裂与条纹不稳定性的抑制有关。
英文摘要：
Machine Learning (ML) is becoming increasingly popular in fluid dynamics. Powerful ML algorithms such as neural networks or ensemble methods are notoriously difficult to interpret. Here, we introduce the novel Shapley Additive Explanations (SHAP) algorithm (Lundberg & Lee, 2017), a game-theoretic approach that explains the output of a given ML model, in the fluid dynamics context. We give a proof of concept concerning SHAP as an explainable AI method providing useful and human-interpretable insight for fluid dynamics. To show that the feature importance ranking provided by SHAP can be interpreted physically, we first consider data from an established low-dimensional model based on the self-sustaining process (SSP) in wall-bounded shear flows, where each data feature has a clear physical and dynamical interpretation in terms of known representative features of the near-wall dynamics, i.e. streamwise vortices, streaks and linear streak instabilities. SHAP determines consistently that only the laminar profile, the streamwise vortex, and a specific streak instability play a major role in the prediction. We demonstrate that the method can be applied to larger fluid dynamics datasets by a SHAP evaluation on plane Couette flow in a minimal flow unit focussing on the relevance of streaks and their instabilities for the prediction of relaminarisation events. Here, we find that the prediction is based on proxies for streak modulations corresponding to linear streak instabilities within the SSP. That is, the SHAP analysis suggests that the break-up of the self-sustaining cycle is connected with a suppression of streak instabilities.
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