解释剩余标量通量的神经网络模型
Interpreting neural network models of residual scalar flux
摘要：
我们表明，除了提供有效的和有竞争力的闭包，当在动力学和物理相关的诊断方面进行分析时，人工神经网络（ANN）既可以解释，又可以在开发和改进湍流闭包的持续任务中提供有用的见解。在大涡模拟（LES）的背景下，在均匀各向同性湍流的被动标量，通过过滤直接数值模拟（DNS）获得的精确子过滤器通量都用于训练深层ANN模型作为过滤变量的函数，并优化系数的湍流普朗特数LES封闭。子滤波器标量方差传递率的\textit{A-priori}分析表明，学习的ANN模型优于优化的湍流普朗特数闭包和克拉克型梯度模型。接下来，\textit{a-posteriori}的解决方案，获得每个模型在几个整数的时间尺度。这些实验表明，与单点和多点诊断，人工神经网络模型在时间上跟踪精确解决标量方差具有更高的精度相比，其他子过滤器通量模型为一个给定的过滤器长度尺度。最后，我们解释人工神经网络统计与差分灵敏度分析表明，人工神经网络模型的功能动态让人想起所谓的“混合模型”，其中混合模型被理解为包括结构和功能组件。除了能够提高被动标量的LES精度之外，我们预计这项工作将有助于利用神经网络模型作为可解释性，鲁棒性和模型发现的工具。
英文摘要：
We show that in addition to providing effective and competitive closures, when analysed in terms of dynamics and physically-relevant diagnostics, artificial neural networks (ANNs) can be both interpretable and provide useful insights in the on-going task of developing and improving turbulence closures. In the context of large-eddy simulations (LES) of a passive scalar in homogeneous isotropic turbulence, exact subfilter fluxes obtained by filtering direct numerical simulations (DNS) are used both to train deep ANN models as a function of filtered variables, and to optimise the coefficients of a turbulent Prandtl number LES closure. \textit{A-priori} analysis of the subfilter scalar variance transfer rate demonstrates that learnt ANN models out-perform optimised turbulent Prandtl number closures and Clark-type gradient models. Next, \textit{a-posteriori} solutions are obtained with each model over several integral timescales. These experiments reveal, with single- and multi-point diagnostics, that ANN models temporally track exact resolved scalar variance with greater accuracy compared to other subfilter flux models for a given filter length scale. Finally, we interpret the artificial neural networks statistically with differential sensitivity analysis to show that the ANN models feature dynamics reminiscent of so-called "mixed models", where mixed models are understood as comprising both a structural and functional component. Besides enabling enhanced-accuracy LES of passive scalars henceforth, we anticipate this work to contribute to utilising neural network models as a tool in interpretability, robustness and model discovery.
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