用于合成湍流和流动重构的湍流通道流相空间中的机器学习概率分布
A machine-learned probability distribution in the phase space of turbulent channel flow for synthetic turbulence and flow reconstruction
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中文总结 AI 辅助
研究湍流通道流相空间中机器学习概率分布能否近似物理不变分布，通过训练基于流的生成模型并评估相关属性，经与直接数值模拟比较及应用验证，该分布能很好近似湍流动力系统自然分布，可用于合成湍流和流动重构。
中文摘要 AI 辅助
尽管湍流流相空间中概率分布的完整表征仍难以捉摸，但准确采样此分布对合成湍流生成和湍流流动重构至关重要。受这些应用的推动，研究了机器学习分布在多大程度上可以近似于雷诺数为180时湍流通道流的物理不变分布。评估了近似的三个重要属性：物理系综统计、一致条件采样和动力学不变性。为此，在最小条件流单元上训练基于流的生成模型，还引入了从条件学习分布中采样的一致程序。与直接数值模拟的比较表明，合成湍流场再现了湍流的关键统计和动力学特征。条件采样的一致性在流动重构问题中得到证明，并随后用于在大域上生成合成湍流速度场。当用作直接数值模拟的初始条件时，这些场产生物理和统计上稳定的系综统计，表明学习到的分布很好地近似了湍流动力系统的自然分布。
英文摘要
Although a complete characterisation of the probability distribution in the phase space of turbulent flows remains elusive, accurately sampling this distribution is essential for both synthetic turbulence generation and turbulent flow reconstruction. Motivated by these applications, we examine to what extent a machine-learned distribution can approximate the physical invariant distribution of turbulent channel flow at $\mathrm{Re}_τ=180$. We assess three important properties of the approximation: physical ensemble statistics, consistent conditional sampling, and dynamical invariance. To this end, a flow-based generative model is trained on a minimal conditional flow unit, which we define as the smallest domain outside which conditional fields, given a single observation at the domain centre, are indistinguishable from unconditional fields in terms of mean-square discrepancy to other conditional fields. We also introduce a consistent procedure for sampling from the conditional learned distribution. Comparisons with direct numerical simulation show that synthetic turbulent fields reproduce key statistical and dynamical features of turbulence, including intermittency and nonlinear energy transfer. The consistency of conditional sampling is demonstrated in a flow reconstruction problem, and subsequently used to generate synthetic turbulent velocity fields on a large domain. When adopted as initial conditions in direct numerical simulations, these fields yield physical and statistically stationary ensemble statistics, indicating that the learned distribution provides a good approximation to the natural distribution of the turbulent dynamical system.
