用于Turbulence建模的输入特征准备方法和机器学习模型的回顾和检查
Review and Examination of Input Feature Preparation Methods and Machine Learning Models for Turbulence Modeling
摘要：
模型外推到看不见的流动是数据驱动湍流建模面临的最大挑战之一，特别是对于涉及许多流动特征的高维输入模型。在这项研究中，我们回顾了以前在数据驱动的雷诺平均朴素斯托克斯（RANS）湍流建模和模型外推方面的工作，主要关注迁移学习领域中使用的流行方法。几个潜在的指标来衡量训练流和测试流之间的差异进行检查。比较不同的机器学习（ML）模型，以了解模型的容量或复杂性如何影响其在数据集迁移时的行为。研究了对协变量偏移具有鲁棒性的数据预处理方案，如归一化、变换和重要性重新加权似然，以了解是否有可能找到衰减训练和测试分布差异的数据投影，同时保持可预测性。提出了三个度量来评估训练/测试数据集之间的差异。为了减弱相异性，使用分布匹配框架来对齐分布的统计。这些修改还允许回归任务在预测目标变量的代表性不足的极值时具有更好的准确性。这些研究结果有助于未来基于ML的湍流模型评估其模型可预测性，并为系统地生成多样化的高保真模拟数据库提供指导。
英文摘要：
Model extrapolation to unseen flow is one of the biggest challenges facing data-driven turbulence modeling, especially for models with high dimensional inputs that involve many flow features. In this study we review previous efforts on data-driven Reynolds-Averaged Naiver Stokes (RANS) turbulence modeling and model extrapolation, with main focus on the popular methods being used in the field of transfer learning. Several potential metrics to measure the dissimilarity between training flows and testing flows are examined. Different Machine Learning (ML) models are compared to understand how the capacity or complexity of the model affects its behavior in the face of dataset shift. Data preprocessing schemes which are robust to covariate shift, like normalization, transformation, and importance re-weighted likelihood, are studied to understand whether it is possible to find projections of the data that attenuate the differences in the training and test distributions while preserving predictability. Three metrics are proposed to assess the dissimilarity between training/testing dataset. To attenuate the dissimilarity, a distribution matching framework is used to align the statistics of the distributions. These modifications also allow the regression tasks to have better accuracy in forecasting under-represented extreme values of the target variable. These findings are useful for future ML based turbulence models to evaluate their model predictability and provide guidance to systematically generate diversified high-fidelity simulation database.
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