Abstract A surrogate model, based on proper orthogonal decomposition (POD) with the adaptive sampling method, was proposed to predict the transitional flow past rough flat plates simulated by a four-equation k-ω-γ-Ar transition model. Gaussian process regression was used to map the input parameters to the POD expansion coefficients. The variance and gradient of Gaussian process were taken as the criteria for the adaptive sampling. The proposed methodology was applied to a one-dimensional heat conduction problem and two-dimensional transitional flow past rough flat plates. At the same time, the results were compared with those of Halton sequences. With the same sample size, the adaptive method achieved a higher accuracy on the test set, and the proposed adaptive criterion could serve as an indicator for the model discrepancies.

中文翻译：

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在高斯过程中使用自适应采样对过渡流进行基于 POD 的代理建模

摘要 提出了一种基于适当正交分解（POD）和自适应采样方法的替代模型，用于预测通过四方程k-ω-γ-Ar过渡模型模拟的粗糙平板过渡流。高斯过程回归用于将输入参数映射到 POD 扩展系数。以高斯过程的方差和梯度作为自适应采样的标准。所提出的方法被应用于一维热传导问题和通过粗糙平板的二维过渡流。同时，将结果与Halton序列的结果进行了比较。在样本量相同的情况下，自适应方法在测试集上取得了更高的准确率，所提出的自适应准则可以作为模型差异的指标。