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All-at-once approach to multifidelity polynomial chaos expansion surrogate modeling

机译：一次实现多保真多项式混沌扩展代理建模

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摘要

A new approach to multifidelity, gradient-enhanced surrogate modeling using polynomial chaos expansions is presented. This approach seeks complementary additive and multiplicative corrections to low fidelity data whereas current hybrid methods in the literature attempt to balance individually calculated calibrations. An advantage of the new approach is that least squares-optimal coefficients for both corrections and the model of interest are determined simultaneously using the high-fidelity data directly in the final surrogate. The proposed technique is compared to the weighted approach for three analytic functions and the numerical simulation of a vehicle's lift coefficient using Cartesian Euler CFD and panel aerodynamics. Investigation of the individual correction terms indicates the advantage of the proposed approach is that complementary calibrations separately adjust the low-fidelity data in local regions based on agreement or disagreement between the two fidelities. In cases where polynomials are suitable approximations to the true function, the new all-at-once approach is found to reduce error in the surrogate faster than the method of weighted combinations. When the low-fidelity is a good approximation of the true function, the proposed technique out-performs monofidelity approximations as well. Sparse grid constructions alleviate the growth of the training set as root-mean-square-error is calculated for increasingly higher polynomial orders. Utilizing gradient information provides an advantage at lower training grid levels for low-dimensional spaces, but worsens numerical conditioning of the system in higher dimensions. Published by Elsevier Masson SAS.
机译：提出了一种使用多项式混沌展开进行多保真，梯度增强代理建模的新方法。这种方法寻求对低保真度数据的补充加法和乘法校正，而文献中的当前混合方法试图平衡单独计算的校准值。新方法的优势在于，直接在最终替代指标中同时使用高保真度数据，同时确定用于校正和目标模型的最小二乘最优系数。将所提出的技术与加权方法的三个解析函数进行比较，并使用笛卡尔欧拉CFD和面板空气动力学对车辆的升力系数进行数值模拟。对单个校正项的研究表明，所提出方法的优势在于，互补校准会根据两个保真度之间的一致或不同，分别调整本地区域中的低保真度数据。在多项式适合于真函数的情况下，发现新的一次性算法可以比加权组合方法更快地减少代理中的误差。当低保真度是真实函数的良好逼近时，所提出的技术也优于单保真度逼近。稀疏的网格结构减轻了训练集的增长，因为对于越来越高的多项式阶数计算出均方根误差。利用梯度信息为低维空间在较低的训练网格级别提供了一个优势，但在高维环境中恶化了系统的数值条件。由Elsevier Masson SAS发布。

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