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首页> 外文期刊>Journal of Computational and Applied Mathematics >Gradient-enhanced surrogate modeling based on proper orthogonal decomposition
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Gradient-enhanced surrogate modeling based on proper orthogonal decomposition

机译：基于适当正交分解的梯度增强代理模型

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摘要

A new method for enhanced surrogate modeling of complex systems by exploiting gradient information is presented. The technique combines the proper orthogonal decomposition (POD) and interpolation methods capable of fitting both sampled input values and sampled derivative information like Kriging (aka spatial Gaussian processes). In contrast to existing POD-based interpolation approaches, the gradient-enhanced method takes both snapshots and partial derivatives of snapshots of the associated full-order model (FOM) as an input. It is proved that the resulting predictor reproduces these inputs exactly up to the standard POD truncation error. Hence, the enhanced predictor can be considered as (approximately) first-order accurate at the snapshot locations. The technique applies to all fields of application, where derivative information can be obtained efficiently, for example via solving associated primal or adjoint equations. This includes, but is not limited to Computational Fluid Dynamics (CFD). The method is demonstrated for an academic test case exhibiting the main features of reduced-order modeling of partial differential equations.
机译：提出了一种利用梯度信息增强复杂系统替代模型的新方法。该技术将适当的正交分解（POD）和插值方法结合在一起，能够同时拟合采样的输入值和采样的导数信息，例如Kriging（又称空间高斯过程）。与现有的基于POD的插值方法相比，梯度增强方法将关联的全序模型（FOM）的快照和快照的偏导数作为输入。事实证明，所得到的预测变量将精确地再现这些输入，直至达到标准POD截断误差。因此，可以将增强的预测变量视为快照位置处的（大约）一阶准确。该技术适用于所有应用领域，在这些领域中，可以有效地获取派生信息，例如通过求解关联的原始方程或伴随方程。这包括但不限于计算流体动力学（CFD）。该方法在一个学术测试案例中得到了证明，该案例展示了偏微分方程降阶建模的主要特征。

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