论文标题
功能输入高斯流程，并应用于逆散射问题
Functional-Input Gaussian Processes with Applications to Inverse Scattering Problems
论文作者
论文摘要
基于高斯工艺（GP）的替代建模在分析科学和工程中的复杂问题时受到了越来越多的关注。尽管对GP建模进行了广泛的研究，但功能投入的发展仍然很少。由反向散射问题激发，其中代表散射器的支持和材料属性的功能输入参与了部分微分方程，为GPS引入了用于功能输入的新类核函数。基于提出的GP模型，得出了所得平方平方预测误差的渐近收敛性能，并通过数值示例证明了有限样本性能。在对反散射的应用中，替代模型是由功能输入构建的，这对于在给定的远场模式中恢复了不均匀的各向同性散射区域的反射指数至关重要。
Surrogate modeling based on Gaussian processes (GPs) has received increasing attention in the analysis of complex problems in science and engineering. Despite extensive studies on GP modeling, the developments for functional inputs are scarce. Motivated by an inverse scattering problem in which functional inputs representing the support and material properties of the scatterer are involved in the partial differential equations, a new class of kernel functions for functional inputs is introduced for GPs. Based on the proposed GP models, the asymptotic convergence properties of the resulting mean squared prediction errors are derived and the finite sample performance is demonstrated by numerical examples. In the application to inverse scattering, a surrogate model is constructed with functional inputs, which is crucial to recover the reflective index of an inhomogeneous isotropic scattering region of interest for a given far-field pattern.
