Kernel-based learning methods for stochastic partial differential equations

发布时间: 2024-12-03 17:09:00

    This article delves into the study of kernel-based learning methods for stochastic partial differential equations. The theory of generalized data and kernel-based probability measures is introduced to construct kernel-based learning estimators, kernel-based learning functions, and discrete kernel-based learning solutions for addressing stochastic differentials, elliptic stochastic partial differential equations, and parabolic stochastic partial differential equations, respectively. The convergence theorems of kernel-based learning algorithms are demonstrated by combining meshfree approximation and kriging interpolation. Moreover, the numerical examples show the efficiency and robustness of kernel-based learning algorithms using various positive definite kernels.

参考文献：

    1. Ye, Q. (2024). Kernel-based learning methods for stochastic partial differential equations. Engineering Analysis with Boundary Elements, 169(Part A), 105960. https://doi.org/10.1016/j.enganabound.2024.105960