Kernel-based learning methods for stochastic partial differential equations

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements Pub Date : 2024-09-24 DOI:10.1016/j.enganabound.2024.105960

Qi Ye

引用次数: 0

Abstract

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.

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基于核的随机偏微分方程学习方法

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本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Engineering Analysis with Boundary Elements 工程技术-工程：综合

CiteScore

5.50

自引率

18.20%

发文量

368

审稿时长

56 days

期刊介绍： This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods. Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness. The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields. In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research. The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods Fields Covered: • Boundary Element Methods (BEM) • Mesh Reduction Methods (MRM) • Meshless Methods • Integral Equations • Applications of BEM/MRM in Engineering • Numerical Methods related to BEM/MRM • Computational Techniques • Combination of Different Methods • Advanced Formulations.