报告时间：2026年6月27日（周六）下午 15:30-16:30
报告地点：苏州大学天赐庄校区精正楼306
报告人：李海波 副教授，华中科技大学
报告摘要：
Learning convolution kernels in operators from data arises in numerous applications and represents an ill-posed inverse problem of broad interest. With scant prior information, kernel methods offer a natural nonparametric approach with regularization. However, a major challenge is to select a proper reproducing kernel, especially as operators and data vary. In this talk, I will present a Data-Adaptive RKHS (DA-RKHS) regularization framework for learning convolution kernels from data. We show that the input data and forward operator themselves induce a data-adaptive RKHS, and there is a finite set of automatic basis functions to represent the estimators in the DA-RKHS when the observation data is discrete and finite. We propose Tikhonov regularization, iterative regularization, and divide-and-conquer methods for small, large, and huge data, respectively. Theoretical results show that the DA-RKHS estimator can achieve optimal minimax convergence rate under certain source conditions. Numerical experiments confirm that our automatic RKHS regularization outperforms standard ridge regression and Gaussian process methods with preselected kernels.
报告人简介：
李海波，华中科技大学数学与统计永利皇宫 副教授，分别于山东大学、清华大学获得本科、博士学位。曾在华为公司从事AI for Science工作，以及墨尔本大学从事博士后研究。主要研究领域包括反问题、数值线性代数与科学机器学习，在 SIOPT、SISC、SIMAX、JSC 等计算与应用数学主流期刊发表论文16篇。
邀请人：董自康