报告题目：RFF-CoRes: A Gaussian Process Framework with Explicit Random Fourier Feature and Corrective Residual for Forward and Inverse PDE Problems

报告人：李新民

时间：10月17日 8：30-9：30

地点：国产自拍 106会议室

报告摘要：We develop RFF-CoRes, a Gaussian-process framework for forward and inverse partial differential equations (PDEs) in which random Fourier features (RFFs) play two distinct but mathematically compatible roles. The first role is representational: a finite RFF expansion approximates the deterministic mean function, which is the expectation of the latent solution process and is used to capture the dominant global and oscillatory structure of the PDE solution. The second role is covariance approximation: an independently tunable, typically larger, RFF expansion approximates a stationary Gaussian covariance kernel and yields a low-rank corrective residual process. several, but not all, configurations. Five-realization tests reveal benchmark-dependent random-feature sensitivity. The resulting framework provides a principled interpretation of RFF-CoRes as a two-resolution spectral representation rather than merely a low-rank Gaussian-process approximation.

报告人简介：李新民，青岛大学数学与国产自拍 教授，博士生导师，青岛大学统计与数据分析研究中心主任。主要研究领域：Fiducial推断、计算机试验、模型平均、大数据统计等。在Science China Mathematics, Journal of Computational and Graphical Statistics，Statistica Sinica, Statistics and Computing等国内外重要期刊发表高水平学术论文，先后主持了国家自然科学基金面上项目2项和国家社会科学基金一般项目项。学术兼职主要有：中国现场统计研究会理事，全国工业统计教学研究会理事，中国现场统计研究会贝叶斯分会副理事长及多个分会常务理事，中国数学会均匀设计分会常务理事及多个学术期刊编委。