报告题目: Wasserstein Gradient Flow of Maximum Mean Discrepancy with Energy Kernel
报告人：王力汉（新加坡国立大学）
邀请人&主持人：黄辉
报告时间与地点：11月12日 晚上7点， 腾讯会议：815-562-454
报告摘要: Wasserstein gradient flows of Maximum Mean Discrepancy have recently found applications in statistics and machine learning. The standard theory of Wasserstein gradient flows in spaces of probability measures provides well-posedness for smooth kernels, however, the kernels that perform well in applications are not differentiable and the theory does not apply. Here we consider the “energy kernels” k(x, y) = −|x−y|^q for q ∈ (0, 2) which allow for long-range effects. We develop well-posedness theory in L^p spaces and show that these solutions can be approximated well by interacting particles, which justifies their use. We also provide results that show that at least in 1D the convergence can be exponential when the solution is close to the target and also prove that no quantitative rate of convergence holds for general initial data. Joint work with Matthew Rosenzweig and Dejan Slepčev (CMU).
报告人介绍：王力汉，2016 年本科毕业于清华大学数学科学系，2021 年博士毕业于美国杜克大学。2021-2025 年在美国卡内基梅隆大学和德国马克斯普朗克应用数学研究所从事博士后研究，2025 年加入新加坡国立大学任助理教授。研究方向为与概率论和应用数学相关的偏微分方程理论研究，包括Langevin方程与 Fokker-Planck 方程，统计采样与机器学习中的梯度流问题等。
