Beijing Institute of Mathematical Sciences and Applications

Stephen S-T. Yau

Jiayi Kang

Monday, April 3, 2023 2:30 PM - 3:00 PM

Online

In this report, I will report a paper where they propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, they reduce this problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox of spline interpolation. Unlike previous approaches to measure-valued splines, their interpolated curves (i) have a clear interpretation as governing particle flows, which is natural for applications, and (ii) come with the first approximation guarantees on Wasserstein space. Finally, they demonstrate the broad applicability of our interpolation methodology by fitting surfaces of measures using thin-plate splines.

Jiayi Kang received his Ph.D. in Mathematics from Tsinghua University in 2024. He joined the Beijing Institute of Mathematical Sciences and Applications (BIMSA) as an Assistant Researcher in July 2024, and became an Assistant Professor at the Hetao Institute for Mathematical and Interdisciplinary Sciences (HIMIS) in November 2025. His research focuses on the intersection of deep learning, nonlinear filtering, and computational biology. His main research interests include: neural network-based filtering algorithms and their mathematical foundations, sampling methods in Wasserstein geometry, nonlinear filtering theory (including the Yau-Yau method) and its applications in climate science and other fields, as well as computational genomics and evolutionary system modeling. He is committed to solving complex problems in science and engineering using mathematical and machine learning methods.