彭任锋 博士（香港城市大学）

袁亚湘 院士

Physics-Informed Functional Tucker Method with RKHS Factors for Sparse Spatiotemporal Reconstruction

9月1日（周二）15:30-16:30，蓝白楼311

Reconstructing physical dynamics from sparse and irregular spatiotemporal observations is a fundamental challenge in scientific research. However, sparsity leaves large regions of the field unconstrained, making the inverse problem ill-posed: a model may fit the observed sensors while producing nonphysical off-sensor structures or unreliable predictions between support times. To address this challenge, we propose PhysFTM---a physics-informed functional Tucker method that parameterizes Tucker mode factors in reproducing kernel Hilbert space (RKHS) and enforces governing physical laws through finite-difference residuals at collocation points. These physical constraints are essential for credible reconstruction, since most query locations are never directly supervised by data. Specifically, PhysFTM first reconstructs continuous spatial fields at observed times via an alternating minimization scheme, with separate treatments for the Tucker core tensor and the RKHS-based factors. To further enable continuous temporal resolution, PhysFTM constructs a continuous trajectory in Tucker-core space, which is decoded by the learned spatial RKHS-FTM representation to recover the full spatiotemporal field at arbitrary query times. Experiments on Allen--Cahn and Navier--Stokes with varying observation ratios demonstrate that PhysFTM achieves superior reconstruction accuracy, improved physical consistency, and stronger continuous-time modeling capability.

报告人简介：彭任锋，香港城市大学科研助理。本科毕业于同济大学数学科学学院，博士毕业于中国科学院数学与系统科学研究院，导师袁亚湘研究员。曾任中国科学院―SIAM学生分会主席，获得过中国科学院数学院华罗庚奖学金、院长奖学金优秀奖等荣誉。他的研究兴趣集中在低秩矩阵和张量优化、流形优化、机器学习、量子信息论等领域，相关成果发表在 MP、SIAM系列等期刊。