Solving Multiscale Problems with Subsampled Data by Integrating PDE Analysis with Data Science
In many practical applications, we often need to provide solutions to quantities of interest to a large-scale problem but with only subsampled data and partial information of the physical model. Traditional PDE solvers cannot be used directly for this purpose. On the other hand, many powerful techniques have been developed in data science to represent and compress data for useful information. A crucial factor for the success of these methods is to exploit some low rank or sparsity structures in these high-dimensional data. In this talk, we will describe our recent effort in developing effective numerical methods to solve multiscale problems using subsampled data. The PDE analysis will help reveal certain important solution structures so that we can use techniques from data science to give accurate approximations for these quantities of interest.
Thomas Yizhao Hou is the Charles Lee Powell professor of applied and computational mathematics at Caltech. His research interests are centered around developing mathematical analysis and effective computational methods for vortex dynamics, interfacial flows, multiscale problems and data analysis. He received his Ph.D. in mathematics from UCLA in 1987, and joined the Courant Institute as a junior faculty member in 1989. He moved to Caltech in 1993 and was named the Charles Lee Powell Professor in 2004. He was the founding Editor-in-Chief of the SIAM Journal on Multiscale Modeling and Simulation from 2002 to 2007 and served on the IMA Board of Governors from 2010 to 2014. Dr. Hou is a Fellow of American Academy of Arts and Sciences, a SIAM Fellow and an AMS Fellow.