**Abstract**: In this work, we study a few basic questions for partial differential equations (PDE) learning from observed solution data. Using various types of PDEs, we show how the approximate dimension (richness) of the data space spanned by all snapshots along a solution trajectory depends on the differential operator and initial data, and identifiability of a differential operator from solution data on local patches. Then we propose a consistent and sparse local regression method for general PDE identification. Our method requires minimal amount of local measurements in space and time from a single solution trajectory by enforcing global consistency and sparsity.

**Speaker’s Bio**: Hongkai Zhao got his Ph.D from University of California (UC)-Los Angeles in 1996 and went to Stanford as Gabor Szego Assistant Professor. He joined UC Irvine in 1999 and was the Chancellor’s Professor before he moved to Duke in 2020. Hongkai Zhao received the Sloan Fellowship in 2002 and the Feng Kang Prize in Scientific Computing in 2007. He was elected as Society for Industrial and Applied Mathematics (SIAM) Fellow in 2022 for “seminal contributions to scientific computation, numerical analysis, and applications in science and engineering.” Currently he is the Chair for SIAM Activity Group in Imaging Science.

Last Updated: June 6, 2022 - 1:41 pm