This seminar will only take place online. Please contact the APAM Department ahead of time for the Zoom link.

Speaker: Bamdad Hosseini

Title: "Solving and Learning Nonlinear PDEs with Gaussian Processes" 

Abstract: In this talk I present a simple, rigorous, and interpretable framework for solution of nonlinear PDEs based on the framework of Gaussian Processes. The proposed approach provides a natural generalization of kernel methods to nonlinear PDEs; has guaranteed convergence; and inherits the state-of-the-art computational complexity of linear solvers for dense kernel matrices. I will outline our approach by focusing on an example nonlinear elliptic PDE followed by further numerical examples. I will also briefly comment on extending our approach to solving inverse problems.

Biography: Dr. Hosseini is a senior postdoctoral scholar in the Department of Computing and Mathematical Sciences at Caltech, sponsored by Profs. Houman Owhadi and Andrew Stuart. In the fall of 2021, he is starting as an Assistant Professorship in the Department of Applied Mathematics at University of Washington. He works on problems at the intersection of probability, statistics, and applied mathematics with a particular focus on data science and uncertainty quantification as well as their applications in engineering and sciences.