Michael P. Brenner
Michael F. Cronin Professor of Applied Mathematics & Applied Physics and Professor of Physics, Harvard University

Title: Machine Learning of Partial Differential Equations

Abstract: Our understanding and ability to computer the solutions to nonlinear partial differential equations has been strongly curtailed by our inability to effectively parametrize the inertial manifold of their solutions. I will discuss our ongoing efforts for using machine learning to advance the state of the art, both for developing a qualitative understanding of “turbulent” solutions and for efficient computational approaches. We aim to learn parameterizations of the solutions that give more insight into the dynamics and/or increase computational efficiency. I will touch on three topics: (i) using machine learning to develop models of the small scale behavior of spatio-temporal complex solutions, with the goal of maintaining accuracy albeit at a highly reduced computational cost relative to full simulation (ii) “larger scale” efforts to classify and understand patterns in nonlinear pdes, relating them to invariant (but unstable) solutions of the underlying equations (iii) using these ideas to simplify and accelerate experimental measurements of complex fluid flows.

Biography: Francis Michael P. Brenner is a Michael F. Cronin Professor of Applied Mathematics & Applied Physics and a Professor of Physics at Harvard University. Additionally, Brenner is a research scientist at Google Research. Brenner earned a Bachelor’s of Science degree at the University of Pennsylvania and obtained a doctorate at the University of Chicago.  Brenner’s research focuses on methods and ideas of applied mathematics to address a wide variety of problems in science and engineering. His current research projects range from efforts to understand the design rules for creating synthetic materials with life-like properties, to efforts to use machine learning to accelerate scientific discovery, to specific problems in fluid mechanics, material science and biology.

This seminar will take place via Zoom. Please send an email to [email protected] ahead of time to request the link.

Host: Prof. Qiang Du