Michael Brenner

Abstract

Our understanding and ability to compute the solutions to nonlinear partial differential equations has been strongly curtailed by our inability to effectively parameterize 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 discuss our recent work 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 a full simulation.

References: https://www.pnas.org/content/116/31/15344 and https://arxiv.org/pdf/2102.01010.pdf

Our speaker

Michael P. Brenner is the 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. He recently wrote a book on Science and Cooking, published by WH Norton, based on a class he developed at Harvard.