Bio: John Harlim is a Professor in the Department of Mathematics and the Department of Meteorology and Atmospheric Sciences. Harlim received his undergraduate degree in Mathematics from the Universitas Padjadaran (Indonesia), a master’s from the University of Guelph in Applied Mathematics, and a PhD in Applied Mathematics and Scientific Computation from the University of Maryland at College Park. His research interests in applied mathematics include parameter estimation, machine learning, manifold learning, operator estimation, data assimilation.
The recent success of machine learning has drawn tremendous interest in applied mathematics and scientific computations. In this talk, I would address the classical closure problem that is also known as model error, missing dynamics, or reduced-order-modeling in various community. Particularly, I will discuss a general framework to compensate for the model error. The proposed framework reformulates the model error problem into a supervised learning task to approximate a very high-dimensional target function involving the Mori-Zwanzig representation of projected dynamical systems. Connection to traditional parametric approaches will be clarified as specifying the appropriate hypothesis space for the target function. Theoretical convergence and numerical demonstration on modeling problems arising from PDE’s will be discussed.