Applications have inspired the development of mathematical fields, while mathematics, driven by compelling ideas, has had important applications quite distant from the original context. This Colloquium Series highlights this dynamic exchange between mathematics and engineering, computation, the physical sciences, the biological sciences and the social sciences.

**Wednesday, April 3, 2019**

4:30 pm, Davis Auditorium, CEPSR (map/directions)

530 West 120th Street

*Refreshments in 200 Mudd, APAM Department, at 3:45 PM*

**Prof. Weinan E**

Princeton University

**"Machine Learning and Multi-scale Modeling"**

Abstract: Modern machine learning has had remarkable success in all kinds of AI applications, and is also poised to change fundamentally the way we do physical modeling. In this talk, I will give an overview on some of the theoretical and practical issues that I consider most important in this exciting area. The first part of this talk will be focused on the following question: How can we make use of modern machine learning tools to help build reliable and practical physical models? Here we will address two issues (mostly using the example of molecular dynamics): (1) building machine learning models that satisfy physical constraints; (2) using microscopic models to generate the optimal data set. The second part of the talk will be devoted to some of the theoretical issues. Serious difficulties arise due to the fact that the underlying dimensionality is high, the neural network models are non-convex and highly over-parametrized. We don’t yet have a complete mathematical picture about neural network-based machine learning but we will discuss the current status. Specifically, we will discuss the representation of high dimensional functions, optimal a priori estimates of the generalization error for neural networks, and gradient decent dynamics.

Biography: Weinan E received his Ph.D. from UCLA in 1989. After being a visiting member at the Courant Institute of NYU and the Institute for Advanced Study at Princeton, he joined the faculty at NYU in 1994. He is now a professor of mathematics at Princeton University, a position he has held since 1999. Weinan E’s work centers around multi-scale modeling and machine learning. Most recently he has been working on integrating machine learning and physical modeling to solve problems in traditional areas of science and engineering, such as molecular dynamics, PDEs, control theory, etc. Weinan E is the recipient of the SIAM R. E. Kleinman Prize, von Karman Prize, Peter Henrici Prize (to be awarded at ICIAM 2019), and the ICIAM Collatz Prize. He is a member of the Chinese Academy of Sciences, a fellow of the American Mathematical Society, a SIAM fellow and a fellow of the Institute of Physics.

*This event is cosponsored by the Center for Foundations of Data Science and the TRIPODs Institute of Columbia University.*

**Organizing Committee**

Qiang Du (APAM)

Don Goldfarb (IEOR)

Eitan Grinspin (Computer Science / APAM)

Ioannis Karatzas (Mathematics)

Andrei Okounkov (Mathematics)

Michael I. Weinstein (APAM / Mathematics)

This lecture series is made possible with the generous support of Columbia Engineering Dean Mary C. Boyce.

For information, please contact **Professor M.I. Weinstein,** miw2103@columbia.edu.

Columbia University makes every effort to accommodate individuals with disabilities. If you require disability accommodations to attend an event at Columbia University, please contact the Office of Disability Services at 212.854.2388 or access@columbia.edu.

Morningside Accessibility Map:

https://www.columbia.edu/files/columbia/content/accessibilitymap2014.pdf

**Distinguished Colloquium Series in Interdisciplinary and Applied Mathematics Archive**