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Learning Theory for the AI for Science Era

Series: Department Seminar

Speaker: Prof. Ambuj Tewari, Professor, Department of Statistics and the Department of Electrical Engineering and Computer Science (by courtesy), University of Michigan, Ann Arbor

Date/Time: Sep 07 12:00:00

Location: CSA Auditorium, (Room No. 104, Ground Floor)

Abstract:
Many problems in AI for Science can be viewed as learning an operator, a map from one space of functions to another. Examples include learning fast surrogates for PDE solvers and other scientific simulations. These problems break existing learning theory paradigms because the outputs are infinite-dimensional and only partially observed through discretization.

In this talk, I argue that operator learning is a genuinely new learning-theoretic problem in which intuitions and techniques from finite-dimensional settings break down. I will first explain why classical multi-output learning results fail to extend to infinite-dimensional outputs. I will then discuss what governs learnability in the simplest setting of linear operators.

I next show that operator learning reveals new sources of error not seen in classical learning theory. These include errors arising from truncating infinite basis expansions as well as discretization errors. Finally, I demonstrate how changing the data collection protocol from passive to active can dramatically alter what is learnable. Active data collection is especially natural in scientific applications where simulations can be run for user-specified initial conditions.

I conclude by pointing to directions for further exciting work, including time generalization, zero-shot super-resolution, and learning protocols that expose more internal details of the scientific solver.

Speaker Bio:
Ambuj Tewari is a Professor in the Department of Statistics and the Department of Electrical Engineering and Computer Science (by courtesy) at the University of Michigan, Ann Arbor. He is affiliated with the Michigan Center for Applied and Interdisciplinary Mathematics (MCAIM) and the Michigan Institute for Data & AI in Society (MIDAS). His research interests lie in machine learning, with an emphasis on statistical learning theory, online learning, reinforcement learning and control, and optimization. He also collaborates closely with domain scientists to develop principled machine learning methods for applications in the behavioral sciences, psychiatry, and the molecular sciences.

Host Faculty: Prof. Chiranjib Bhattacharyya