Ching-Yao Lai (Stanford): Schmidt AI in Science Speaker Series

Organized by the University of Chicago’s Eric and Wendy Schmidt AI in Science Fellowship Program.

Agenda
4:00pm – 4:45pm:  Presentation
4:45pm – 5:00pm:  Q&A
5:00pm – 5:30pm: Reception

Meeting location
William Eckhardt Research Center. Room 401
5640 S Ellis Avenue, Chicago, IL 60637
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Title: Discoveries in fluid dynamics using neural networks

Abstract: I will discuss two examples of utilizing neural networks (NN) to find solutions
to partial differential equations (PDEs) that facilitate new discoveries. The first concerns
the search for singularities in fluid equations (Wang-Lai-Gómez-Serrano-Buckmaster,
Phys. Rev. Lett. 2023). The second application uses PDE-constrained NNs as an
inverse method in geophysics (Wang, Lai et al., Science 2025). Whether an
incompressible fluid can develop singularities in finite time is an open question in
mathematical fluid dynamics. Unstable singularities, especially in dimensions greater
than 1, are exceptionally elusive. We employ NNs to hunt for singularities, both stable
and unstable ones, for the incompressible 3-dimensional Euler equations and other fluid
equations. In the second part of the talk, I will discuss how the same NNs method trained
with real world data can help uncover the constitutive laws of glacial ice, which differ
from commonly assumed forms in conventional models. Both examples illustrate how
deep learning can help facilitate new discoveries.

Bio: Ching-Yao Lai is an Assistant Professor of Geophysics and
an Affiliated Faculty of the Institute for Computational and
Mathematical Engineering (ICME) at Stanford University. Prior to
Stanford she was an Assistant Professor at Princeton University.
Yao completed her undergraduate study (2013) in Physics at
National Taiwan University, PhD (2018) in Mechanical and
Aerospace Engineering at Princeton University, and postdoctoral
research in earth science at Lamont Earth Observatory at
Columbia University. She was the recipient of the 2023 Google
Research Scholar Award, the 2024 Sloan Research Fellowship,
and NSF CAREER award.