AME Seminar

Speaker: Leonardo Zepeda-Núñez, Senior Research Scientist Google Research and Assistant Professor Department of Mathematics University of Wisconsin-Madison

Talk Title: Dynamical Weighs: Learning Smooth Latent-Dynamics for Advection-Dominated Systems via Consistency-Constrained Hyper-Networks

Abstract: We present a data-driven, space-time continuous framework to learn surrogate models for complex physical systems described by partial differential equations (PDEs). Our approach involves constructing hypernetwork-based latent dynamical models directly on the parameter space of a compact representation network specially tailored to the state space of the target system. The framework leverages the expressive power of the network with a specially designed consistency-inducing regularization to obtain latent trajectories that are both low-dimensional and smooth. These properties render our surrogate models highly efficient at inference time.

We demonstrate the effectiveness of our approach on advection-dominated systems. These systems have slow-decaying Kolmogorov n-widths that hinders standard methods, including reduced order modeling, from producing high-fidelity simulations at low cost. We show that our method is able to generate accurate multi-step rollout predictions at high efficiency, for several one- and two-dimensional PDEs. The resulting rollouts are shown to be stable and reflect statistics that are consistent with the ground truths.

Biography: Leonardo Zepeda-Nunez is a Senior Research Scientist at Google Research and an Assistant Professor of Mathematics at the University of Wisconsin-Madison. He has held postdoctoral positions at Lawrence Berkeley Lab and University of California, working with Lin Lin and Hongkai Zhao respectively. He received a Ph.D. in Mathematics from MIT in 2015 under the direction of Laurent Demanet, an M.Sc. from University of Paris VI in 2010, and a Diploma from École Polytechnique in 2009. His research emcompases scientific machine learning with applications to weather and climate, electronic structure computations, wave-based inverse problems, and fast PDE solvers for wave phenomena.

More Info: https://ame.usc.edu/seminars/

Webcast: https://usc.zoom.us/j/98775609685?pwd=a2lSd01oY0o2KzA4VWphbGxjWk5Qdz09

Location: John Stauffer Science Lecture Hall (SLH) - 102

WebCast Link: https://usc.zoom.us/j/98775609685?pwd=a2lSd01oY0o2KzA4VWphbGxjWk5Qdz09

Audiences: Everyone Is Invited

Contact: Tessa Yao

Event Link: https://ame.usc.edu/seminars/