[Colloquium] Ruoxi Jiang Candidacy Exam/Nov.5th

[via Colloquium]

This is an announcement of Ruoxi Jiang's Candidacy Exam.
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Candidate: Ruoxi Jiang

Date: Tuesday, November 5th, 2024

Time: 1:00pm-2:30pm CT 

Location: JCL 223

Title:  Representations Learning in Dynamical Systems

Abstract: In this talk, focusing on dynamical systems, I will discuss how to learn physically meaningful representations for developing “emulators” that help with (a) simulation-based inference (SBI); and (b) better predictions in complex settings.

In the absence of an analytic statistical model, modern SBI approaches leverage the ability to simulate complex systems to draw inferences about their underlying processes, with some using flow-based models to enhance their capability of data inference. However, parameter inference for dynamical systems, such as weather and climate, is still difficult due to the high-dimensional nature of the data as well as the complexity of the physical models and simulations. We introduce Embed and Emulate, a new likelihood-free inference method for estimating arbitrary parameter posteriors based on contrastive learning. This approach learns a low-dimensional embedding for the data and a corresponding fast emulator in the embedding space, bypassing the need for running expensive simulations or high-dimensional emulators during inference. Theoretically, the symmetric contrastive objectives of Embed and Emulate ensure a robust recovery of the normalization constant of the posterior. 

We also demonstrate applications of representation learning in training neural operators, where uncovering patterns and structures in complex systems can lead to more accurate predictions and a deeper understanding of physical phenomena. Neural operators trained to minimize squared error losses often fail to reproduce statistical or structural properties of the dynamics over longer time horizons and can yield degenerate results. To address this challenge for making long-horizon forecasts, we propose a novel framework designed to learn hierarchical spatial-temporal features in modeling the generative process for chaotic dynamics.

Advisors: Rebecca Willett

Committee Members: Rebecca Willett, Michael Maire, and Yuxin Chen