Transport- and Measure-Theoretic Approaches for Dynamical System Modeling

Measures provide valuable insights into long-term and global behaviors across various dynamical systems. In this talk, I present our recent works employing measure theory and optimal transport to tackle challenges in dynamical system identification. First, we adopt a PDE-constrained optimization perspective to learn ODEs and SDEs from slowly sampled trajectories, enabling stable forward models and uncertainty quantification. We use optimal transport to align physical measures for parameter estimation, even when time-derivative data is unavailable. We also extend the celebrated Takens’ time-delay embedding, a foundational result in dynamical systems, from state space to probability distributions. It establishes a robust theoretical and computational framework for state reconstruction that remains effective under noisy and partial observations. Finally, we show that by comparing invariant measures in time-delay coordinates, one can overcome identifiability challenges and recover the underlying dynamics uniquely. These works demonstrate the excellent research potential of measure-theoretic approaches for dynamical systems.

 

About the speaker
Yunan Yang is an applied mathematician working on inverse problems and optimal transportation. Currently, she is a tenure-track Goenka Family Assistant Professor in the Department of Mathematics at Cornell University. Yunan Yang earned a Ph.D. in mathematics from the University of Texas at Austin in 2018, supervised by Prof. Bjorn Engquist. From September 2018 to August 2021, Yunan was a Courant Instructor at the Courant Institute of Mathematical Sciences, NYU, followed by an Advanced Fellowship at the Institute for Theoretical Studies at ETH Zurich. Yunan won the 19th IMA Leslie Fox Prize in Numerical Analysis as a First Prize and was honored as one of the Rising Stars in Computational and Data Sciences by the Oden Institute.

Date
Speaker: Yunan Yang from Cornell University
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