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Postdoctoral Applicants
Measure Transport for Data-Driven Dynamical Systems
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Speaker: Jonah Botvinick-Greenhouse (Cornell) Fifth-year PhD Student Cornell University Friday, February 13, 2026 1:00PM - 2:00PM and via Webcast: https://yale.zoom.us/j/92864751346?pwd=2biVIU4Mso6YCbsk687pycpd8CiEV4.1 |
Zoom Password: 123
Abstract: Learning dynamical systems in the presence of measurement noise, sparse observations, and uncertainty is a central challenge in data-driven science and engineering. In this talk, I will present new methods based on measure transport that target long-term statistical behavior rather than pointwise time-series reconstruction, making them well suited to regimes where standard trajectory-based methods struggle. Our approach reframes system identification as a distribution-matching problem in which invariant measures extracted from data are compared with synthetic invariant measures obtained as stationary solutions of a Fokker–Planck equation. This leads to a PDE-constrained optimization framework that enables inference from slowly sampled data and uncertainty quantification for downstream forecasting. To ensure identifiability from the invariant measure alone, we introduce a data-driven coordinate transformation inspired by Takens’ embedding theorem. While classical embedding methods assume dynamics are noise-free, we leverage tools from optimal transport to extend these ideas to a probabilistic setting. This formulation poses state reconstruction as a transformation between distributions, yielding a practical computational framework for recovering high-dimensional systems from partial observations. We demonstrate the effectiveness of our methods through numerical studies on fluid flows, Hall-effect thrusters, and large-scale geophysical datasets.
Bio: Jonah Botvinick-Greenhouse is a fifth-year Ph.D. student at Cornell University’s Center for Applied Mathematics (CAM), advised by Yunan Yang. He received Bachelor’s degrees in Math and Physics from Amherst College. His research uses tools from dynamical systems, machine learning, and optimal transport to develop principled data-driven modeling techniques for complex physical systems.
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