BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Optimal Transport for Learning Chaotic Dynamics via Invariant Meas
 ures - Yunan Yang (ETH Zürich)
DTSTART:20220527T090000Z
DTEND:20220527T100000Z
UID:TALK173639@talks.cam.ac.uk
DESCRIPTION:Parameter identification determines the essential system param
 eters required to build real-world dynamical systems by fusing crucial phy
 sical relationships and experimental data. However\, the data-driven appro
 ach faces many difficulties\, such as discontinuous or inconsistent time t
 rajectories and noisy measurements. The ill-posedness of the inverse probl
 em comes from the chaotic divergence of the forward dynamics. Motivated by
  the challenges\, we shift from the Lagrangian particle perspective to the
  state space flow field's Eulerian description. Instead of using pure time
  trajectories as the inference data\, we treat statistics accumulated from
  the Direct Numerical Simulation (DNS) as the observable. The continuous a
 nalog of the latter is closely related to the physical invariant measure\,
  a stationary distributional solution to the continuity equation or the Fo
 kker-Planck equation. The connection motivates us to build a regularized f
 orward model in the form of a PDE and reformulate the original parameter i
 dentification problem as a data-fitting\, PDE-constrained optimization pro
 blem. A finite-volume upwind scheme and the so-called teleportation regula
 rization are used to discretize and regularize the forward problem. We pre
 sent theoretical regularity analysis for evaluating gradients of optimal t
 ransport costs and introduce two different formulations for efficient grad
 ient calculation. Numerical results using the quadratic Wasserstein metric
  from optimal transport demonstrate the robustness of the novel approach f
 or chaotic system parameter identification.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR