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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Optimal Transport for Learning Chaotic Dynamics vi
a Invariant Measures - Yunan Yang (ETH Zürich)
DTSTART;TZID=Europe/London:20220527T100000
DTEND;TZID=Europe/London:20220527T110000
UID:TALK173639AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/173639
DESCRIPTION:Parameter identification determines the essential
system parameters required to build real-world dyn
amical systems by fusing crucial physical relation
ships and experimental data. However\, the data-dr
iven approach faces many difficulties\, such as di
scontinuous or inconsistent time trajectories and
noisy measurements. The ill-posedness of the inver
se problem comes from the chaotic divergence of th
e forward dynamics. Motivated by the challenges\,
we shift from the Lagrangian particle perspective
to the state space flow field's Eulerian descripti
on. 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 analog of the latter is
closely related to the physical invariant measure
\, a stationary distributional solution to the con
tinuity equation or the Fokker-Planck equation. Th
e connection motivates us to build a regularized f
orward model in the form of a PDE and reformulate
the original parameter identification problem as a
data-fitting\, PDE-constrained optimization probl
em. A finite-volume upwind scheme and the so-calle
d teleportation regularization are used to discret
ize and regularize the forward problem. We present
theoretical regularity analysis for evaluating gr
adients of optimal transport costs and introduce t
wo different formulations for efficient gradient c
alculation. Numerical results using the quadratic
Wasserstein metric from optimal transport demonstr
ate the robustness of the novel approach for chaot
ic system parameter identification.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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