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DTSTAMP:20261009T024819Z
SUMMARY:Junior Dynamics Seminar – Kelan Gray (Imperial)
DESCRIPTION:Koopman Operator Learning for Nonlinear PDEs\nAbstract: Koopman
  operators globally linearize nonlinear dynamical systems\, and their spec
 tral information provides a powerful tool for understanding the underlying
  system. Data-driven methods such as Dynamic Mode Decomposition (DMD) have
  exploited this idea and are widely used on nonlinear PDEs. Yet the suppor
 ting theory is almost entirely restricted to finite-dimensional dynamical 
 systems. This talk takes the first steps towards a rigorous framework for 
 learning Koopman operators of infinite-dimensional dynamical systems. In i
 nfinite dimensions\, one must tread carefully: even the existence of a Koo
 pman operator for simple PDEs is not guaranteed. For nonlinear Hamiltonian
  PDEs\, however\, significant progress is possible. We prove that\, for in
 itial data drawn from a Gaussian measure\, the dynamics admit a strongly c
 ontinuous Koopman semigroup\, whose spectral content yields a simple model
  for the PDE solution. We also give error bounds for numerical approximati
 ons of these operators via conditional expectations. Together\, these resu
 lts shed some theoretical light on the topic and suggest practical algorit
 hms.
URL:https://www.imperial.ac.uk/events/214162/junior-dynamics-seminar-amir-k
 hodaeian-karim-imperial/
DTSTART;TZID=Europe/London:20261008T160000
DTEND;TZID=Europe/London:20261008T170000
LOCATION:642\, Huxley Building\, South Kensington Campus\, Imperial College
  London\, London\, SW7 2AZ\, United Kingdom
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