Junior Dynamics Seminar – Kelan Gray (Imperial)

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Koopman Operator Learning for Nonlinear PDEs Abstract: Koopman operators globally linearize nonlinear dynamical systems, and their spectral 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 supporting 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 infinite dimensions, …