Junior Dynamics Seminar – Kelan Gray (Imperial)
Thu 8 Oct · 17:00
Huxley Building, South Kensington Campus
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Kelan Gray will deliver a talk titled Koopman Operator Learning for Nonlinear PDEs as part of the Junior Dynamics Seminar on 8 October 2026. The presentation aims to establish a rigorous framework for learning Koopman operators of infinite-dimensional dynamical systems. It explores the theoretical challenges and progress related to nonlinear Hamiltonian PDEs.
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, one must tread carefully: even the existence of a Koopman operator for simple PDEs is not guaranteed. For nonlinear Hamiltonian PDEs, however, significant progress is possible. We prove that, for initial data drawn from a Gaussian measure, the dynamics admit a strongly continuous Koopman semigroup, whose spectral content yields a simple model for the PDE solution. We also give error bounds for numerical approximations of these operators via conditional expectations. Together, these results shed some theoretical light on the topic and suggest practical algorithms.
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Frequently asked questions
Junior Dynamics Seminar – Kelan Gray (Imperial) takes place on Thursday, 8 October 2026 at 17:00.
Junior Dynamics Seminar – Kelan Gray (Imperial) is held at Huxley Building, South Kensington Campus in London (642, Huxley Building, SW7 2AZ).
Entry to Junior Dynamics Seminar – Kelan Gray (Imperial) is free.
Tickets for Junior Dynamics Seminar – Kelan Gray (Imperial) can be booked via imperial.ac.uk using the "Check Tickets & Live Prices" button on this page, which opens the official booking site in a new tab.
Junior Dynamics Seminar – Kelan Gray (Imperial)
Editorial Summary
Kelan Gray will deliver a talk titled Koopman Operator Learning for Nonlinear PDEs as part of the Junior Dynamics Seminar on 8 October 2026. The presentation aims to establish a rigorous framework for learning Koopman operators of infinite-dimensional dynamical systems. It explores the theoretical challenges and progress related to nonlinear Hamiltonian PDEs.
This summary was automatically generated from event data sourced from official ticketing providers.
Organiser’s full description
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, one must tread carefully: even the existence of a Koopman operator for simple PDEs is not guaranteed. For nonlinear Hamiltonian PDEs, however, significant progress is possible. We prove that, for initial data drawn from a Gaussian measure, the dynamics admit a strongly continuous Koopman semigroup, whose spectral content yields a simple model for the PDE solution. We also give error bounds for numerical approximations of these operators via conditional expectations. Together, these results shed some theoretical light on the topic and suggest practical algorithms.
Description supplied by the event organiser.
📍 Venue
Huxley Building, South Kensington Campus642, Huxley Building, SW7 2AZ
Westminster, London
Get Directions →❓ Frequently asked questions
When is Junior Dynamics Seminar – Kelan Gray (Imperial)?
Junior Dynamics Seminar – Kelan Gray (Imperial) takes place on Thursday, 8 October 2026 at 17:00.
Where is Junior Dynamics Seminar – Kelan Gray (Imperial) taking place?
Junior Dynamics Seminar – Kelan Gray (Imperial) is held at Huxley Building, South Kensington Campus in London (642, Huxley Building, SW7 2AZ).
How much are tickets for Junior Dynamics Seminar – Kelan Gray (Imperial)?
Entry to Junior Dynamics Seminar – Kelan Gray (Imperial) is free.
How do I get tickets for Junior Dynamics Seminar – Kelan Gray (Imperial)?
Tickets for Junior Dynamics Seminar – Kelan Gray (Imperial) can be booked via imperial.ac.uk using the "Check Tickets & Live Prices" button on this page, which opens the official booking site in a new tab.
Price
Free Entry
Date
Until Thursday, 8 October 2026
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