BEGIN:VCALENDAR
PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
 M3//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20260113T112810Z
DTSTART:20260114T110000Z
DTEND:20260114T120000Z
SUMMARY:AI-Fun & ELLIS Invited Speaker Series | Boumediene Hamzi
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}e1b8-mj0754
 11-3fs8ha
DESCRIPTION:On 14 January\, we will have Boumediene Hamzi from Imperial C
 ollege London\, Caltech and the Alan Turing Institute. \n\nTalk title: M
 achine Learning and Dynamical Systems meet in Reproducing Kernel Hilbert
  Spaces\n\nAbstract: \nSince its inception in the 19th century through t
 he efforts of Poincaré and Lyapunov\, the theory of dynamical systems ha
 s addressed the qualitative behavior of dynamical processes as understoo
 d from models. From this perspective\, modeling in applications requires
  a detailed understanding of the mechanisms at play\, leading to mathema
 tical descriptions that approximate the observed reality-often expressed
  as systems of ordinary/partial\, underdetermined (control)\, determinis
 tic/stochastic differential or difference equations. While such models a
 re very precise for many processes\, for some of the most challenging ap
 plications of dynamical systems (such as climate dynamics\, brain dynami
 cs\, biological systems\, or financial markets)\, deriving faithful mode
 ls is notably difficult.\n\nOn the other hand\, machine learning is conc
 erned with algorithms designed to accomplish a given task\, whose perfor
 mance improves with more data. Applications include computer vision\, st
 ock market analysis\, speech recognition\, recommender systems\, and sen
 timent analysis. This data-driven paradigm is invaluable in settings whe
 re no explicit model is available but measurement data is abundant-an in
 creasingly common situation in modern scientific and engineering problem
 s. The intersection of dynamical systems and machine learning remains co
 mparatively underexplored\, and the objective of this talk is to show th
 at working in reproducing kernel Hilbert spaces (RKHS) offers a powerful
  framework for a data-based theory of nonlinear dynamical systems.\n\nIn
  the first part of the talk\, we introduce simple methods to learn surro
 gate models for complex systems. We present variants of Kernel Flows as 
 practical approaches for learning the kernels that appear in the emulato
 rs we use in our work. We discuss parametric and nonparametric kernel fl
 ows for learning chaotic dynamical systems\, as well as learning from ir
 regularly sampled time series and from partial observations. We also int
 roduce Sparse Kernel Flows and Hausdorff-metric–based Kernel Flows (HMKF
 s) and apply them to learn a benchmark library of 132 chaotic dynamical 
 systems. We also illustrate these learned-kernel emulators on climate/ge
 ophysical forecasting tasks\, showing accurate\, low-cost predictions fr
 om data. We further extend Kernel Mode Decomposition to design kernels a
 imed at detecting critical transitions in fast–slow random dynamical sys
 tems\, with applications to seizure detection.\n\nWe then turn to stabil
 ity and optimal control. We introduce a data-based perspective on center
  manifolds\, propose kernel methods for computing center manifolds\, and
  outline a data-based version of the center manifold theorem. We also pr
 esent kernel methods for computing Lyapunov functions. Finally\, we desc
 ribe recent progress on Hamilton–Jacobi–Bellman (HJB) equations and nonl
 inear optimal control using kernel-based LMI methods: the Hamilton–Jacob
 i inequality is rewritten via Schur complement arguments into a convex L
 MI/SDP formulation\, while the value function (and\, crucially\, its gra
 dient) is represented in an RKHS through kernel expansions. To avoid deg
 enerate solutions and connect with classical optimal control\, we impose
  a Riccati–Hessian consistency constraint at the equilibrium\, yielding 
 computationally tractable controllers with accompanying stability and su
 boptimality guarantees.\n\nIn the second part\, we introduce a data-base
 d approach to estimating key quantities that arise in the study of nonli
 near autonomous\, control\, and random dynamical systems. Our approach h
 inges on the observation that much of the existing linear theory may be 
 extended to nonlinear systems-often with a reasonable expectation of suc
 cess-once the nonlinear dynamics are mapped into a high- or infinite-dim
 ensional RKHS. We develop computable\, nonparametric estimators approxim
 ating controllability and observability energies for nonlinear systems\,
  apply them to model reduction of nonlinear control systems\, and show h
 ow controllability-energy estimation provides a practical route to appro
 ximating the invariant measure of an ergodic\, stochastically forced non
 linear system. \n\nBoumediene Hamzi is currently a Senior Scientist at t
 he Department of Computing and Mathematical Sciences\, Caltech. He is al
 so co-leading the Research Interest Group on Machine Learning and Dynami
 cal Systems at the Alan Turing Institute. Broadly speaking\, his researc
 h is at the interface of Machine Learning and Dynamical Systems.\n\nIn p
 erson attendance is encouraged. If you are unable to physically attend\,
  please register via the Ticketsource link provided and you will receive
  online joining instructions.\n
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Lecture Theatre 1.4\, Kilburn Building\, Manchester
END:VEVENT
END:VCALENDAR