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SUMMARY:Statistical Finite Elements via Interacting Particle Langevin Dyna
 mics - Alex Glyn-Davies\, University of Cambridge\, UK
DTSTART:20250530T140000Z
DTEND:20250530T150000Z
UID:TALK229459@talks.cam.ac.uk
CONTACT:Shehara Perera
DESCRIPTION:In this work\, we develop a class of interacting particle Lang
 evin algorithms to solve inverse problems for partial differential equatio
 ns (PDEs). We leverage the statistical finite elements formulation to obta
 in a finite-dimensional statistical model\, where the parameter is that of
  the forward map and the latent variable is the discretised solution of th
 e PDE\, assumed to be partially observed. We then adapt a recently propose
 d expectation-maximisation like scheme\, the interacting particle Langevin
  algorithm (IPLA)\, for this problem and obtain a joint estimation procedu
 re for the parameters and the latent variables. The estimation of an unkno
 wn source term is demonstrated for linear and nonlinear Poisson PDEs\, as 
 well as the diffusivity parameter for the linear Poisson PDE. We provide c
 omputational complexity estimates for forcing estimation in the linear cas
 e\, including comprehensive numerical experiments and preconditioning stra
 tegies that significantly improve the performance.
LOCATION:CivEng Seminar Room (1-33) (Civil Engineering Building)
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