Statistical Finite Elements via Interacting Particle Langevin Dynamics

Add to your list(s) Download to your calendar using vCal

• Alex Glyn-Davies, University of Cambridge, UK
• Friday 30 May 2025, 15:00-16:00
• CivEng Seminar Room (1-33) (Civil Engineering Building).

If you have a question about this talk, please contact Shehara Perera.

In this work, we develop a class of interacting particle Langevin algorithms to solve inverse problems for partial differential equations (PDEs). We leverage the statistical finite elements formulation to obtain a finite-dimensional statistical model, where the parameter is that of the forward map and the latent variable is the discretised solution of the PDE , assumed to be partially observed. We then adapt a recently proposed expectation-maximisation like scheme, the interacting particle Langevin algorithm (IPLA), for this problem and obtain a joint estimation procedure for the parameters and the latent variables. The estimation of an unknown source term is demonstrated for linear and nonlinear Poisson PDEs, as well as the diffusivity parameter for the linear Poisson PDE . We provide computational complexity estimates for forcing estimation in the linear case, including comprehensive numerical experiments and preconditioning strategies that significantly improve the performance.

This talk is part of the Engineering Department Structures Research Seminars series.

This talk is included in these lists:

• All Talks (aka the CURE list)
• Cambridge University Engineering Department Talks
• Cambridge talks
• Centre for Smart Infrastructure & Construction
• CivEng Seminar Room (1-33) (Civil Engineering Building)
• Civil Engineering Talks
• Computational Continuum Mechanics Group Seminars
• Engineering Department Structures Research Seminars
• Featured lists
• Interested Talks
• School of Technology
• Trust & Technology Initiative - interesting events
• bld31
• yk449

Note that ex-directory lists are not shown.