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Statistical Finite Elements via Interacting Particle Langevin Dynamics

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This approach demonstrates joint estimation of parameters in partial differential equations, implying enhanced parameters identification performance.

The method estimates parameters and latent variables in partial differential equations using interacting particle Langevin dynamics, enhancing inference accuracy.
Forcing estimation in linear Poisson PDE involves computational complexity assessments, showcasing effectiveness in parameter identification.
Adaptation of the expectation-maximization-like scheme allows joint estimation of both known and partially observed variables within the model framework.
Numerical experiments reveal significant performance boosts from preconditioning strategies, indicating practical implications for statistical modeling in PDE contexts.

Glyn-Davies et al. (2025) studied this question.

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This approach demonstrates joint estimation of parameters in partial differential equations, implying enhanced parameters identification performance.