This was part of Expressing and Exploiting Structure in Modeling, Theory, and Computation with Gaussian Processes

Statistical Finite Elements for Nonlinear PDEs

Connor Duffin, University of Cambridge
Monday, August 29, 2022


In this talk, I will present a statistical finite element method for nonlinear, time-dependent phenomena. The statistical finite element method (statFEM) is a statistical augmentation of the finite element method that enables model-data synthesis through the admission of model misspecification inside of the governing equations, as represented by a Gaussian process. The method is Bayesian, coherently updates model mismatch upon receipt of observed data, and is applicable to a wide range of problems across science and engineering for which finite element methods are appropriate. Scalability is ensured through making a low-rank approximation to the posterior covariance matrix. I'll first introduce the statFEM, before detailing the methodology for nonlinear problems. I will discuss various case studies, applying the method to experimental and synthetic data in canonical nonlinear PDEs.