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Variational Bayesian inference for PDE based inverse problems

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If you have a question about this talk, please contact Qingyuan Zhao.

In this talk I will discuss inference in PDE based Bayesian inverse problems and present our recent work on variational inference as an alternative to MCMC for this class of problems. In this work, we propose a family of Gaussian trial distributions parametrised by precision matrices, taking advantage of the inherent sparsity of the inverse problem encoded in its finite element discretisation. We utilise stochastic optimisation to efficiently estimate the variational objective and provide an empirical assessment of the performance. Furthermore, I will mention some recent work that utilises physics-informed neural network as an alternative to the classical finite element solvers and illustrate how these can be used in PDE based forward and inverse problems.

This talk is part of the Statistics series.

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