Optimal State and Parameter Estimation Algorithms and Applications to Biomedical Problems

Abstract: In this talk, I will present an overview of recent works aiming at solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a notion of optimal performance in terms of the smallest possible reconstruction error that any reconstruction algorithm can achieve, I will present practical numerical algorithms based on nonlinear reduced models for which we can prove that they can deliver a performance close to optimal. The proposed concepts may be viewed as exploring alternatives to Bayesian inversion in favor of more deterministic notions of accuracy quantification. I will illustrate the performance of the approach on simple benchmark examples and we will also discuss applications of the methodology to biomedical problems which are challenging due to shape variability.

arxiv.org/pdf/2203.07769.pdf arxiv.org/pdf/2009.02687.pdf

data structures and algorithmsmachine learningmathematical physicsinformation theoryoptimization and controldata analysis, statistics and probability

Audience: researchers in the topic

Mathematics, Physics and Machine Learning (IST, Lisbon)

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