From 29 August–1 September 2017, the Alan Turing Institute will host a summer school on Mathematical Aspects of Inverse Problems organised by Claudia Schillings (Mannheim) and Aretha Teckentrup (Edinburgh and Alan Turing Institute), two of my former colleagues at the University of Warwick. The invited lecturers are:
- Masoumeh Dashti (Sussex): Bayesian Approach to Inverse Problems
- Michela Ottobre (Maxwell Institute, Edinburgh): Hamiltonian Monte Carlo
- Carola-Bibiane Schönlieb and Clarice Poon (Cambridge): A Comparison of Variational Methods and Deep Neural Networks for Inverse Problems
- Alison Fowler (Reading): The Value of Observations for Numerical Weather Prediction
In two weeks Hanne Kekkonen (University of Warwick) will give a talk on “Large noise in variational regularisation”.
Time and Place. Monday 12 June 2017, 11:00–12:00, ZIB Seminar Room 2006, Zuse Institute Berlin, Takustraße 7, 14195 Berlin
Abstract. We consider variational regularisation methods for inverse problems with large noise, which is in general unbounded in the image space of the forward operator. We introduce a Banach space setting that allows to define a reasonable notion of solutions for more general noise in a larger space provided one has sufficient mapping properties of the forward operator. As an example we study the particularly important cases of one- and p-homogeneous regularisation functionals. As a natural further step we study stochastic noise models and in particular white noise, for which we derive error estimates in terms of the expectation of the Bregman distance. As an example we study total variation prior. This is joint work with Martin Burger and Tapio Helin.
Published on Friday 26 May 2017 at 17:00 UTC #event
Next week's colloquium at the Einstein Center for Mathematics Berlin will be on the topic of Optimisation. The speakers will be:
- Sebastian Sager (Magdeburg): Mathematical Optimization for Clinical Diagnosis and Decision Support
- Werner Römisch (HU Berlin): Stochastic Optimization: Complexity and Numerical Methods
- Karl Kunisch (Graz): Sparsity in PDE-constrained Open and Closed Loop Control
Time and Place. Friday 20 January 2017, 14:00–17:00, Humboldt-Universität zu Berlin, Main Building Room 2.097, Unter den Linden 6, 10099 Berlin
Published on Tuesday 10 January 2017 at 12:00 UTC #event
Next week Jon Cockayne (University of Warwick) will give a talk on “Probabilistic Numerics for Partial Differential Equations”.
Time and Place. Friday 14 October 2016, 12:00–13:00, ZIB Seminar Room 2006, Zuse Institute Berlin, Takustraße 7, 14195 Berlin
Abstract. Probabilistic numerics is an emerging field which constructs probability measures to capture uncertainty arising from the discretisation which is often necessary to solve complex problems numerically. We explore probabilistic numerical methods for Partial differential equations (PDEs). We phrase solution of PDEs as a statistical inference problem, and construct probability measures which quantify the epistemic uncertainty in the solution resulting from the discretisation .
We analyse these probability measures in the context of Bayesian inverse problems, parameter inference problems whose dynamics are often constrained by a system of PDEs. Sampling from parameter posteriors in such problems often involves replacing an exact likelihood with an approximate one, in which a numerical approximation is substituted for the true solution of the PDE. Such approximations have been shown to produce biased and overconfident posteriors when error in the forward solver is not tightly controlled. We show how the uncertainty from a probabilistic forward solver can be propagated into the parameter posteriors, thus permitting the use of coarser discretisations while still producing valid statistical inferences.
 Jon Cockayne, Chris Oates, Tim Sullivan, and Mark Girolami. “Probabilistic Meshless Methods for Partial Differential Equations and Bayesian Inverse Problems.” arXiv preprint, 2016. arXiv:1605.07811