Georg Stadler

OED Mini course at the University of Goettingen, June 28–30, 2023

Material from lectures:

1. Part I (Jun 28): [Slides with iPad notes] Topics: Deterministic vs. Bayesian approach to inverse problems; IP examples; a concrete example
2. Part II (Jun 29): [Slides Part1], [Slides Part2] Topics: Large-scale linear and linearized problems, low rank approximations, Gaussian distributions in infinite dimensions, A-optimal sensor placement. Gaussian random fields and PDE operators: [Code example]; Inverse adv-diff initial condition inversion example: [hippylib code]
3. Part III (Jun 30): [Slides] Topics: Computational aspects, OED under model error, OED for nonlinear problems.

Literature referred to in the lecture:

Papers on Bayesian IP:

• [ABL+] Estimating Parameters in Physical Models through Bayesian Inversion: A Complete Example by Moritz Allmaras, Wolfgang Bangerth, Jean Marie Linhart, Javier Polanco, Fang Wang, Kainan Wang, Jennifer Webster and Sarah Zedler, SIREV, 2013. [link]
• [S] Inverse problems: A Bayesian perspective by Andrew Stuart, Acta Numerica 19, 2010. [link]
• [BGMS] A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion by Tan Bui-Thanh, Omar Ghattas, James Martin, and Georg Stadler, SISC 2013. [link]

Papers on Optimal Experimental Design:

• [APSG] A-Optimal Design of Experiments for Infinite-Dimensional Bayesian Linear Inverse Problems with Regularized l0-Sparsification by Alen Alexanderian, Noemi Petra, Georg Stadler, and Omar Ghattas, SISC, 2014 [link]
• [A] Optimal experimental design for infinite-dimensional Bayesian inverse problems governed by PDEs: a review by Alen Alexanderian, Inverse Problems, 2021. [link]
• [KAS] Optimal experimental design under irreducible uncertainty for inverse problems governed by PDEs by Karina Koval, Alan Alexanderian and Georg Stadler, Inverse Problems 36, 2020. [link]

Further reading on OED:

• [HY] Sequential Bayesian optimal experimental design via approximate dynamic programming by Xun Huan, Youssef M. Marzouk, 2016. [link]
• [ANP] Optimal design of large-scale nonlinear Bayesian inverse problems under model uncertainty by Alen Alexanderian, Ruanui Nicholson, Noemi Petra, 2022. [link]
• [AGG] On Bayesian A-and D-optimal experimental designs in infinite dimensions, by Alen Alexanderian, Philip J Gloor, Omar Ghattas, Bayesian Analysis, 2016. [link]

Software on Bayesian IP and OED

• [hippylib] Library for Bayesian IP involving PDEs building on Fenics. [https://hippylib.github.io/]
• [PyOED] An Extensible Suite for Data Assimilation and Model-Constrained Optimal Design of Experiments by Ahmed Attia, Shady E. Ahmed, 2023. [link to paper]

© G.St.