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Bayesian optimal experimental design (OED) seeks to conduct the most informative experiment under budget constraints to update the prior knowledge of a system to its posterior from the experimental data in a Bayesian framework. Such…

Machine Learning · Computer Science 2024-02-29 Rafael Orozco , Felix J. Herrmann , Peng Chen

This work considers Bayesian experimental design for the inverse boundary value problem of linear elasticity in a two-dimensional setting. The aim is to optimize the positions of compactly supported pressure activations on the boundary of…

Numerical Analysis · Mathematics 2023-09-06 Sarah Eberle-Blick , Nuutti Hyvönen

This paper presents a novel framework for goal-oriented optimal static sensor placement and dynamic sensor steering in PDE-constrained inverse problems, utilizing a Bayesian approach accelerated by low-rank approximations. The framework is…

Numerical Analysis · Mathematics 2025-07-09 Marco Mattuschka , Noah An der Lan , Max von Danwitz , Daniel Wolff , Alexander Popp

We present a systematic approach to the optimal placement of finitely many sensors in order to infer a finite-dimensional parameter from point evaluations of the solution of an associated parameter-dependent elliptic PDE. The quality of the…

Optimization and Control · Mathematics 2021-03-30 Ira Neitzel , Konstantin Pieper , Boris Vexler , Daniel Walter

We propose an optimization algorithm to compute the optimal sensor locations in experimental design in the formulation of Bayesian inverse problems, where the parameter-to-observable mapping is described through an integral equation and its…

Computation · Statistics 2019-12-30 Jing Yu , Mihai Anitescu

We consider finite-dimensional Bayesian linear inverse problems with Gaussian priors and additive Gaussian noise models. The goal of this note is to present a simple derivation of the well-known fact that solving the Bayesian D-optimal…

Statistics Theory · Mathematics 2023-12-27 Alen Alexanderian

A model-based optimal experiment design (OED) of nonlinear systems is studied. OED represents a methodology for optimizing the geometry of the parametric joint-confidence regions (CRs), which are obtained in an a posteriori analysis of the…

Optimization and Control · Mathematics 2020-08-14 Anwesh Reddy Gottu Mukkula , Radoslav Paulen

Bayesian Optimal Experimental Design (BOED) is a powerful tool to reduce the cost of running a sequence of experiments. When based on the Expected Information Gain (EIG), design optimization corresponds to the maximization of some…

Machine Learning · Statistics 2025-03-14 Jacopo Iollo , Christophe Heinkelé , Pierre Alliez , Florence Forbes

Optimal experimental design (OED) concerns itself with identifying ideal methods of data collection, e.g.~via sensor placement. The \emph{greedy algorithm}, that is, placing one sensor at a time, in an iteratively optimal manner, stands as…

Optimization and Control · Mathematics 2025-10-15 Christian Aarset

We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the…

Optimization and Control · Mathematics 2026-04-21 Jochen Schmid , Philipp Seufert , Jan Schwientek , Tobias Seidel , Karl-Heinz Küfer

Bayesian optimal experimental design is a sub-field of statistics focused on developing methods to make efficient use of experimental resources. Any potential design is evaluated in terms of a utility function, such as the (theoretically…

Machine Learning · Computer Science 2022-10-21 Noble Kennamer , Steven Walton , Alexander Ihler

Optimal experimental design is a classic topic in statistics, with many well-studied problems, applications, and solutions. The design problem we study is the placement of sensors to monitor spatiotemporal processes, explicitly accounting…

Methodology · Statistics 2026-01-05 Daniel Waxman , Fernando Llorente , Katia Lamer , Petar M. Djurić

Inverse problems are crucial for many applications in science, engineering and medicine that involve data assimilation, design, and imaging. Their solution infers the parameters or latent states of a complex system from noisy data and…

Methodology · Statistics 2026-03-06 Lucas Amoudruz , Sergey Litvinov , Costas Papadimitriou , Petros Koumoutsakos

The \emph{sensor placement problem} for stochastic linear inverse problems consists of determining the optimal manner in which sensors can be employed to collect data. Specifically, one wishes to place a limited number of sensors over a…

Optimization and Control · Mathematics 2025-10-15 Christian Aarset

We study sparse solutions of optimal control problems governed by PDEs with uncertain coefficients. We propose two formulations, one where the solution is a deterministic control optimizing the mean objective, and a formulation aiming at…

Numerical Analysis · Mathematics 2018-11-20 Chen Li , Georg Stadler

These lecture notes summarize various summer schools that I have given on the topic of solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a…

Numerical Analysis · Mathematics 2022-03-16 Olga Mula

Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model that must be estimated. However, high…

Numerical Analysis · Mathematics 2022-10-27 Joseph Hart , Bart van Bloemen Waanders

Data collected from arrays of sensors are essential for informed decision-making in various systems. However, the presence of anomalies can compromise the accuracy and reliability of insights drawn from the collected data or information…

Applications · Statistics 2024-03-19 Katie Buchhorn , Kerrie Mengersen , Edgar Santos-Fernandez , James McGree

We propose a computational approach to constructing exact designs on finite design spaces that are optimal for multiresponse regression experiments under a combination of the standard linear and specific 'sparsity' constraints. The linear…

Methodology · Statistics 2026-02-13 Lenka Filová , Pál Somogyi , Radoslav Harman

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

Applications · Statistics 2015-11-02 Isabell M. Franck , P. S. Koutsourelakis