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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

We analyze a goal-oriented adaptive algorithm that aims to efficiently compute the quantity of interest $G(u^\star)$ with a linear goal functional $G$ and the solution $u^\star$ to a general second-order nonsymmetric linear elliptic partial…

Numerical Analysis · Mathematics 2024-11-18 Philipp Bringmann , Maximilian Brunner , Dirk Praetorius , Julian Streitberger

We use the ideas of goal-oriented error estimation and adaptivity to design and implement an efficient adaptive algorithm for approximating linear quantities of interest derived from solutions to elliptic partial differential equations…

Numerical Analysis · Mathematics 2019-03-21 Alex Bespalov , Dirk Praetorius , Leonardo Rocchi , Michele Ruggeri

We present a mathematical framework and computational methods to optimally design a finite number of sequential experiments. We formulate this sequential optimal experimental design (sOED) problem as a finite-horizon partially observable…

Machine Learning · Computer Science 2024-03-28 Wanggang Shen , Xun Huan

Questions of `how best to acquire data' are essential to modeling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates…

Methodology · Statistics 2026-05-01 Xun Huan , Jayanth Jagalur , Youssef Marzouk

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

In this work, we describe a new approach that uses variational encoder-decoder (VED) networks for efficient goal-oriented uncertainty quantification for inverse problems. Contrary to standard inverse problems, these approaches are…

Numerical Analysis · Mathematics 2023-10-02 Babak Maboudi Afkham , Julianne Chung , Matthias Chung

Optimal experimental design (OED) aims to choose the observations in an experiment to be as informative as possible, according to certain statistical criteria. In the linear case (when the observations depend linearly on the unknown…

Numerical Analysis · Mathematics 2026-02-25 Ruhui Jin , Martin Guerra , Qin Li , Stephen Wright

In computational inverse problems, the optimal experimental design (OED) problem seeks the best locations in time and space at which to take measurements. We investigate the nonlinear OED problem in the context of continuously-indexed…

Numerical Analysis · Mathematics 2025-06-10 Ruhui Jin , Qin Li , Stephen O. Mussmann , Stephen J. Wright

We consider optimal sensor placement for hyper-parameterized linear Bayesian inverse problems, where the hyper-parameter characterizes nonlinear flexibilities in the forward model, and is considered for a range of possible values. This…

Numerical Analysis · Mathematics 2020-11-24 Nicole Aretz-Nellesen , Peng Chen , Martin A. Grepl , Karen Veroy

We consider optimal design of PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We focus on the A-optimal design criterion, defined as the average posterior variance and quantified by the trace of the…

Numerical Analysis · Mathematics 2020-04-02 Elizabeth Herman , Alen Alexanderian , Arvind K. Saibaba

We apply optimum experimental design (OED) to organic semiconductors modeled by the extended Gaussian disorder model (EGDM) which was developed by Pasveer et al. We present an extended Gummel method to decouple the corresponding system of…

Mathematical Physics · Physics 2015-06-12 Christoph Karl Felix Weiler , Stefan Körkel

In this paper optimal experimental designs for inverse quadratic regression models are determined. We consider two different parameterizations of the model and investigate local optimal designs with respect to the $c$-, $D$- and…

Methodology · Statistics 2008-09-30 H. Dette , C. Kiss

Designing learnable information-theoretic objectives for robot exploration remains challenging. Such objectives aim to guide exploration toward data that reduces uncertainty in model parameters, yet it is often unclear what information the…

Robotics · Computer Science 2026-05-13 Youwei Yu , Jionghao Wang , Zhengming Yu , Wenping Wang , Lantao Liu

Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected…

Machine Learning · Statistics 2020-01-15 Adam Foster , Martin Jankowiak , Eli Bingham , Paul Horsfall , Yee Whye Teh , Tom Rainforth , Noah Goodman

We consider optimal experimental design (OED) problems in selecting the most informative observation sensors to estimate model parameters in a Bayesian framework. Such problems are computationally prohibitive when the…

Computational Engineering, Finance, and Science · Computer Science 2024-09-10 Jinwoo Go , Peng Chen

We deal with the numerical solution of linear partial differential equations (PDEs) with focus on the goal-oriented error estimates including algebraic errors arising by an inaccurate solution of the corresponding algebraic systems. The…

Numerical Analysis · Mathematics 2020-01-08 Vít Dolejší , Petr Tichý

Consider the problem of finding an optimal value of some objective functional subject to constraints over numerical domain. This type of problem arises frequently in practical engineering tasks. Nowdays almost all general methods for…

Optimization and Control · Mathematics 2019-09-13 Sergey Karpukhin

Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…

Machine Learning · Computer Science 2026-02-18 Jens U. Kreber , Christian Weißenfels , Joerg Stueckler

We address an optimal sensor placement problem through Bayesian experimental design for seismic full waveform inversion for the recovery of the associated moment tensor. The objective is that of optimally choosing the location of the…