# Goal-Oriented Optimal Design of Experiments for Large-Scale Bayesian Linear Inverse Problems

arXiv: https://arxiv.org/abs/1802.06517 · HTML: https://mlsanity.com/paper/1802.06517/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2018.

## Built on by (most cited first, 19 of 19)

- [Goal-Oriented Bayesian Optimal Experimental Design for Nonlinear Models using Markov Chain Monte Carlo](https://mlsanity.com/paper/2403.18072/) (2024)
- [Variational Sequential Optimal Experimental Design using Reinforcement Learning](https://mlsanity.com/paper/2306.10430/) (2023)
- [Expected information gain estimation via density approximations: Sample allocation and dimension reduction](https://mlsanity.com/paper/2411.08390/) (2024)
- [Uncertainty Quantification and Experimental Design for Large-Scale Linear Inverse Problems under Gaussian Process Priors](https://mlsanity.com/paper/2109.03457/) (2021)
- [Nonlinear Bayesian optimal experimental design using logarithmic Sobolev inequalities](https://mlsanity.com/paper/2402.15053/) (2024)
- [Coupled Input-Output Dimension Reduction: Application to Goal-oriented Bayesian Experimental Design and Global Sensitivity Analysis](https://mlsanity.com/paper/2406.13425/) (2024)
- [A Likelihood-Free Approach to Goal-Oriented Bayesian Optimal Experimental Design](https://mlsanity.com/paper/2408.09582/) (2024)
- [Goal-Oriented Sequential Bayesian Experimental Design for Causal Learning](https://mlsanity.com/paper/2507.07359/) (2025)
- [Goal-oriented Uncertainty Quantification for Inverse Problems via Variational Encoder-Decoder Networks](https://mlsanity.com/paper/2304.08324/) (2023)
- [Robust A-Optimal Experimental Design for Bayesian Inverse Problems](https://mlsanity.com/paper/2305.03855/) (2023)
- [Probabilistic Approach to Black-Box Binary Optimization with Budget Constraints: Application to Sensor Placement](https://mlsanity.com/paper/2406.05830/) (2024)
- [Sequential Bayesian Optimal Experimental Design in Infinite Dimensions via Policy Gradient Reinforcement Learning](https://mlsanity.com/paper/2601.05868/) (2026)
- [Stochastic Learning Approach to Binary Optimization for Optimal Design of Experiments](https://mlsanity.com/paper/2101.05958/) (2021)
- [Neural Optimal Design of Experiment for Inverse Problems](https://mlsanity.com/paper/2512.23763/) (2025)
- [A Probabilistic Approach to Trajectory-Based Optimal Experimental Design](https://mlsanity.com/paper/2601.11473/) (2026)
- [Goal-driven Bayesian Optimal Experimental Design for Robust Decision-Making Under Model Uncertainty](https://mlsanity.com/paper/2605.26093/) (2026)
- [ShaplEIG: Bayesian Experimental Design for Shapley Value Estimation](https://mlsanity.com/paper/2606.02247/) (2026)
- [A Decision-Theoretic View of Test-Time Training: When, How Far, and Which Directions to Adapt](https://mlsanity.com/paper/2606.15569/) (2026)
- [Counterfactual Evaluation of Temporal Observation Protocols](https://mlsanity.com/paper/2608.22221/) (2026)

## Abstract (arXiv)

We develop a framework for goal-oriented optimal design of experiments (GOODE) for large-scale Bayesian linear inverse problems governed by PDEs. This framework differs from classical Bayesian optimal design of experiments (ODE) in the following sense: we seek experimental designs that minimize the posterior uncertainty in the experiment end-goal, e.g., a quantity of interest (QoI), rather than the estimated parameter itself. This is suitable for scenarios in which the solution of an inverse problem is an intermediate step and the estimated parameter is then used to compute a QoI. In such problems, a GOODE approach has two benefits: the designs can avoid wastage of experimental resources by a targeted collection of data, and the resulting design criteria are computationally easier to evaluate due to the often low-dimensionality of the QoIs. We present two modified design criteria, A-GOODE and D-GOODE, which are natural analogues of classical Bayesian A- and D-optimal criteria. We analyze the connections to other ODE criteria, and provide interpretations for the GOODE criteria by using tools from information theory. Then, we develop an efficient gradient-based optimization framework for solving the GOODE optimization problems. Additionally, we present comprehensive numerical experiments testing the various aspects of the presented approach. The driving application is the optimal placement of sensors to identify the source of contaminants in a diffusion and transport problem. We enforce sparsity of the sensor placements using an ℓ1-norm penalty approach, and propose a practical strategy for specifying the associated penalty parameter.