# A-optimal design of experiments for infinite-dimensional Bayesian linear inverse problems with regularized ℓ0-sparsification

arXiv: https://arxiv.org/abs/1308.4084 · HTML: https://mlsanity.com/paper/1308.4084/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2013.

## Built on by (most cited first, 8 of 8)

- [Derivative-Informed Neural Operator: An Efficient Framework for High-Dimensional Parametric Derivative Learning](https://mlsanity.com/paper/2206.10745/) (2022)
- [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)
- [Optimal Experimental Design for Reliable Learning of History-Dependent Constitutive Laws](https://mlsanity.com/paper/2603.12365/) (2026)
- [Stochastic Learning Approach to Binary Optimization for Optimal Design of Experiments](https://mlsanity.com/paper/2101.05958/) (2021)
- [Scalable method for Bayesian experimental design without integrating over posterior distribution](https://mlsanity.com/paper/2306.17615/) (2023)
- [Neural Optimal Design of Experiment for Inverse Problems](https://mlsanity.com/paper/2512.23763/) (2025)

## Abstract (arXiv)

We present an efficient method for computing A-optimal experimental designs for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we address the problem of optimizing the location of sensors (at which observational data are collected) to minimize the uncertainty in the parameters estimated by solving the inverse problem, where the uncertainty is expressed by the trace of the posterior covariance. Computing optimal experimental designs (OEDs) is particularly challenging for inverse problems governed by computationally expensive PDE models with infinite-dimensional (or, after discretization, high-dimensional) parameters. To alleviate the computational cost, we exploit the problem structure and build a low-rank approximation of the parameter-to-observable map, preconditioned with the square root of the prior covariance operator. This relieves our method from expensive PDE solves when evaluating the optimal experimental design objective function and its derivatives. Moreover, we employ a randomized trace estimator for efficient evaluation of the OED objective function. We control the sparsity of the sensor configuration by employing a sequence of penalty functions that successively approximate the ℓ0-"norm"; this results in binary designs that characterize optimal sensor locations. We present numerical results for inference of the initial condition from spatio-temporal observations in a time-dependent advection-diffusion problem in two and three space dimensions. We find that an optimal design can be computed at a cost, measured in number of forward PDE solves, that is independent of the parameter and sensor dimensions. We demonstrate numerically that ℓ0-sparsified experimental designs obtained via a continuation method outperform ℓ1-sparsified designs.