# Accurate, scalable, and efficient Bayesian optimal experimental design with derivative-informed neural operators

arXiv: https://arxiv.org/abs/2312.14810 · HTML: https://mlsanity.com/paper/2312.14810/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2023.

## Built on by (most cited first, 10 of 10)

- [Derivative-informed neural operator acceleration of geometric MCMC for infinite-dimensional Bayesian inverse problems](https://mlsanity.com/paper/2403.08220/) (2024)
- [LazyDINO: Fast, scalable, and efficiently amortized Bayesian inversion via structure-exploiting and surrogate-driven measure transport](https://mlsanity.com/paper/2411.12726/) (2024)
- [Variationally correct operator learning: Reduced basis neural operator with a posteriori error estimation](https://mlsanity.com/paper/2512.21319/) (2025)
- [Bayesian Experimental Design for Model Discrepancy Calibration: An Auto-Differentiable Ensemble Kalman Inversion Approach](https://mlsanity.com/paper/2504.20319/) (2025)
- [Deep Hilbert--Galerkin Methods for Infinite-Dimensional PDEs and Optimal Control](https://mlsanity.com/paper/2603.19463/) (2026)
- [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)
- [Toward AI-Driven Digital Twins for Metropolitan Floods: A Conditional Latent Dynamics Network Surrogate of the Shallow Water Equations](https://mlsanity.com/paper/2605.13761/) (2026)
- [Bayesian Experimental Design for Model Discrepancy Calibration: A Rivalry between Kullback--Leibler Divergence and Wasserstein Distance](https://mlsanity.com/paper/2601.16425/) (2026)
- [Universal Approximation of Nonlinear Operators and Their Derivatives](https://mlsanity.com/paper/2605.15285/) (2026)

## Abstract (arXiv)

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 parameter-to-observable (PtO) map is expensive to evaluate, the parameters are high-dimensional, and the optimization for sensor selection is combinatorial and high-dimensional. To address these challenges, we develop an accurate, scalable, and efficient computational framework based on derivative-informed neural operators (DINO). We propose to use derivative-informed dimension reduction to reduce the parameter dimensions, based on which we train DINO with derivative information as an accurate and efficient surrogate for the PtO map and its derivative. Moreover, we derive DINO-enabled efficient formulations in computing the maximum a posteriori (MAP) point, the eigenvalues of approximate posterior covariance, and three commonly used optimality criteria for the OED problems. Furthermore, we provide detailed error analysis for the approximations of the MAP point, the eigenvalues, and the optimality criteria. We also propose a modified swapping greedy algorithm for the sensor selection optimization and demonstrate that the proposed computational framework is scalable to preserve the accuracy for increasing parameter dimensions and achieves high computational efficiency, with an over 1000× speedup accounting for both offline construction and online evaluation costs, compared to high-fidelity Bayesian OED solutions for a three-dimensional nonlinear convection-diffusion-reaction example with tens of thousands of parameters.