# Large-scale Bayesian optimal experimental design with derivative-informed projected neural network

arXiv: https://arxiv.org/abs/2201.07925 · HTML: https://mlsanity.com/paper/2201.07925/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jan 2022.

## Built on by (most cited first, 17 of 17)

- [Derivative-Informed Neural Operator: An Efficient Framework for High-Dimensional Parametric Derivative Learning](https://mlsanity.com/paper/2206.10745/) (2022)
- [Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems](https://mlsanity.com/paper/2210.03008/) (2022)
- [Efficient PDE-Constrained optimization under high-dimensional uncertainty using derivative-informed neural operators](https://mlsanity.com/paper/2305.20053/) (2023)
- [Residual-Based Error Corrector Operator to Enhance Accuracy and Reliability of Neural Operator Surrogates of Nonlinear Variational Boundary-Value Problems](https://mlsanity.com/paper/2306.12047/) (2023)
- [Variationally correct operator learning: Reduced basis neural operator with a posteriori error estimation](https://mlsanity.com/paper/2512.21319/) (2025)
- [A Framework for Strategic Discovery of Credible Neural Network Surrogate Models under Uncertainty](https://mlsanity.com/paper/2403.08901/) (2024)
- [Active Learning of Model Discrepancy with Bayesian Experimental Design](https://mlsanity.com/paper/2502.05372/) (2025)
- [Expected information gain estimation via density approximations: Sample allocation and dimension reduction](https://mlsanity.com/paper/2411.08390/) (2024)
- [Coupled Input-Output Dimension Reduction: Application to Goal-oriented Bayesian Experimental Design and Global Sensitivity Analysis](https://mlsanity.com/paper/2406.13425/) (2024)
- [Bayesian Experimental Design for Model Discrepancy Calibration: An Auto-Differentiable Ensemble Kalman Inversion Approach](https://mlsanity.com/paper/2504.20319/) (2025)
- [A reduced-order derivative-informed neural operator for subsurface fluid-flow](https://mlsanity.com/paper/2509.13620/) (2025)
- [Active Subspaces in Infinite Dimension](https://mlsanity.com/paper/2510.11871/) (2025)
- [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)
- [Accelerated Bayesian Optimal Experimental Design via Conditional Density Estimation and Informative Data](https://mlsanity.com/paper/2507.15235/) (2025)
- [Approximation of differential entropy in Bayesian optimal experimental design](https://mlsanity.com/paper/2510.00734/) (2025)
- [Bayesian Experimental Design for Model Discrepancy Calibration: A Rivalry between Kullback--Leibler Divergence and Wasserstein Distance](https://mlsanity.com/paper/2601.16425/) (2026)

## Abstract (arXiv)

We address the solution of large-scale Bayesian optimal experimental design (OED) problems governed by partial differential equations (PDEs) with infinite-dimensional parameter fields. The OED problem seeks to find sensor locations that maximize the expected information gain (EIG) in the solution of the underlying Bayesian inverse problem. Computation of the EIG is usually prohibitive for PDE-based OED problems. To make the evaluation of the EIG tractable, we approximate the (PDE-based) parameter-to-observable map with a derivative-informed projected neural network (DIPNet) surrogate, which exploits the geometry, smoothness, and intrinsic low-dimensionality of the map using a small and dimension-independent number of PDE solves. The surrogate is then deployed within a greedy algorithm-based solution of the OED problem such that no further PDE solves are required. We analyze the EIG approximation error in terms of the generalization error of the DIPNet and show they are of the same order. Finally, the efficiency and accuracy of the method are demonstrated via numerical experiments on OED problems governed by inverse scattering and inverse reactive transport with up to 16,641 uncertain parameters and 100 experimental design variables, where we observe up to three orders of magnitude speedup relative to a reference double loop Monte Carlo method.