# Neural Optimal Design of Experiment for Inverse Problems

arXiv: https://arxiv.org/abs/2512.23763 · HTML: https://mlsanity.com/paper/2512.23763/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 53 references that are in the map.
- First posted on arXiv 28 Dec 2025.

## Builds on (most cited first, 13 of 13)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Goal-Oriented Optimal Design of Experiments for Large-Scale Bayesian Linear Inverse Problems](https://mlsanity.com/paper/1802.06517/) (2018)
- [Variational Bayesian Optimal Experimental Design with Normalizing Flows](https://mlsanity.com/paper/2404.13056/) (2024)
- [Probabilistic Bayesian optimal experimental design using conditional normalizing flows](https://mlsanity.com/paper/2402.18337/) (2024)
- [A-optimal design of experiments for infinite-dimensional Bayesian linear inverse problems with regularized ℓ0-sparsification](https://mlsanity.com/paper/1308.4084/) (2013)
- [Design Amortization for Bayesian Optimal Experimental Design](https://mlsanity.com/paper/2210.03283/) (2022)
- [Paired Autoencoders for Likelihood-free Estimation in Inverse Problems](https://mlsanity.com/paper/2405.13220/) (2024)
- [Good Things Come in Pairs: Paired Autoencoders for Inverse Problems](https://mlsanity.com/paper/2505.06549/) (2025)
- [Deep Optimal Experimental Design for Parameter Estimation Problems](https://mlsanity.com/paper/2406.14003/) (2024)
- [A control-oriented approach to optimal sensor placement](https://mlsanity.com/paper/2502.15062/) (2025)
- [A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarios](https://mlsanity.com/paper/2512.23748/) (2025)

## Abstract (arXiv)

We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural reconstruction model and a fixed-budget set of continuous design variables representing sensor locations, sampling times, or measurement angles, within a single optimization loop. By optimizing measurement locations directly rather than weighting a dense grid of candidates, the proposed approach enforces sparsity by design, eliminates the need for l1 tuning, and substantially reduces computational complexity. We validate NODE on an analytically tractable exponential growth benchmark, on MNIST image sampling, and illustrate its effectiveness on a real world sparse view X ray CT example. In all cases, NODE outperforms baseline approaches, demonstrating improved reconstruction accuracy and task-specific performance.