Neural Optimal Design of Experiment for Inverse Problems

TL;DR

Neural Optimal Design of Experiments (NODE) is a learning-based framework that optimizes sensor placement and measurement strategies directly, improving inverse problem solutions without classical regularization or complex bilevel optimization.

Contribution

NODE introduces a unified, end-to-end trainable approach for optimal experimental design that enforces sparsity by design and reduces computational complexity.

Findings

NODE outperforms baseline methods in accuracy and task performance.

Validated on exponential growth, MNIST sampling, and real X-ray CT data.

Enforces sparsity without l1 regularization or tuning.

Abstract

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.