Optimal Sensor Placement via Graph-constrained Flow Matching

Abstract

Optimal sensor placement is a fundamental problem in graph signal processing (GSP), where a limited number of sensors are deployed to reconstruct a continuous signal field. Existing GSP methods rely on combinatorial optimization over discretized graphs, resulting in high computational cost and sensor locations restricted to graph vertices. We reformulate sensor placement as a continuous-space generative modeling problem. An offline GSP optimization routine first generates training samples of optimal sensor configurations, from which a flow matching (FM) model learns their distribution. At inference, the learned velocity field directly generates continuous sensor coordinates, eliminating online combinatorial optimization. We further develop a permutation-invariant conditional generation framework for deployment with fixed anchor sensors. Experiments on a realistic radio propagation simulator demonstrate the effectiveness of the proposed framework for sensor placement.