Data-Induced Interactions of Sparse Sensors Using Statistical Physics

TL;DR

This paper models the interactions of sparse sensors in high-dimensional data using a statistical physics approach, specifically an Ising model, to improve sensor placement, reconstruction accuracy, and uncertainty quantification.

Contribution

It introduces a novel Ising model framework for sensor interaction landscapes and a regularized reconstruction method that enhances sparse sensing performance.

Findings

Recast sensor placement landscape as an Ising model

Regularized reconstruction reduces error with few sensors

Provides uncertainty quantification for sparse sensing

Abstract

Large-dimensional empirical data in science and engineering frequently have a low-rank structure and can be represented as a combination of just a few eigenmodes. Because of this structure, we can use just a few spatially localized sensor measurements to reconstruct the full state of a complex system. The quality of this reconstruction, especially in the presence of sensor noise, depends significantly on the spatial configuration of the sensors. Multiple algorithms based on gappy interpolation and QR factorization have been proposed to optimize sensor placement. Here, instead of an algorithm that outputs a single "optimal" sensor configuration, we take a statistical mechanics view to compute the full landscape of sensor interactions induced by the training data. The two key advances of this paper are the recasting of the sensor placement landscape in an Ising model form and a regularized reconstruction that significantly decreases reconstruction error for few sensors. In addition, we provide first uncertainty quantification of the sparse sensing reconstruction and open questions about the shape of reconstruction risk curve. Mapping out these data-induced sensor interactions allows combining them with external selection criteria and anticipating sensor replacement impacts.