Designing an Optimal Sensor Network via Minimizing Information Loss
Daniel Waxman, Fernando Llorente, Katia Lamer, Petar M. Djurić
TL;DR
The paper tackles sensor placement for spatiotemporal processes by leveraging physics-based simulations within a Bayesian experimental design framework. It introduces the Minimizing Information Loss (MIL) criterion, grounded in a sparse variational Gaussian process (ST-SVGP) backbone, to select sensor locations that preserve information captured by simulators while enabling scalable, continuous optimization. MIL connects to inducing-point variational inference, allowing joint learning of hyperparameters and sensor placements, and accommodates practicalities like existing sensors and sensor removal. A Phoenix, Arizona case study using the Weather Research and Forecasting model demonstrates that MIL-based designs with relatively few sensors achieve superior predictive performance and calibrated uncertainty compared with traditional baselines, highlighting the approach’s potential for climate and physics-informed sensing tasks.
Abstract
Optimal experimental design is a classic topic in statistics, with many well-studied problems, applications, and solutions. The design problem we study is the placement of sensors to monitor spatiotemporal processes, explicitly accounting for the temporal dimension in our modeling and optimization. We observe that recent advancements in computational sciences often yield large datasets based on physics-based simulations, which are rarely leveraged in experimental design. We introduce a novel model-based sensor placement criterion, along with a highly-efficient optimization algorithm, which integrates physics-based simulations and Bayesian experimental design principles to identify sensor networks that "minimize information loss" from simulated data. Our technique relies on sparse variational inference and (separable) Gauss-Markov priors, and thus may adapt many techniques from Bayesian experimental design. We validate our method through a case study monitoring air temperature in Phoenix, Arizona, using state-of-the-art physics-based simulations. Our results show our framework to be superior to random or quasi-random sampling, particularly with a limited number of sensors. We conclude by discussing practical considerations and implications of our framework, including more complex modeling tools and real-world deployments.