Data-Driven Methods for Sparse Sensor Problems in Spatiotemporal Systems

Abstract

Spatiotemporal systems across various fields are often complex and high-dimensional. This thesis addresses several key problems related to sparse sensing, focusing on the exploitation of low-dimensional structures within high-dimensional data to optimize limited sensor usage for system understanding. We first examine the power grid system and optimize PMU sensor placements such that the dynamical modes and their properties inferred from measurements can be used to characterize faults at different locations. Then, we shift our attention to mobile sensor applications and their associated challenges. Leveraging system observability as a critical metric for path planning, we employ a Kalman filter estimator to optimize sensor trajectories. We introduce a greedy path planning method that enhances the conditioning of system observability along the path, assuming no constraints on sensor movement. We further extend the exploration of mobile sensor path planning by considering the additional complexity of sensor control and movement introduced by background flows. We design an end-to-end model using deep reinforcement learning to simultaneously optimize path decisions and sensor control for mobile sensors. Lastly, we delve into nonlinear reconstruction for mobile sensors using decoder networks and address the challenges of long time dependency and sensitivity to measurement noise. Our proposed robust state space decoder model, with intricately designed parameter initialization, demonstrates improved performance compared to existing estimation models.