DyPSI: Dynamic Physics Sensing via Joint Field and Sensor-Trajectory Generation

Physics sensing in evolving environments requires reconstructing dense spatiotemporal fields from sparse observations while adapting where future observations should be collected. Existing reconstruction and sensor-placement methods have made substantial progress, but they typically rely on static sensing assumptions: they either use a single layout across all frames or optimize placements independently at each frame, which limits their ability to produce temporally coherent sensing trajectories. We introduce DyPSI, a dynamic physics sensing framework that formulates this problem as the joint generation of future fields and sensor trajectories conditioned on historical observations. DyPSI lifts discrete sensor coordinates into continuous Sensor Position Fields, encodes fields and sensing configurations with a shared Functional Tucker representation, and trains a joint diffusion model to generate future fields and sensing trajectories simultaneously in the resulting latent space. A Gaussian-process temporal kernel correlates the perturbation injected during diffusion training, biasing the denoiser toward temporally smooth recoveries, and we further provide an analysis linking the EDM training objective to a sequence-aggregated A-optimality criterion and a kernel-induced bound on discrete trajectory variation. Experiments on turbulent flow, GLORYS12 sea-surface temperature, and 3D car aerodynamics show that DyPSI consistently outperforms static and frame-wise placement strategies, with substantial error reduction under tight sensor budgets. The code is available at https://github.com/mengqi132/DyPSI.