DyPSI learns to predict physical fields and plan sensor paths together

Reconstructing a whole flow or temperature field from a handful of measurements requires deciding not only what lies between sensors, but where those sensors should go next. A fixed arrangement can miss a migrating structure. Optimizing each moment separately creates another problem: the best location now may be impossibly far from the best location a moment later.

In a preprint posted on November 4, 2026, Yizhou Zhang and colleagues introduce DyPSI, a system that generates future physical fields and sensor trajectories together, conditioned on historical observations. The central proposal is to learn their relationship across a sequence rather than choose sensor positions independently for each frame.

Putting fields and sensors into one representation

Physical fields and sensor locations have different mathematical forms. A temperature field assigns a value across a spatial domain; a sensor arrangement is a short list of coordinates. DyPSI bridges that mismatch by turning each sensor location into a smooth Gaussian-shaped bump. Together, those bumps form a Sensor Position Field: a representation of the sensing arrangement, not an additional physical quantity.

The model then compresses the physical field and this sensor-position field using a shared Functional Tucker representation. In accessible terms, both are expressed through common spatial building blocks, with separate coefficients carrying their specific information. A diffusion model learns to recover the combined representation from noisy versions, generating both modalities within one model.

To encourage continuity through time, the researchers correlate the training noise between frames using a Matérn-3/2 Gaussian-process kernel. Rather than perturbing every frame independently, this couples the denoising task across time. The authors credit earlier work, SDIFT, for the Functional Tucker and correlated-noise ingredients; DyPSI extends them to make sensor trajectories an output alongside physical fields.

Training also depends on an expensive preparatory step. An offline optimizer uses known field sequences and a pretrained reconstruction model to construct informative trajectories, penalizing irregular motion and violations of speed and acceleration limits. DyPSI learns from these paired fields and paths. At inference, it uses historical observations without future ground truth or test-time trajectory optimization.

What the benchmarks show

The researchers evaluate turbulent channel flow, sea-surface temperature from the GLORYS12 reanalysis, and simulated pressure over a three-dimensional car surface. These cover regular grids, an ocean domain with land excluded, and an irregular mesh. The temperature model trains on daily snapshots from 1993–2019 and is tested on 2020–2021.

Performance is measured with relative L2 error, which compares the size of reconstruction mistakes with the size of the reference field. Against the optimized static PhySense-opt baseline, the authors report error reductions of 10.87–15.35% for turbulence, 8.43–9.84% for sea temperature, and 17.47–19.43% for car aerodynamics across the tested sensor budgets.

With 50 turbulence sensors, for example, error falls from 0.1558 for static placement to 0.1352 for DyPSI. Experiments use five independent training runs, with variability and paired significance tests reported in the appendix.

Ablations support the design choices in one tested setting. For turbulence with 50 sensors, replacing independent noise with Matérn-3/2-correlated noise lowers error from 0.1515 to 0.1352 and reduces the reported trajectory-irregularity measure. Joint generation also outperforms separate diffusion models sharing only a history encoder.

Smoother does not mean guaranteed feasible

DyPSI does not beat every comparator on reconstruction accuracy. An oracle that optimizes each future frame using ground truth achieves lower errors, but violates the speed limit in 89% of transitions for turbulence and 75% for sea temperature. DyPSI reduces those rates to 8% and 4%, respectively—not zero.

Its advantage is a trade-off: generating a 64-frame sequence takes 1.9 seconds for the reported turbulence setting and 2.1 seconds for sea temperature, compared with hundreds or more than a thousand seconds for the oracle optimizers. Those timings are reported on an NVIDIA A100-80GB GPU.

The theory likewise has boundaries. One analysis connects idealized denoising risk to accumulated posterior uncertainty under Gaussian assumptions. Another characterizes trajectory variation under a Gaussian-process prior. Neither proves that the deployed neural sampler always produces feasible motion.

The evaluation is history-conditioned and open-loop, not a demonstrated sensing cycle that repeatedly collects new measurements and replans. The authors also identify teacher dependence, possible unreliability under unfamiliar dynamics or strongly non-Gaussian noise, and the omission of full platform dynamics such as ocean currents. DyPSI therefore provides benchmark evidence for jointly learning reconstruction and sensor motion, rather than a demonstrated guarantee of autonomous operation.