Abstract
arXiv:2510.03589v2 Announce Type: replace Abstract: Spatio-temporal sensor data in real-world systems is often sparse, noisy, and irregular, making latent field reconstruction fundamentally underconstrained. Under extreme sparsity, multiple physically plausible fields may remain consistent with the same observations, requiring models to rely on inductive biases about locality, transport, and spatial regularity. In such regimes, reliable reconstruction is concentrated around the observational support induced by the sensor network, making sensor-space modeling a more identifiable objective than unconstrained global field recovery. We introduce FieldFormer, a mesh-free transformer architecture for locality-aware sensor-space modeling in persistent sensor networks. For each query, FieldFormer aggregates local evidence using learnable velocity-scaled offsets that adapt neighborhood geometry to spatio-temporal dependencies. Neighborhoods are constructed as fixed maximal sparse contexts over nearby sensors and bounded temporal windows, enabling stable and scalable inference under extreme sparsity. A local transformer encoder integrates neighborhood information, while a coordinate-based neural field formulation supports mesh-free prediction. We evaluate FieldFormer on five synthetic and real-world benchmarks, including anisotropic heat diffusion, shallow-water dynamics, atmospheric transport, and pollution monitoring datasets. Results show that locality-aware reconstruction provides strong advantages when local domains of dependence remain observed, enabling FieldFormer to consistently outperform state-of-the-art baselines on sparse sensor-space prediction tasks.