FieldFormer: Physics-Informed Transformers for Spatio-Temporal Field Reconstruction from Sparse Sensors

• URL: http://arxiv.org/abs/2510.03589v1
• Date: Sat, 04 Oct 2025 00:37:28 GMT
• Title: FieldFormer: Physics-Informed Transformers for Spatio-Temporal Field Reconstruction from Sparse Sensors
• Authors: Ankit Bhardwaj, Ananth Balashankar, Lakshminarayanan Subramanian,
• Abstract summary: We introduce FieldFormer, a transformer-based framework for mesh-free-temporal field reconstruction.<n>For each query, FieldFormer gathers a local neighborhood using a learnable velocity-scaled distance metric.<n>Our results demonstrate that FieldFormer enables accurate (RMSE$10-2$), efficient, and physically consistent field reconstruction from sparse (0.4%-2%) and noisy(10%) data.
• Score: 4.027064713296126
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Spatio-temporal sensor data is often sparse, noisy, and irregular, and existing interpolation or learning methods struggle here because they either ignore governing PDEs or do not scale. We introduce FieldFormer, a transformer-based framework for mesh-free spatio-temporal field reconstruction that combines data-driven flexibility with physics-based structure. For each query, FieldFormer gathers a local neighborhood using a learnable velocity-scaled distance metric, enabling anisotropic adaptation to different propagation regimes. Neighborhoods are built efficiently via per-batch offset recomputation, and refined in an expectation-maximization style as the velocity scales evolve. Predictions are made by a local transformer encoder, and physics consistency is enforced through autograd-based PDE residuals and boundary-specific penalties. Across three benchmarks--a scalar anisotropic heat equation, a vector-valued shallow-water system, and a realistic advection-diffusion pollution simulation--FieldFormer consistently outperforms strong baselines by more than 40%. Our results demonstrate that FieldFormer enables accurate (RMSE$<10^{-2}$), efficient, and physically consistent field reconstruction from sparse (0.4%-2%) and noisy(10%) data.

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