Overcoming "Physics Shock" in Earth Observation A Heteroscedastic Uncertainty Framework for PINN-based Flood Inference

A new Uncertainty-Aware Physics-Informed Neural Network (PINN) framework overcomes "Physics Shock" — catastrophic gradient divergence caused by enforcing rigid flood equations onto noisy satellite radar data — by dynamically relaxing physical constraints in high-noise areas. The probabilistic Attention-Gated FNO-UNet achieved a 25% relative improvement in flood mapping accuracy on the Sen1Floods11 dataset compared to deterministic baselines. The approach provides disaster response agencies with physically consistent, calibrated confidence bounds for real-time flood extent mapping from Synthetic Aperture Radar (SAR) imagery.

arXiv:2605.24106v1 Announce Type: new Abstract: Rapid and accurate flood extent mapping from Remote Sensing data, such as Synthetic Aperture Radar SAR , is critical for operational disaster response, but standard Deep Learning models often produce physically impossible predictions due to a lack of hydrological constraints. While PhysicsInformed Neural Networks PINNs attempt to address this by embedding governing laws directly into the loss function, their application to real-world remote sensing data frequently fails. Enforcing rigid spatial derivatives e.g., the 2D Shallow Water Equations onto unconditioned latent spaces attempting to fit noisy SAR speckle causes catastrophic gradient divergence, a phenomenon we term Physics Shock. In this paper, we propose a novel Uncertainty-Aware PINN framework tailored specifically for applied Earth Observation that addresses this instability. By integrating a dynamic Warm-Start protocol and modeling heteroscedastic aleatoric uncertainty via a negative log-likelihood objective, the network learns to dynamically relax physical constraints in regions of high sensor noise while strictly enforcing them in high-confidence areas. Evaluated on the Sen1Floods11 dataset, our probabilistic Attention-Gated FNO-UNet successfully stabilizes multi-objective optimization, achieving a +25% relative improvement in Intersection over Union IoU compared to deterministic baselines. Furthermore, through Deep Ensembles, we successfully disentangle intrinsic sensor noise from out-of-distribution terrain ignorance, providing operational agencies with highly calibrated, physically consistent confidence bounds for robust disaster mitigation and real-time decision-making.