Uncertainty-Aware PINN Framework Overcomes 'Physics Shock' in Flood Mapping

A new approach tackles the shortcomings of Physics-Informed Neural Networks (PINNs) in the context of Earth observation, particularly in mapping flood extents using Synthetic Aperture Radar (SAR) data. Conventional deep learning techniques frequently yield physically implausible outcomes due to the absence of hydrological constraints. While PINNs strive to integrate governing equations, such as the 2D Shallow Water Equations, into the loss function, the imposition of strict spatial derivatives on noisy SAR speckle results in severe gradient divergence, known as 'Physics Shock.' The Uncertainty-Aware PINN framework proposes a dynamic Warm-Start protocol and accounts for heteroscedastic aleatoric uncertainty to enhance training stability. This method is designed for practical Earth Observation, facilitating swift and precise flood mapping essential for effective disaster response. The research is available on arXiv (2605.24106).