PIFF: A Physics-Informed Generative Flow Model for Real-Time Flood Depth Mapping

TL;DR

PIFF presents a physics-informed, flow-based generative model for near real-time flood depth mapping by learning a conditional vector field that maps DEMs to flood depths under 24-hour rainfall, guided by a lightweight hydrodynamic prior (SPM) and a transformer-based rainfall encoder. The method leverages optimal transport flow matching with an ODE-based sampling scheme, achieving fast inference while respecting mass-conservation and hydrodynamic plausibility. Experiments on a 26 km$^2$ study area in Tainan show_PIFF_ outperforms physics-based and AI baselines across multiple metrics, with particular strength in real-event rainfall scenarios and flood-depth accuracy (MD reductions, improved FID). The work demonstrates the practical potential of combining physics-informed priors with diffusion-like flow models for real-time flood prediction and response, reducing computational cost relative to traditional hydrodynamic simulations while maintaining accuracy.

Abstract

Flood mapping is crucial for assessing and mitigating flood impacts, yet traditional methods like numerical modeling and aerial photography face limitations in efficiency and reliability. To address these challenges, we propose PIFF, a physics-informed, flow-based generative neural network for near real-time flood depth estimation. Built on an image-to-image generative framework, it efficiently maps Digital Elevation Models (DEM) to flood depth predictions. The model is conditioned on a simplified inundation model (SPM) that embeds hydrodynamic priors into the training process. Additionally, a transformer-based rainfall encoder captures temporal dependencies in precipitation. Integrating physics-informed constraints with data-driven learning, PIFF captures the causal relationships between rainfall, topography, SPM, and flooding, replacing costly simulations with accurate, real-time flood maps. Using a 26 km study area in Tainan, Taiwan, with 182 rainfall scenarios ranging from 24 mm to 720 mm over 24 hours, our results demonstrate that PIFF offers an effective, data-driven alternative for flood prediction and response.

Figures (5)

• Figure 1: Overview of PIFF's forward and backward processes: the forward diffusion (top) progressively diffuse DEM image $x_0$, whereas the backward process (bottom) iteratively denoises $\hat{x}_1$ to reconstruct $\hat{x}_0$, which is then decoded to obtain the output $\hat{x}_0$
• Figure 2: DEM image from Tainan, Taiwan. The study area includes a channel in the northern part, and the overall ground slope decreases gently from east to west. The average terrain slope is approximately 0.014, with a total elevation difference of about 10 m across the area.
• Figure 3: Comparison of uniform, non-uniform, and real-event rainfall patterns over a 24-hour duration
• Figure 4: Comparison of ground truth and PIFF's generated flooded images at different timesteps ($t$) from $t=12$ to $t=20$ in \ref{['fig::rainfall']}. Note: Image contrast is enhanced using min-max normalization with $min = 200$ and $max = 255$.
• Figure 5: Four-metric (POD, 1-FAR, Bias, CSI) Plot for Algorithm Performance on Uniform, Non-uniform, and Real Event Rainfalls