Physics-guided spatiotemporal neural models for fuel density prediction

Wildfire spread is traditionally predicted using physics-based simulators, which are physically interpretable but whose cost increases with each additional ensemble member. We ask how well deep learning surrogates can reproduce these simulations at a fraction of this cost, training them on 10,584 fire spread simulations at 2m resolution for the Rectoret region in Catalonia, Spain. Four architectures are compared: a patch-based U-Net, a transfer-learned ResNet-50, a physics-informed network constrained by the wind-driven advection equation and a Swin-Unet transformer. Among the terrain and vegetation variables, only surface fuel load predicts burn probability with any strength (r = 0.27) and including it lowers prediction error by 21%. The remaining variables correlate weakly and are highly duplicative. Next, an experiment with saliency, occlusion and rotation demonstrates the models' learning. Convolutional models rely primarily on distance from the current fire front, while Swin-Unet assigns more weight to fuel and terrain, a finding also noted in an unrelated wildfire dataset. When applied without retraining to the second region, Pedriza, all three convolutional models still predict fire spread, losing accuracy by a small but systematic margin.

Predicting complex spatiotemporal dynamics in physical processes often demands computationally expensive numerical methods or data-driven neural networks that suffer from high training costs, error accumulation, and limited generalizability to unseen parameters. An effective approach to address these challenges is leveraging physics priors in training neural networks, known as physics-informed deep learning (PiDL). In this work, we introduce the Multi-Resolution Finite-Volume-inspired network, MuRFiV, designed to capitalize on the conservative property of finite volume on the global scale and the expressive power of deep learning on the local scale. We demonstrate the effectiveness of MuRFiV on several spatio-temporal systems governed by partial differential equations (PDEs), including Burgers' equation, shallow water equations, and incompressible Navier-Stokes equations. By embedding PDE information into the deep learning architecture, MuRFiV achieves strong long-term prediction accuracy and remains stable over very long autoregressive rollouts, significantly outperforming data-driven neural network baselines. This result highlights the promise of combining multiresolution learning with finite-volume-inspired inductive bias for accurate and robust long-term prediction of complex dynamics.

Accurate flood forecasting is essential for mitigating disaster risks and protecting communities. However, purely data-driven machine learning models often struggle in data-scarce environments and may violate fundamental hydrological principles. Standard Long Short-Term Memory (LSTM) networks can generate physically inconsistent predictions, particularly when extrapolating to extreme weather conditions. To address these limitations, we propose a Physics-Informed Machine Learning (PIML) framework that incorporates hydrological knowledge directly into the loss function of an LSTM model. Specifically, a Trend Alignment constraint penalizes directional inconsistencies between precipitation and discharge trends, improving model robustness without requiring complex hydrodynamic equations. This regularization encourages the model to learn physically plausible hydrograph behavior, even with limited training data, while enhancing reliability during peak flood events. Experimental results show that the proposed physics-informed model outperforms a standard LSTM baseline in data-scarce settings, increasing the Nash-Sutcliffe Efficiency (NSE) from 0.20 to 0.23 when trained on only 5% of the available data. Additional stress tests under simulated extreme climate scenarios demonstrate that the baseline model exhibits unstable behavior, whereas the physics-informed model maintains directional consistency and physical plausibility. Although accurately predicting extreme peak magnitudes remains challenging with limited data, the proposed approach substantially reduces unphysical fluctuations common in purely data-driven models. These findings demonstrate that simple physical constraints can significantly improve the reliability of deep learning models for real-time flood forecasting, offering a practical solution for ungauged basins and evolving climate conditions.