N-Tree Diffusion for Long-Horizon Wildfire Risk Forecasting

This study presents a probabilistic surrogate model for localized wildfire spread based on a conditional flow matching algorithm. The approach models fire progression as a stochastic process by learning the conditional distribution of fire arrival times given the current fire state along with environmental and atmospheric inputs. Model inputs include current burned area, near-surface wind components, temperature, relative humidity, terrain height, and fuel category information, all defined on a high-resolution spatial grid. The outputs are samples of arrival time within a three-hour time window, conditioned on the input variables. Training data are generated from coupled atmosphere-wildfire spread simulations using WRF-SFIRE, paired with weather fields from the North American Mesoscale model. The proposed framework enables efficient generation of ensembles of arrival times and explicitly represents uncertainty arising from incomplete knowledge of the fire-atmosphere system and unresolved variables. The model supports localized prediction over subdomains, reducing computational cost relative to physics-based simulators while retaining sensitivity to key drivers of fire spread. Model performance is evaluated against WRF-SFIRE simulations for both single-step (3-hour) and recursive multi-step (24-hour) forecasts. Results demonstrate that the method captures variability in fire evolution and produces accurate ensemble predictions. The framework provides a scalable approach for probabilistic wildfire forecasting and offers a pathway for integrating machine learning models with operational fire prediction systems and data assimilation.

Long-horizon spatiotemporal prediction remains a challenging problem due to cumulative errors, noise amplification, and the lack of physical consistency in existing models. While diffusion models provide a probabilistic framework for modeling uncertainty, conventional approaches often rely on mean squared error objectives and fail to capture the underlying dynamics governed by physical laws. In this work, we propose PDYffusion, a dynamics-informed diffusion framework that integrates PDE-based regularization and uncertainty-aware forecasting for stable long-term prediction. The proposed method consists of two key components: a PDE-regularized interpolator and a UKF-based forecaster. The interpolator incorporates a differential operator to enforce physically consistent intermediate states, while the forecaster leverages the Unscented Kalman Filter to explicitly model uncertainty and mitigate error accumulation during iterative prediction. We provide theoretical analyses showing that the proposed interpolator satisfies PDE-constrained smoothness properties, and that the forecaster converges under the proposed loss formulation. Extensive experiments on multiple dynamical datasets demonstrate that PDYffusion achieves superior performance in terms of CRPS and MSE, while maintaining stable uncertainty behavior measured by SSR. We further analyze the inherent trade-off between prediction accuracy and uncertainty, showing that our method provides a balanced and robust solution for long-horizon forecasting.

Traditional wildfire models rely on rigid, low-dimensional parameters and static fuel maps, frequently underpredicting fire spread. To address this weakness, we introduce a hybrid deep-learning parameterized Probabilistic Cellular Automata (CA) framework implemented in JAX. Our approach employs a Multi-Scale Convolutional Neural Network to dynamically generate spatially varying parameters that govern fire-spread probability, wind alignment, and slope influence. This hybrid design captures complex, nonlinear environmental interactions while preserving the physical interpretability of the underlying three-state CA. The JAX implementation enables hardware acceleration and gradient-based parameter calibration. Evaluated on six large-scale wildfires in the western United States, the model maintains IoU > 0.6 over 72-hour forecast horizons after a 10-day data assimilation window during which the model is fitted incrementally to observed perimeters; the resulting forecast is a conditional projection of fire growth under the suppression regime already ncoded in those observations.