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In this paper, we propose a feedback control strategy to protect vulnerable areas from wildfires. We consider a system of coupled partial differential equations (PDEs) that models heat propagation and fuel depletion in wildfires and study…

Analysis of PDEs · Mathematics 2025-09-11 Mohamed Camil Belhadjoudja , Mohamed Maghenem , Emmanuel Witrant , Didier Georges

We present a general stochastic forest-fire model which shows a variety of different structures depending on the parameter values. The model contains three possible states per site (tree, burning tree, empty site) and three parameters (tree…

Condensed Matter · Physics 2009-10-22 B. Drossel , F. Schwabl

Wildfires can be devastating, causing significant damage to property, ecosystem disruption, and loss of life. Forecasting the evolution of wildfire boundaries is essential to real-time wildfire management. To this end, substantial attention…

Methodology · Statistics 2023-02-13 Myungsoo Yoo , Christopher K. Wikle

Given the recent increase in wildfires, developing a better understanding of their dynamics is crucial. For this purpose, the advection-diffusion-reaction model has been widely used to study wildfire dynamics. In this study, we introduce…

Fluid Dynamics · Physics 2024-12-02 Luca Nieding , Cordula Reisch , Dirk Langemann , Adrián Navas-Montilla

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…

Machine Learning · Computer Science 2026-03-31 Bryan Shaddy , Haitong Qin , Brianna Binder , James Haley , Riya Duddalwar , Kyle Hilburn , Assad Oberai

In this paper we use a variant of the Watts-Strogatz small-world model to predict wildfire behavior near the critical propagation/nonpropagation threshold. We find that forest fire patterns are fractal and that critical exponents are…

Physics and Society · Physics 2008-05-23 Porterie Bernard , Kaiss Ahmed , Clerc Jean Pierre , Zekri Nouredine , Lotfi Zekri

The understanding and prediction of large wildland fire events around the world is a growing interdisciplinary research area advanced rapidly by development and use of computational models. Recent models bidirectionally couple computational…

Atmospheric and Oceanic Physics · Physics 2020-07-06 J. L. Coen , W. Schroeder , S. Conway , L. Tarnay

Wildfire forecasting problems usually rely on complex grid-based mathematical models, mostly involving Computational fluid dynamics(CFD) and Celluar Automata, but these methods have always been computationally expensive and difficult to…

Machine Learning · Computer Science 2023-08-21 Hansong Xiao

A wildfire model is formulated based on balance equations for energy and fuel, where the fuel loss due to combustion corresponds to the fuel reaction rate. The resulting coupled partial differential equations have coefficients that can be…

This paper presents the development of a new continuous forest fire model implemented as a weighted local small-world network approach. This new approach was designed to simulate fire patterns in real, heterogeneous landscapes. The wildland…

Atmospheric and Oceanic Physics · Physics 2013-07-02 F. Aguayo , A. Fuentes , J. -P. Clerc , B. Porterie

In recent years, advances in computational power and spatial data analysis (GIS, remote sensing, etc) have led to an increase in attempts to model the spread and behvaiour of wildland fires across the landscape. This series of review papers…

Geophysics · Physics 2010-07-28 A. L. Sullivan

Various flame tracking techniques are often used in hydrodynamic simulations. Their use is indispensable when resolving actual scale of the flame is impossible. We show that parameters defining "artificial flame" propagation found from…

Astrophysics · Physics 2007-05-23 Andrey V. Zhiglo

This paper presents a novel approach in wildfire prediction through the integration of multisource spatiotemporal data, including satellite data, and the application of deep learning techniques. Specifically, we utilize an ensemble model…

Machine Learning · Computer Science 2025-01-07 Ayoub Jadouli , Chaker El Amrani

With the increased size and frequency of wildfire eventsworldwide, accurate real-time prediction of evolving wildfirefronts is a crucial component of firefighting efforts and for-est management practices. We propose a wildfire…

Computer Vision and Pattern Recognition · Computer Science 2020-09-10 Maxfield E. Green , Karl Kaiser , Nat Shenton

Modelling wildfire occurrences is important for disaster management including prevention, detection and suppression of large catastrophic events. We present a spatial Poisson hurdle model for exploring geographical variation of monthly…

Applications · Statistics 2020-07-02 Justin A. Kasin , Ioannis Papastathopoulos

In this paper we consider a classical model of gasless combustion in a one dimensional formulation under the assumption of ignition temperature kinetics. We study the propagation of flame fronts in this model when the initial distribution…

Pattern Formation and Solitons · Physics 2024-03-06 Amanda Matson , Leonid Kagan , Claude-Michel Brauner , Gregory Sivashinsky , Peter V. Gordon

In this paper, we introduce a generalized asymmetric fronts propagation model based on the geodesic distance maps and the Eikonal partial differential equations. One of the key ingredients for the computation of the geodesic distance map is…

Computational Geometry · Computer Science 2017-12-12 Da Chen , Laurent D. Cohen

In this work, we pose and solve the time-optimal navigation problem considered on a slippery mountain slope modeled by a Riemannian manifold of an arbitrary dimension, under the action of a cross gravitational wind. The impact of both…

Differential Geometry · Mathematics 2025-07-29 Nicoleta Aldea , Piotr Kopacz

In wildfires, atmospheric turbulence plays a major role in the transfer of turbulent kinetic energy. Understanding how turbulence feeds back into a dynamical system is important, down to the varying small scales of fuel structures (i.e.…

Fluid Dynamics · Physics 2024-09-11 Dorianis M. Perez , Jesse M. Canfield , Rodman R. Linn , Kevin Speer

We analyze turbulent velocity signals measured by two probes in the atmosphere, both at the height of 35 meters but displaced by 40 cm nominally orthogonal to the mean wind. Choosing a suitable coordinate system with respect to that of the…