Deterministic Mathematical Models Applied to Forest Fire Phenomena: A Systematic Review

Altamirano-Fernández A.; Vásquez-Coronel J.A. · Archives of Computational Methods in Engineering (2026) · DOI: 10.1007/s11831-026-10763-9

Resumen

Predicting the spread of forest fires depends on precise mathematical tools to ensure environmental safety. Deterministic models simulate fire dynamics using continuous differential equations rooted in fluid mechanics and thermodynamics. Changes in landscape heterogeneity and climate conditions demand adaptive frameworks for accurate risk assessment. This systematic review analyses 56 studies published between 2015 and 2025. The PICO strategy and PRISMA protocol guided the literature selection from the Scopus and Web of Science databases. Within this review, deterministic formulations are defined by physical conservation laws. Hybrid architectures, such as neural networks informed by physics, are included only when they preserve this physical core. Within the evaluated models, topography, wind speed, and fuel characteristics frequently emerge as key variables driving macroscopic fire spread. Modern simulators integrate these physical equations with empirical observations to improve spatial accuracy and validate flame temperatures using data from the United States, China, and Russia. Nevertheless, substantial computational limitations persist. Traditional numerical solvers do not accurately parameterise heterogeneous fuels. Meanwhile, neural networks exhibit mathematical convergence issues, high sensitivity to sparse data, high computational costs, and scalability across large spatial domains. To mitigate these limitations, future predictive tools must implement bidirectionally coupled fire-atmosphere systems. These advanced systems merge continuous physical laws with dynamic data assimilation to improve the reliability of predictions. © The Author(s) under exclusive licence to International Center for Numerical Methods in Engineering (CIMNE) 2026.

Instituciones: Universidad Tecnológica del Perú