Neural Networks for Solving a PDE-Based Wildfire Propagation Model

Wildfire spread represents a major environmental and societal challenge, requiring reliable models capable of describing and predicting the dynamics of fire propagation. Mathematical models based on Partial Differential Equations (PDEs), particularly reaction-diffusion formulations, provide a powerful framework to capture key mechanisms of wildfire dynamics, such as flame front propagation and interactions with the surrounding environment. However, traditional numerical approaches used to solve these PDEs, including finite difference and finite element methods, can become computationally expensive and difficult to apply in real-time scenarios or over complex and irregular terrains. In this work, we focus on a reaction-diffusion model for wildfire spread and investigate the use of Neural Networks (NNs) as an efficient alternative for approximating its solutions. By leveraging the approximation capabilities of NNs, we aim to obtain accurate and computationally efficient predictions of flame front evolution. This approach highlights the potential of neural-network-based solvers to support wildfire monitoring, forecasting, and risk assessment in time-sensitive applications.