Bayesian Physics Informed Neural Networks for Data Assimilation and Spatio-Temporal Modelling of Wildfires

We apply Physics Informed Neural Networks (PINNs) to the problem of wildfire fire-front modelling. The PINN is an approach that integrates a differential equation into the optimisation loss function of a neural network to guide the neural network to learn the physics of a problem. We apply the PINN to the level-set equation, which is a Hamilton-Jacobi partial differential equation that models a fire-front with the zero-level set. This results in a PINN that simulates a fire-front as it propagates through a spatio-temporal domain. We demonstrate the agility of the PINN to learn physical properties of a fire under extreme changes in external conditions (such as wind) and show that this approach encourages continuity of the PINN's solution across time. Furthermore, we demonstrate how data assimilation and uncertainty quantification can be incorporated into the PINN in the wildfire context. This is significant contribution to wildfire modelling as the level-set method -- which is a standard solver to the level-set equation -- does not naturally provide this capability.