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.

翻译：我们对野火消防建模问题应用了物理知情神经网络(PINN) 。 PINN 是一种将差异方程式纳入神经网络优化损失功能以引导神经网络学习问题物理学的方法。 我们将 PINN 应用于水平设置方程式, 即汉密尔顿- 贾科比部分方程式, 以零层建模作为消防前方模型。 这导致一个PINN 模拟消防前方程式, 因为它通过时空空域传播。 我们展示了 PINN 在外部条件(如风)的极端变化下学习火灾物理特性的敏捷性, 并表明这种方法鼓励PINN解决方案的连续性。 此外, 我们演示如何在野火环境中将数据同化和不确定性量化纳入 PINN 。 这极大地促进了野火建模作为标准方程式的野火建模方法 -- -- 是水平方程式的标准解算器 -- -- 自然不能提供这种能力。