Neural Network Modeling of the Transient Heating of Icy Mountains due to Foehn Winds

Foehn winds are dry, warm winds that are caused by the adiabatic warming of air as it descends down the leeward side of a mountain. This phenomenon has substantial effects on the melting of ice and snow on icy mountains. In this research, we present a physics informed neural network (PINN) model for simulating the transient heating of icy mountains under the influence of Foehn winds. We initially created a mathematical model of this transient heating process. First, we inserted the icy mountain into a wind tunnel to compute the wind velocity profile. Second, we used the velocities to compute the convective heat transfer coefficient along the mountain. Third, we computed the wind temperature taking into account adiabatic cooling and heating. Finally, we computed the temperature profile of the mountain. We solved this mathematical model for 24000 time steps to generate a collocation dataset for supervised training of the PINN. We also developed a custom loss function for unsupervised training of the PINN. After training, the PINN solved the transient heating of three 2D icy mountains in 0.893 sec, 0.875 sec, and 1.026 sec, which were 6351, 6649, and 6883 times faster than the finite difference method, respectively. The PINN solved the transient heating of a 3D icy mountain in 5 sec, which was 3974 times faster than the finite difference method. This model has the potential to better our understanding of Foehn winds and has potential applications in predicting avalanches, erosion, and ice shelf collapse.