A physics informed neural network approach to simulating ice dynamics governed by the shallow ice approximation
This work addresses the problem of predicting temporal ice thickness variations for glaciology and climate science, representing an incremental extension of PINNs to time-dependent obstacle problems.
The authors tackled simulating ice sheet dynamics governed by the Shallow Ice Approximation using a Physics Informed Neural Network (PINN) approach, extending it from stationary to time-dependent problems and validating it with 1D and 2D simulations, including a real-world application to the Devon Ice Cap with data from 2000 and 2018.
In this article we develop a Physics Informed Neural Network (PINN) approach to simulate ice sheet dynamics governed by the Shallow Ice Approximation. This problem takes the form of a time-dependent parabolic obstacle problem. Prior work has used this approach to address the stationary obstacle problem and here we extend it to the time dependent problem. Through comprehensive 1D and 2D simulations, we validate the model's effectiveness in capturing complex free-boundary conditions. By merging traditional mathematical modeling with cutting-edge deep learning methods, this approach provides a scalable and robust solution for predicting temporal variations in ice thickness. To illustrate this approach in a real world setting, we simulate the dynamics of the Devon Ice Cap, incorporating aerogeophysical data from 2000 and 2018.