A Physics-Informed Neural Network Approach to Simulating Ice Dynamics Governed by the Shallow Ice Approximation
Abstract
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.
Fields of Study & Subjects
Arctic and Antarctic ice dynamics
Cryospheric studies and observations
Meteorological Phenomena and Simulations
Publication details
- Journal / source
- International Journal of Numerical Analysis and Modeling
- Publisher
- Global Science Press
- Volume
- 23
- Issue
- 4
- Pages
- 523–550
- Publication date
- 29 May 2026
- Language
- EN