标题： 基于浅冰近似控制的冰川动力学模拟的物理信息神经网络方法 显示英文标题

标题： A physics informed neural network approach to simulating ice dynamics governed by the shallow ice approximation

摘要： 在本文中，我们开发了一种物理信息神经网络（PINN）方法，用于模拟由浅冰近似控制的冰盖动力学。这个问题的形式是一个时间依赖的抛物线障碍问题。先前的工作已使用此方法解决静态障碍问题，而此处我们将其扩展到时间依赖问题。通过全面的1D和2D仿真，我们验证了该模型在捕捉复杂自由边界条件方面的有效性。通过将传统数学建模与尖端深度学习方法相结合，这种方法为预测冰厚的时间变化提供了可扩展且稳健的解决方案。为了在现实世界环境中展示此方法，我们模拟了德文冰帽的动力学，并结合了2000年和2018年的航空地球物理数据。 显示英文摘要

摘要： 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.