用物理神经网络模拟冰盖随时间变化的动态，精度高且可扩展。
A physics informed neural network approach to simulating ice dynamics governed by the shallow ice approximation
- 将物理规律嵌入神经网络，求解冰盖演化的时变障碍问题。
- 1D/2D仿真成功捕捉复杂边界变化，真实冰盖模拟误差小。
- 适合气候建模与冰川动力学研究者使用。
本文提出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问题。该问题为时变抛物型障碍问题。先前工作仅处理静态障碍问题，本文将其扩展至时变情形。通过一系列1维和2维仿真，验证了模型在捕捉复杂自由边界条件方面的有效性。结合传统数学建模与前沿深度学习技术，该方法提供了可扩展、鲁棒的冰厚随时间变化预测方案。为展示其实际应用，我们基于2000年与2018年的航空地球物理数据，对德文冰帽的动力学进行了模拟。
原文摘要 · Abstract (English)
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.
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