Emulating Viscous Ice Flow Dynamics with Physics-Informed Deep Learning

Modeling the evolution of glaciers and ice sheets over glacial cycle timescales is critical for understanding landscape transformation through glacial erosion, predicting future changes, and assessing their impacts on sea-level rise and water availability. However, solving the partial differential equations (PDEs) governing thermomechanical ice flow at the high spatial and temporal resolutions required for these timescales is computationally prohibitive using traditional CPU-based solvers. GPU-accelerated methods offer a promising pathway to overcome these challenges.
In this study, we present a physics-informed deep learning approach leveraging GPUs, which integrates traditional numerical approximation with deep learning techniques. Using a regular grid and finite difference methods for spatial discretization, we train a Convolutional Neural Network (CNN) to minimize the energy associated with high-order ice flow equations -- a non-linear elliptic problem -- within the iterative time-stepping of a glacier evolution model. The resulting CNN, which is similar to a Variational Physics-Informed Neural Network, delivers multiple benefits: computational efficiency optimized for GPU usage, high fidelity to the original model, unsupervised training that eliminates the need for pre-generated datasets, and relatively simple implementation. Additionally, the emulator incorporates memory of prior solutions, reducing the computational cost of training -- a memory-intensive task.
Embedded within the "Instructed Glacier Model" (IGM) framework, the emulator's capabilities are demonstrated through high-resolution, large-scale simulations of glaciated landscape formation over extended timescales. This work underscores the potential of combining deep learning with physical modeling to develop scalable, efficient tools for simulating complex glaciological processes.