Predicting Glacier Dynamics with Neural Operator-Based Surrogate Models.

Traditional numerical solvers for simulating glacier dynamics are computationally demanding, particularly for large-scale and long-period projections. Recent use of neural networks(NNs) based surrogate models, including data-driven and physics-informed convolutional neural networks (CNNs), have shown considerable success in accelerating simulation while maintaining adequate accuracy. However, conventional NN-based surrogate models typically map finite-dimensional Euclidean spaces, making them confined to particular discretization or resolution. As a result, these models often exhibit limited generalization capabilities and require frequent retraining when applied to new geometries or solution scenarios outside their training domain. Neural operators (NOs) offer a promising alternative. Unlike classical NNs, NOs learn the mapping between functions in infinite-dimensional spaces, making predictions more invariant with regard to resolution. They learn the parametric dependence of solutions across entire families of partial differential equations, making them better at generalization. Despite these advantages, limited existing literature uses neural operators for glacier flow simulation. 

This study presents different versions of a NO-based surrogate model to predict glacier velocity. These implementations will be evaluated against classical NN-based approaches, focusing on their computational efficiency, accuracy, and generalization across varying resolutions. Additionally, the study will explore key hyperparameters that influence the stability and performance of NO models and perform sensitivity analysis to identify the most effective configurations. The first results are promising and give insight into the performance and potential of NO-based surrogate models for ice-flow simulations.