# Domain-Decomposed Graph Neural Network Surrogate Modeling for Ice Sheets

arXiv: https://arxiv.org/abs/2512.01888 · HTML: https://mlsanity.com/paper/2512.01888/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 65 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Builds on (most cited first, 29 of 29)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [A Note on Over-Smoothing for Graph Neural Networks](https://mlsanity.com/paper/2006.13318/) (2020)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations](https://mlsanity.com/paper/2107.07871/) (2021)
- [Towards Deeper Graph Neural Networks with Differentiable Group Normalization](https://mlsanity.com/paper/2006.06972/) (2020)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [A Non-Asymptotic Analysis of Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2212.10701/) (2022)
- [Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems](https://mlsanity.com/paper/2406.19662/) (2024)
- [On the Activation Function Dependence of the Spectral Bias of Neural Networks](https://mlsanity.com/paper/2208.04924/) (2022)
- [AdapterGNN: Parameter-Efficient Fine-Tuning Improves Generalization in GNNs](https://mlsanity.com/paper/2304.09595/) (2023)
- [Reversible and irreversible bracket-based dynamics for deep graph neural networks](https://mlsanity.com/paper/2305.15616/) (2023)
- [Scalable algorithms for physics-informed neural and graph networks](https://mlsanity.com/paper/2205.08332/) (2022)
- [Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systems](https://mlsanity.com/paper/2209.10740/) (2022)
- [Machine learning and domain decomposition methods -- a survey](https://mlsanity.com/paper/2312.14050/) (2023)
- [Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheet](https://mlsanity.com/paper/1410.1221/) (2014)
- [A multifidelity approach to continual learning for physical systems](https://mlsanity.com/paper/2304.03894/) (2023)
- [MG-GNN: Multigrid Graph Neural Networks for Learning Multilevel Domain Decomposition Methods](https://mlsanity.com/paper/2301.11378/) (2023)
- [A Hybrid Deep Neural Operator/Finite Element Method for Ice-Sheet Modeling](https://mlsanity.com/paper/2301.11402/) (2023)
- [Graph Neural Networks and Applied Linear Algebra](https://mlsanity.com/paper/2310.14084/) (2023)
- [Graph convolutional network as a fast statistical emulator for numerical ice sheet modeling](https://mlsanity.com/paper/2402.05291/) (2024)
- [Performance portable ice-sheet modeling with MALI](https://mlsanity.com/paper/2204.04321/) (2022)
- [Transfer Learning on Multi-Dimensional Data: A Novel Approach to Neural Network-Based Surrogate Modeling](https://mlsanity.com/paper/2410.12241/) (2024)
- [DDU-Net: A Domain Decomposition-Based CNN for High-Resolution Image Segmentation on Multiple GPUs](https://mlsanity.com/paper/2407.21266/) (2024)
- [Resolving Extreme Data Scarcity by Explicit Physics Integration: An Application to Groundwater Heat Transport](https://mlsanity.com/paper/2507.06062/) (2025)
- [Domain decomposition architectures and Gauss-Newton training for physics-informed neural networks](https://mlsanity.com/paper/2510.27018/) (2025)

## Abstract (arXiv)

Accurate yet efficient surrogate models are essential for large-scale simulations of partial differential equations (PDEs), particularly for uncertainty quantification (UQ) tasks that demand hundreds or thousands of evaluations. We develop a physics-inspired graph neural network (GNN) surrogate that operates directly on unstructured meshes and leverages the flexibility of graph attention. To improve both training efficiency and generalization properties of the model, we introduce a domain decomposition (DD) strategy that partitions the mesh into subdomains, trains local GNN surrogates in parallel, and aggregates their predictions. We then employ transfer learning to fine-tune models across subdomains, accelerating training and improving accuracy in data-limited settings. Applied to ice sheet simulations, our approach accurately predicts full-field velocities on high-resolution meshes, substantially reduces training time relative to training a single global surrogate model, and provides a ripe foundation for UQ objectives. Our results demonstrate that graph-based DD, combined with transfer learning, provides a scalable and reliable pathway for training GNN surrogates on massive PDE-governed systems, with broad potential for application beyond ice sheet dynamics.