mlsanityData to 14 Oct 2026

Domain-Decomposed Graph Neural Network Surrogate Modeling for Ice Sheets

arXiv 2512.01888 ↗First posted 1 Dec 2025cs.LG cs.NA math-phcited by 0

Not on the map. Why?

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.

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

29 of 65 references.

References · 29

  1. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  2. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,919
  3. 2018On the Spectral Bias of Neural Networkscited by 1,341
  4. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,102
  5. 2020Learning Mesh-Based Simulation with Graph Networkscited by 868
  6. 2020A Note on Over-Smoothing for Graph Neural Networkscited by 249
  7. 2023A Survey on Oversmoothing in Graph Neural Networkscited by 247
  8. 2021Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equationscited by 145
  9. 2020Towards Deeper Graph Neural Networks with Differentiable Group Normalizationcited by 114
  10. 2019Hamiltonian Graph Networks with ODE Integratorscited by 108
  11. 2022A Non-Asymptotic Analysis of Oversmoothing in Graph Neural Networkscited by 49
  12. 2024Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problemscited by 35
17 more
  1. 2022On the Activation Function Dependence of the Spectral Bias of Neural Networkscited by 28
  2. 2023AdapterGNN: Parameter-Efficient Fine-Tuning Improves Generalization in GNNscited by 26
  3. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 26
  4. 2022Scalable algorithms for physics-informed neural and graph networkscited by 21
  5. 2022Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systemscited by 20
  6. 2023Machine learning and domain decomposition methods -- a surveycited by 14
  7. 2014Scalable 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 sheetcited by 13
  8. 2023A multifidelity approach to continual learning for physical systemscited by 13
  9. 2023MG-GNN: Multigrid Graph Neural Networks for Learning Multilevel Domain Decomposition Methodscited by 12
  10. 2023A Hybrid Deep Neural Operator/Finite Element Method for Ice-Sheet Modelingcited by 11
  11. 2023Graph Neural Networks and Applied Linear Algebracited by 6
  12. 2024Graph convolutional network as a fast statistical emulator for numerical ice sheet modelingcited by 6
  13. 2022Performance portable ice-sheet modeling with MALIcited by 3
  14. 2024Transfer Learning on Multi-Dimensional Data: A Novel Approach to Neural Network-Based Surrogate Modelingcited by 3
  15. 2024DDU-Net: A Domain Decomposition-Based CNN for High-Resolution Image Segmentation on Multiple GPUscited by 2
  16. 2025Resolving Extreme Data Scarcity by Explicit Physics Integration: An Application to Groundwater Heat Transportcited by 1
  17. 2025Domain decomposition architectures and Gauss-Newton training for physics-informed neural networkscited by 1

Built on by

Not cited yet.