Domain-Decomposed Graph Neural Network Surrogate Modeling for Ice Sheets

2025-12-01

AI Summary

Uncertainty quantification (UQ) in large-scale partial differential equation (PDE) simulations demands efficient, high-fidelity surrogate models—particularly for complex geometries and unstructured meshes. Method: We propose a physics-informed domain decomposition graph neural network (GNN) framework: the computational domain is partitioned into subdomains on unstructured grids; local GNN submodels are trained in parallel; and graph attention mechanisms coupled with transfer learning enable cross-subdomain knowledge sharing. Contribution/Results: Compared to global GNN surrogates, our approach significantly improves training efficiency and generalization capability. In high-resolution ice-sheet simulations, it achieves high-accuracy full-field ice velocity prediction while reducing training time by an order of magnitude. The framework provides a scalable, physics-consistent, and data-efficient surrogate modeling paradigm for large-scale scientific simulations on complex geometries.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

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.

Problem

• Develops a GNN surrogate for ice sheet simulations
• Uses domain decomposition to improve training efficiency
• Enables scalable uncertainty quantification on large PDE systems

Innovation

• Domain decomposition partitions mesh into subdomains for parallel training
• Transfer learning fine-tunes models across subdomains to boost accuracy
• Graph neural network surrogate operates directly on unstructured meshes