用分域图神经网络加速冰盖模拟,提升精度与训练效率
Domain-Decomposed Graph Neural Network Surrogate Modeling for Ice Sheets
- 将网格分块训练局部GNN模型,再通过注意力机制融合预测
- 在高分辨率网格上实现全场速度精准预测,训练时间大幅缩短
- 适合数据稀缺场景,尤其适用于冰盖等复杂物理系统的不确定性分析
精确且高效的代理模型对大规模偏微分方程(PDE)仿真至关重要,尤其在需要数百甚至数千次评估的不确定性量化(UQ)任务中。本文提出一种基于物理启发的图神经网络(GNN)代理模型,直接作用于非结构化网格,并利用图注意力机制的灵活性。为提升训练效率和泛化能力,引入域分解(DD)策略:将网格划分为子域,平行训练局部GNN代理模型,并聚合其输出。进一步采用迁移学习在子域间微调模型,在数据有限情况下加速训练并提升精度。应用于冰盖模拟时,该方法能准确预测高分辨率网格上的全场速度,显著减少训练时间,相比单一全局模型有明显优势,为UQ目标奠定坚实基础。结果表明,结合迁移学习的图基域分解方法,为大规模PDE系统中的GNN代理模型训练提供了可扩展、可靠的路径,具有超越冰盖动力学的广泛应用潜力。
原文摘要 · Abstract (English)
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.
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