用图神经网络学习任意域上PDE的解算子，精度高且对分辨率变化鲁棒。
RIGNO: A Graph-based framework for robust and accurate operator learning for PDEs on arbitrary domains
- 基于图神经网络构建端到端框架，通过区域网格下采样实现点云间数据映射。
- 在多种时变与稳态PDE问题上，精度显著优于现有神经算子基线。
- 适用于任意形状域，对空间和时间分辨率变化具有强泛化能力，适合科研与工程建模。
在任意域上学习偏微分方程（PDE）的解算子极具挑战性，不仅因为域形状多样，还因物理机制复杂。本文提出一种基于图神经网络（GNN）的端到端神经算子框架，直接从任意域上的点云数据中学习解算子。所提多尺度模型通过下采样的区域网格在输入/输出点云间传递数据，并引入新机制以确保时空分辨率不变性。该模型命名为RIGNO，已在包含多种时变与稳态PDE、定义于多样化域的基准测试集上验证。结果表明，RIGNO相比现有神经算子基线显著更准确，且对未见过的空间与时间分辨率均表现出稳健泛化能力。代码已公开于github.com/camlab-ethz/rigno。
原文摘要 · Abstract (English)
Learning the solution operators of PDEs on arbitrary domains is challenging due to the diversity of possible domain shapes, in addition to the often intricate underlying physics. We propose an end-to-end graph neural network (GNN) based neural operator to learn PDE solution operators from data on point clouds in arbitrary domains. Our multi-scale model maps data between input/output point clouds by passing it through a downsampled regional mesh. The approach includes novel elements aimed at ensuring spatio-temporal resolution invariance. Our model, termed RIGNO, is tested on a challenging suite of benchmarks composed of various time-dependent and steady PDEs defined on a diverse set of domains. We demonstrate that RIGNO is significantly more accurate than neural operator baselines and robustly generalizes to unseen resolutions both in space and in time. Our code is publicly available at github.com/camlab-ethz/rigno.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。