用Transformer融合几何信息，实现任意形状的快速物理模拟。
Geometry-Informed Neural Operator Transformer
- 通过注意力机制处理无序点云，融合几何与求解点信息。
- 在多组2D/3D复杂几何上表现高精度与强泛化能力。
- 适合需要频繁求解偏微分方程的仿真场景，如工程设计优化。
基于机器学习的代理模型相比传统数值方法具有显著的计算效率优势，尤其适用于需重复求解偏微分方程的问题。本文提出几何感知神经算子变压器（GINOT），将Transformer架构与神经算子框架结合，实现对任意几何形状的前向预测。GINOT采用采样与分组策略，配合注意力机制，编码无序、非均匀密度、点数各异的表面点云。几何信息通过注意力机制无缝融入解码器中的查询点。在多个挑战性数据集上验证了其性能，展现出对复杂且任意2D和3D几何的高精度与强泛化能力。
原文摘要 · Abstract (English)
Machine-learning-based surrogate models offer significant computational efficiency and faster simulations compared to traditional numerical methods, especially for problems requiring repeated evaluations of partial differential equations. This work introduces the Geometry-Informed Neural Operator Transformer (GINOT), which integrates the transformer architecture with the neural operator framework to enable forward predictions on arbitrary geometries. GINOT employs a sampling and grouping strategy together with an attention mechanism to encode surface point clouds that are unordered, exhibit non-uniform point densities, and contain varying numbers of points for different geometries. The geometry information is seamlessly integrated with query points in the solution decoder through the attention mechanism. The performance of GINOT is validated on multiple challenging datasets, showcasing its high accuracy and strong generalization capabilities for complex and arbitrary 2D and 3D geometries.
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