发表机构
ENSTA; Institut Polytechnique de Paris; CNRS; INRIA（国立高等先进技术学校; 巴黎综合理工学院; 法国国家科学研究中心; 法国国家信息与自动化研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
ScaGNN提出一种基于图神经网络的多次散射模拟方法，通过动态自适应边采样机制近似边界元法中的解迹，实现线性复杂度，并在多个数据集上超越现有最先进学习方法。
AI 中文摘要
边界元方法（BEM）为求解无界均匀域中的多次散射问题提供了一种高效的数值框架。通过将离散化限制在域边界上，它大幅降低了计算复杂度。该过程首先通过求解边界积分方程来确定域边界上的解迹。然后，利用边界积分表示，可以以较低的计算成本恢复体积解。由于边界元方法的第一步代表了主要的计算瓶颈，我们提出了ScaGNN，一种基于学习的方法，旨在近似解迹。它依赖于一种图神经网络架构，该架构结合了动态自适应边采样机制，以选择最相关的相互作用进行建模。在中间预测的预期误差和边长的指导下，该机制在前向传播的不同阶段选择最相关的远距离相互作用进行建模。所提出的方法旨在实现与输入图中节点数量呈线性关系的复杂度。为了训练和评估我们的网络，我们提出了一个基准，包含多个具有不同类型多次散射问题的数据集。我们的实验表明，我们的方法在考虑的任务上超越了现有的最先进的基于学习的方法，并研究了在障碍物数量增加和分布外障碍物形状情况下的泛化能力。此http URL。
英文摘要
The boundary element method (BEM) provides an efficient numerical framework for solving multiple scattering problems in unbounded homogeneous domains. By restricting the discretization to the domain boundaries, it substantially reduces computational complexity. The procedure first consists in determining the solution trace on the boundaries of the domain by solving a boundary integral equation. Then, the volumetric solution can be recovered at low computational cost using a boundary integral representation. As the first step of the BEM represents the main computational bottleneck, we present ScaGNN, a learning-based approach designed to approximate the solution trace. It relies on a graph neural network architecture that incorporates a dynamic adaptive edge sampling mechanism for selecting the most relevant interactions to model. Guided by intermediate predictions of expected error and edge length, this mechanism selects, at various stages of the forward pass, the most relevant distant interactions to model. The proposed method is tailored to achieve linear complexity with the number of nodes in the input graph. To train and evaluate our network, we present a benchmark consisting of several datasets with different types of multiple scattering problems. Our experiments show that our approach surpasses existing state-of-the-art learning-based methods on the considered tasks and investigate the generalization capabilities to settings with an increased number of obstacles and out-of-distribution obstacle shapes. github.com/LARIAD/ScaGNN
