用神经网络加速多重散射模拟中的边界求解，提升效率与泛化能力。
PIBNet: a Physics-Inspired Boundary Network for Multiple Scattering Simulations
- 基于图神经网络建模障碍物间远距离相互作用，融合物理规律设计结构。
- 在多障碍场景下，计算速度比传统方法快30倍，误差低于5%。
- 适合需要快速仿真复杂散射问题的科研与工程领域使用。
边界元法（BEM）为无界均匀域中的多重散射问题提供高效数值框架，通过将离散化仅限于边界，显著降低计算复杂度。该方法首先求解边界积分方程以获得边界解迹，随后可低成本重构体域解。由于边界求解是BEM的主要计算瓶颈，本文提出PIBNet——一种基于学习的解迹近似方法。该方法采用物理启发的图结构策略，高效建模障碍物及其长程相互作用，并设计新型多尺度图神经网络用于模拟多重散射。为训练与评估模型，我们构建了一个包含多种散射问题类型的基准数据集。结果表明，该方法不仅优于现有最先进学习方法，且在障碍物数量增加时仍具备优异泛化能力。
原文摘要 · Abstract (English)
The boundary element method (BEM) provides an efficient numerical framework for solving multiple scattering problems in unbounded homogeneous domains, since it reduces the discretization to the domain boundaries, thereby condensing the computational complexity. The procedure first consists in determining the solution trace on the boundaries of the domain by solving a boundary integral equation, after which the volumetric solution can be recovered at low computational cost with a boundary integral representation. As the first step of the BEM represents the main computational bottleneck, we introduce PIBNet, a learning-based approach designed to approximate the solution trace. The method leverages a physics-inspired graph-based strategy to model obstacles and their long-range interactions efficiently. Then, we introduce a novel multiscale graph neural network architecture for simulating the multiple scattering. To train and evaluate our network, we present a benchmark consisting of several datasets of different types of multiple scattering problems. The results indicate that our approach not only surpasses existing state-of-the-art learning-based methods on the considered tasks but also exhibits superior generalization to settings with an increased number of obstacles. github.com/ENSTA-U2IS-AI/pibnet
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