发表机构
HKUST（香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于协方差和KL展开的物理感知降阶方法，利用图神经网络代理高效重建协方差矩阵，以加速声波散射问题求解，在不牺牲精度的情况下实现稳健加速。
AI 中文摘要
本文提出了一种物理感知的降阶方法（ROM），用于高效计算波散射问题。标准的模型降阶技术通常将散射视为通用参数化系统，常常忽视潜在的物理结构，从而限制了其在实际应用中的有效性。为解决这一局限，我们提出了一种算法框架，利用诱导对比源密度的内在低秩结构。通过将入射波建模为由指定先验概率测度控制的随机变量，我们将对比源表述为一个空间随机场，其协方差函数捕捉了必要的空间相关性和物理相互作用。随后，通过Karhunen-Loève（KL）展开构造降阶基，有效提取散射过程中的主导特征，以求解多种散射场景。一个核心算法贡献在于，针对任意散射体几何形状和指定的入射波先验，高效重建协方差矩阵。为避免组装高保真协方差矩阵的过高计算成本，我们引入了一种非侵入式、物理信息的图神经网络（GNN）代理模型，学习从散射体几何到源相关核的复杂映射，从而实现了适用于大规模散射配置的高效离线-在线计算范式。大量数值实验表明，所提出的框架在全阶模型上实现了稳健的计算加速，且不牺牲精度。
英文摘要
This paper presents a physics-aware reduced-order method (ROM) for the efficient computation of wave-scattering problems. Standard model order reduction techniques, typically treating scattering as generic parameterized systems, frequently overlook the underlying physical structure, limiting their effectiveness in practice. To address this limitation, we propose an algorithmic framework that utilizes the intrinsic low-rank structure of the induced contrast source density. By modeling the incident wave as a random variable governed by a specified prior probability measure, we formulate the contrast source as a spatial random field whose covariance function captures essential spatial correlation and physical interactions. The reduced-order basis is then constructed via the Karhunen-Loève (KL) expansion, effectively extracting the dominant features from the scattering process to resolve multiple scattering scenarios. A central algorithmic contribution is the efficient reconstruction of the covariance matrix for arbitrary scatterer geometries and specified incident wave priors. To circumvent the prohibitive computational cost of assembling high-fidelity covariance matrices, we introduce a non-intrusive, physics-informed graph neural network (GNN) surrogate to learn the complex mapping from scatterer geometry to the source correlation kernel, enabling a highly efficient offline-online computational paradigm suitable for large-scale scattering configurations. Extensive numerical experiments demonstrate that the proposed framework achieves robust computational acceleration over full-order models without sacrificing accuracy.
