发表机构
Princeton University（普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出神经模态分解框架，仅由系统级可观测量监督，端到端学习极点-留数模态分解，实现端口数量泛化，消除O(N²)扩展障碍，并在射频电磁建模中验证。
AI 中文摘要
许多工程构建模块表现为多端口线性时不变系统。射频腔、光子器件和超导量子芯片，尽管其底层物理机制不同，但其端口级响应均共享共同的数学结构。响应矩阵的每个条目是少量固有谐振模态贡献之和，即极点-留数形式。一个能够预测任意几何形状和任意端口配置下此类响应，同时提取底层本征模态结构的模型，将建立跨越所有这些领域的基础设计原则。我们提出一个神经框架，以端到端方式学习这种模态分解，仅由系统级可观测量监督，而不监督模态参数本身。该架构分解为一个与端口无关的极点预测器和两个与端口相关的耦合预测器，其输出按条目组合，从而分离固有特征与端口相关特征。这种分解使得单个训练模型能够泛化到训练中未见过的端口数量，消除了直接回归的$\mathcal{O}(N^2)$扩展障碍。尽管没有模态监督，自由参数化的极点收敛到物理上有意义的本征模态，通过与AAA有理逼近算法的交叉验证得到证实。我们在射频电磁替代建模中实例化该框架。仅用2端口数据训练的模型能准确预测训练中未见过的N端口响应。
英文摘要
Many engineering building blocks behave as multi-port linear time-invariant systems. RF cavities, photonic devices, and superconducting quantum chips, despite their different underlying physics, all share a common mathematical structure for their port-level response. Each entry of the response matrix is a sum of contributions from a small number of intrinsic resonant modes, the pole-residue form. A model capable of predicting such responses for arbitrary geometries and arbitrary port configurations, while simultaneously extracting the underlying eigenmode structure, would therefore establish a foundational design principle spanning all these domains. We propose a neural framework that learns this modal decomposition end-to-end, supervised only by system-level observables and without supervising the modal parameters themselves. The architecture decomposes into a port-independent pole predictor and two port-dependent coupling predictors whose outputs are combined entry-wise, separating intrinsic from port-dependent features. This factorization yields a single trained model that generalizes to port counts unseen during training, dissolving the $\mathcal{O}(N^2)$ scaling barrier of direct regression. Despite no modal supervision, the freely-parameterized poles converge to physically meaningful eigenmodes, verified by cross-validation against the AAA rational approximation algorithm. We instantiate the framework in radio-frequency electromagnetic surrogate modeling. A model trained only on 2-port data accurately predicts $N$-port responses unseen during training.
