High-fidelity electromagnetic (EM) simulations are indispensable for the design of microwave and wave devices, yet repeated full-wave evaluations over high-dimensional design spaces are often computationally prohibitive. While neural surrogates can amortize this cost, learning high-dimensional EM response mappings remains difficult under limited simulation budgets due to strong and heterogeneous parameter couplings. In this work, we introduce low-rank tensor function representations as a principled surrogate modeling paradigm for EM problems and provide a systematic study of representative low-rank formats, including Tucker-style low-rank tensor function representation (LRTFR) as well as neural functional tensor-train (TT) and tensor-ring (TR) baselines. Building on these insights, we propose a pairwise low-rank tensor network (PLRNet) that uses learnable pairwise interaction factors over compact coordinate-wise embeddings. Experiments on representative EM surrogate tasks demonstrate that the proposed framework achieves a more favorable overall trade-off between accuracy, robustness, and parameter efficiency, with stable optimization in high-dimensional regimes.

翻译：高保真电磁仿真对微波与波导器件的设计至关重要，然而在高维设计空间中重复进行全波仿真往往面临计算成本过高的问题。尽管神经代理模型能够分摊这一成本，但在有限仿真预算下，由于参数耦合作用强且具有异质性，学习高维电磁响应映射仍存在困难。本研究将低秩张量函数表征作为电磁问题中一种严谨的代理建模范式，并对代表性低秩格式展开系统研究，包括塔克型低秩张量函数表征以及神经函数张量链和张量环基线模型。基于这些见解，我们提出了一种成对低秩张量网络，该网络通过紧凑的坐标向嵌入中的可学习成对交互因子实现建模。在代表性电磁代理任务上的实验表明，所提出框架在精度、鲁棒性和参数效率之间实现了更优的整体权衡，且在高维场景下具有稳定的优化性能。