Surrogate Modeling with Low-Rank Function Representation for Electromagnetic Simulation
This work addresses the computational bottleneck in electromagnetic simulation design for microwave and wave devices, offering an incremental improvement in surrogate modeling efficiency.
The paper tackles the challenge of learning high-dimensional electromagnetic response mappings under limited simulation budgets by introducing low-rank tensor function representations as a principled surrogate modeling paradigm. The proposed pairwise low-rank tensor network (PLRNet) achieves a more favorable trade-off between accuracy, robustness, and parameter efficiency in experiments on representative EM surrogate tasks.
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.