Surrogate Modeling with Low-Rank Function Representation for Electromagnetic Simulation
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917354632380416 |
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| author | Sun, Mingze Li, Liang Zhao, Xile Tan, Zheng Hu, Yulu Li, Xing Li, Bin |
| author_facet | Sun, Mingze Li, Liang Zhao, Xile Tan, Zheng Hu, Yulu Li, Xing Li, Bin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19735 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Surrogate Modeling with Low-Rank Function Representation for Electromagnetic Simulation Sun, Mingze Li, Liang Zhao, Xile Tan, Zheng Hu, Yulu Li, Xing Li, Bin Computational Engineering, Finance, and Science Numerical Analysis 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. |
| title | Surrogate Modeling with Low-Rank Function Representation for Electromagnetic Simulation |
| topic | Computational Engineering, Finance, and Science Numerical Analysis |
| url | https://arxiv.org/abs/2603.19735 |