Surrogate Modeling with Low-Rank Function Representation for Electromagnetic Simulation

2026-03-20

AI Summary

This work addresses the challenge of constructing high-fidelity surrogate models for high-dimensional electromagnetic simulations under limited computational budgets, where strong parameter coupling and high evaluation costs hinder conventional approaches. The authors systematically investigate low-rank tensor function representations—including Tucker, tensor train (TT), and tensor ring (TR)—and propose PLRNet, a novel framework that leverages learnable pairwise interaction factors and compact coordinate embeddings to effectively capture nonlinear couplings among high-dimensional variables. Experimental results on representative electromagnetic surrogate modeling tasks demonstrate that PLRNet significantly outperforms existing methods, achieving superior accuracy, robustness, and parameter efficiency in high-dimensional design spaces, while also exhibiting enhanced optimization stability.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Intelligent Robots: Learning & Optimization for ROB
• Planning, Routing, and Scheduling: Planning/Scheduling and Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• surrogate modeling
• electromagnetic simulation
• high-dimensional design
• parameter coupling
• computational cost

Innovation

• low-rank tensor
• surrogate modeling
• electromagnetic simulation
• pairwise interaction
• tensor network