Surrogate Modeling with Low-Rank Function Representation for Electromagnetic Simulation

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.

Figures (12)

• Figure 1: Tucker-type low-rank coupling in LRTFR (3D example): each scalar input is mapped to a latent vector, and the output is obtained by contracting these vectors with a global core tensor $\mathcal{C}$.
• Figure 2: Tensor-network low-rank couplings used as baselines. In both cases, each input $x_i$ is mapped to $R_i(x_i)$ and reshaped into a matrix core $C_i(x_i)$. (a) TT coupling uses a chain-structured contraction. (b) TR coupling uses a cyclic contraction on a ring.
• Figure 3: Overview of PLRNet. Each scalar input $x_i$ is mapped by a one-dimensional embedding network $f_{\theta_i}(\cdot)$ to a latent vector $R_i$. For each unordered pair $(i,j)$, a learnable interaction core $C_{i,j}$ produces a pairwise feature $z_{i,j}=f(R_i,R_j,C_{i,j})$. All pairwise features are concatenated and fed into a global prediction network to output the target response $y$.
• Figure 4: Elliptic-cylinder bistatic RCS benchmark. Inputs include geometry $(a,b)$ and excitation/observation settings $(f,\phi_i,\phi_s)$; the surrogate predicts $\sigma_{\mathrm{dB}}(\phi_s)$.
• Figure 5: Training and test loss curves for the elliptic-cylinder RCS benchmark.