发表机构
CMAP; CNRS; Ecole polytechnique; Institut Polytechnique de Paris（CMAP; 法国国家科学研究中心; 巴黎综合理工学院; 巴黎理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对色散介质共振预测的非线性谱问题，以渐近分析为引导，结合亚波长展开特征学习残差并通过符号回归生成紧凑公式，提升了单谐振器与二聚体的共振预测精度，为数据驱动修正提供了可解释的低维特征空间。
AI 中文摘要
我们研究色散介质中的共振预测问题，该问题被表述为体积积分算子的非线性谱问题。核心思路是将渐近分析不仅用作基线近似，还用作构建预测修正模型的指导。我们利用亚波长展开建议的特征（包括二维特有的对数尺度）学习渐近共振与参考共振之间的残差。所得修正显著提升了单谐振器和二聚体的预测精度，符号回归则为学习到的残差生成了紧凑公式。结果表明，渐近分析不仅可用于近似共振，还可用于设计特征空间，使数据驱动的修正变得准确、低维且可解释。
英文摘要
We study resonance prediction in dispersive media, formulated as nonlinear spectral problems for volume integral operators. The main idea is to use asymptotic analysis not only as a baseline approximation, but also as a guide for constructing predictive correction models. We learn the residual between asymptotic and reference resonances using features suggested by the subwavelength expansion, including the logarithmic scales specific to two dimensions. The resulting corrections substantially improve single-resonator and dimer predictions, and symbolic regression produces compact formulas for the learned residual. The results show that asymptotic analysis can be used not only to approximate resonances, but also to design the feature space in which data-driven corrections become accurate, low-dimensional, and interpretable.
Comments25 pages, 11 figures, 6 tables
