用渐近分析指导数据模型，提升色散介质共振预测精度
Asymptotics-guided learning and symbolic regression for dispersive resonances
- 以渐近分析为特征提取依据，构建预测修正模型
- 对单共振器和二聚体的预测误差显著降低
- 符号回归生成简洁可解释的物理公式，适合物理建模者
我们研究色散介质中的共振预测问题，将其建模为体积积分算子的非线性谱问题。核心思想是将渐近分析不仅作为近似基准，更用于引导构建预测修正模型。通过子波长展开建议的特征，包括二维特有的对数尺度，学习渐近解与参考共振之间的残差。所得到的修正显著提升了单共振器和二聚体的预测性能，符号回归进一步生成了紧凑的残差表达式。结果表明，渐近分析不仅能近似共振，还能设计出使数据驱动修正具有高精度、低维度和可解释性的特征空间。
原文摘要 · Abstract (English)
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.
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