Asymptotics-guided learning and symbolic regression for dispersive resonances

2026-08-17

AI Summary

This study addresses the limited accuracy and lack of interpretability in predicting nonlinear spectral resonances within dispersive media by proposing an interpretable residual learning framework guided by asymptotic analysis. By translating asymptotic analysis into feature space design principles and constructing subwavelength expansion features, the method employs machine learning to correct theoretical residuals while utilizing symbolic regression to derive compact analytical expressions. This approach facilitates a paradigm shift from conventional approximation tools to data-driven corrections, significantly enhancing resonance prediction accuracy for both single resonators and dimers. Ultimately, this work yields a predictive model that simultaneously achieves high precision, low dimensionality, and physical interpretability, effectively bridging rigorous theoretical analysis with modern data-driven methodologies for complex electromagnetic systems.

Abstract

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.

Problem

• Dispersive media
• Resonance prediction
• Nonlinear spectral problems
• Volume integral operators

Innovation

• Asymptotics-guided learning
• Symbolic regression
• Dispersive resonances
• Subwavelength expansion
• Interpretable correction