Asymptotics-guided learning and symbolic regression for dispersive resonances
2026-08-17 • Machine Learning
Machine Learning
AI summaryⓘ
The authors explore how to better predict resonance frequencies in materials where waves spread unevenly, using mathematical tools called volume integral operators. They start with a rough estimate from asymptotic analysis, then teach a model to correct the difference between this estimate and actual resonance data, focusing on special features relevant in two dimensions. Their approach improves predictions for single and paired resonators and creates simple formulas to explain these corrections. This shows that asymptotic analysis can guide both initial estimates and the creation of learned corrections that are easy to understand and use.
resonance predictiondispersive medianonlinear spectral problemsvolume integral operatorsasymptotic analysissubwavelength expansionlogarithmic scalessymbolic regressionsingle resonatordimer
Authors
Konstantinos Alexopoulos, Josselin Garnier
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.