Comparative machine-learning modelling and optimisation-based inverse design for the localised surface plasmon resonance of gold nanoparticles

Abstract

The optical behaviour of gold nanoparticles is mainly governed by the localised surface plasmon resonance (LSPR), which forms the basis for biosensing, bioimaging, and photothermal therapy applications. Conventional electromagnetic methods predict LSPR well, but come with a high computational cost that limits the speed of parameter space exploration. Consequently, we trained and evaluated three supervised machine-learning (ML) models, namely artificial neural network (ANN), support vector regression (SVR), and Gaussian process regression employing a dataset of 3230 extinction spectra generated from Mie and Gans theories, aiming to predict resonance wavelength, peak intensity, and full width at half maximum (FWHM). All three models achieve R2=0.98 for resonance wavelength and intensity, and paired significance tests reveal a distinct complementarity among them: SVR is optimal for resonance wavelength, GPR for intensity, and ANN for FWHM. Partitioning methods that break the regularity of the sampling grid demonstrate that this accuracy arises from interpolation within a densely sampled design space and does not extend to extrapolation. Combining the surrogates with a differential-evolution optimiser provides an inverse-design scheme that retrieves particle geometries from a specified wavelength, matching the analytical simulator to an average of 0.45 nm. We characterise the reachable domain, utilise the non-uniqueness of the inverse problem as a multi-objective design parameter, and constrain the domain of physical validity using a retardation-corrected dipole model. In comparison with twelve experimentally characterised nanorods, the framework differs from measurements by 79.0 nm; we show that this discrepancy arises from the underlying physical model rather than the learned surrogate. This framework offers a fast physics-based tool for the rational design of plasmonic nanostructures.