Machine-Learned Decision Trees for Predicting Gold Nanorod Sizes from Spectra

Electron microscopy is often required to correlate the size and shape of plasmonic nanoparticles with their optical properties. Eliminating the need for electron microscopy is one crucial step toward in situ sensing applications, especially for complicated sample conditions such as during irreversible chemical reactions or when particles are embedded in a matrix. Here, we show that a machine learning decision tree can accurately predict gold nanorod dimensions over a wide range of sizes. The model is trained by using ∼450 nanorod geometries and corresponding scattering spectra obtained from finite-difference time-domain simulations. We test the model using a set of experimental spectra and sizes obtained from correlated scanning electron microscopy images, resulting in predictions of the dimensions of gold nanorods within ∼10% of their true values (root-mean-squared percentage error) over a large range of sizes. Analysis of the decision tree structure reveals that a relationship with resonance energy and line width of the localized surface plasmon resonance is sufficient to predict nanorod dimensions, notably outperforming more complicated models. Our findings illustrate the advantages of using machine learning models to infer single particle structural features from their optical spectra.