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

Abstract

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.

Incorporating plasmonic featurization with machine learning to achieve accurate and bidirectional prediction of nanoparticle size and size distribution

“…[8][9][10][11][12][13] Instead of these traditional analytical frameworks, machine learning (ML) algorithms demonstrate immense potential to analyze plasmonic nanoparticles' optical spectra and achieve accurate estimations of their dimensional parameters. [14][15][16][17][18] ML algorithms can (1) uncover functions that connect inputs with outputs and in the process elucidate complex underlying trends/patterns within a dataset and (2) continuously learn in every iteration to improve prediction accuracy. [19][20][21] The key to ML success is the quality of input data (features) that are used in the algorithm.…”

“…[19][20][21] Current ML-UV-vis studies employ statistical feature selection methods to compute the contribution of each datapoint (feature) towards prediction report significant errors of B10%. 16,18 This is because each datapoint in the spectra (assuming 1 datapoint/nm, we will have B600 datapoints/spectra) encodes very little information. It is also challenging to find the optimal number and permutation of datapoints (feature) within the dataset for nanoparticle size prediction.…”

“…It is also challenging to find the optimal number and permutation of datapoints (feature) within the dataset for nanoparticle size prediction. 16,18,22,23 We hypothesize that feature engineering based on established plasmonic knowledge can better complement ML predict nanoparticle size and size distribution. Besides extracting primary information such as LSPR positions, featurization allows us to derive secondary spectral information, such as LSPR full width at half maximum (FWHM) that is not readily obtainable from the B600 original datapoints, as inputs for the ML model.…”

Correlating structure, morphology and properties of metal nanostructures by combining single-particle optical spectroscopy and electron microscopy

“…Finally, inferring structural information directly from the optical spectra can be investigated as another strategy to overcome the limitations of electron beam damage, temporal resolution and statistics arising from the need of EM to correlate morphology to optical properties of NSs. 78,[135][136][137][138] For example, Payne et al used high throughput quantitative extinction microscopy in combination with electromagnetic simulations to measure the size and shape of metal NSs fully optically. 135 Dawson and co-workers demonstrated that it is also possible to detect the shape of anisotropic gold NSs in dispersion by optical means.…”

Intelligent metaphotonics empowered by machine learning

“…It may become an extremely useful assisting tool for experimental measurements. The demonstrations in this field include characterization of orientation [204] or size [205] of metallic nanoparticles using measured spectral data. ML find its applications in a variety of microscopy and imaging techniques [206,207] as well as for tracking [208], localization [209] and analysis of single molecules [210].…”