Machine Learning for Predicting the Surface Plasmon Resonance of Perfect and Concave Gold Nanocubes

Abstract

Using the combination of the discrete dipole approximation (DDA) and machine learning methods, we have developed a computational tool to predict the wavelength at which the dipole surface plasmon resonance (SPR) of gold concave nanocubes (GCNCs) takes place. First, we have used the DDA to generate SPR data considering two main features, the length and the concavity of the nanocube. Then, for training, test, and validation, two mechanisms were considered. Mechanism A consisted in splitting 100% of the generated data into two separate sets, one covering 75% and other with the remaining 25% of the whole data. The two separate subsets were used as training and test sets, respectively. Mechanism B basically consisted of SPR data set splitting into k subsets, following a k-fold cross validation procedure. For the machine learning algorithms, we used the K-nearest neighbors model, the ridge regression, and the artificial neural network regressor. The three models utilized here lead to different accuracies that depend on the selection of the mechanism used, either A or B. It was found that the accuracy in the prediction is sensitive to the L 2 regularization when the ridge regression is used. On the other hand, when the K-nearest neighbors model is employed, the accuracy depends on the number of nearest neighbors utilized during the calculations. With ridge regression or Knearest neighbors, the accuracy obtained is between 80 and 94%. The best method for the SPR prediction of the GCNCs is the artificial neural network with eight neurons and L 2 = 10 because the accuracy for the predicted values is around 93%.

Modeling of plasmonic properties of nanostructures for next generation solar cells and beyond

“…He et al [235] fitted a multilayer NN (with hundreds of neurons per layer) to finite-difference time domain (FDTD) solutions of the Maxell's equations for nanospheres and nanorods and their dimers and also achieved both the forward prediction of the optical properties and the inverse prediction of dimensional parameters of NPs. Arzola-Flores and González [236] compared ridge regression (Tikhonov-regularized linear regression), a multilayer perceptron neural network, and K-nearest neighbors when machined-learning the wavelength of the dipole surface plasmon resonance (SPR) of gold concave nanocubes as a function of geometries features (edge lengths and depth radius) to data computed with discrete dipole approximation (DDA) [237], which is a simple model employing dipoles arranged in a cubic lattice that yield the response to an applied electric field. The best approach in this case was found to be the NN (with two hidden layers) with an accuracy of 94% (which was defined as the R 2 value between the predicted and exact values of the peak wavelength), which is roughly in line with Pearson coefficients obtained by He et al [235] A large NN was also used by Li et al [238] to map the geometry of a nanostructure to the spectrum by training on FDTD data.…”

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“…Thus, it is time-and power-intensive to accurately simulate nanostructures of high complexity for production or research purposes. Moreover, the design process for plasmonic devices of various material compositions and topologies mostly employs trial-and-error iterations to achieve the desired functionality [47], further lengthening the computing time. Apart from simulations, many state-of-the-art spectroscopic and microscopy techniques require a novel data-driven approach to enhance the imaging quality and analyze the result data [48,49].…”

“…Three ML approaches were used namely ridge regression, K nearest neighbour, and artificial neural network (ANN). ANN proved to be the most suitable for predicting the SPR location in this scenario [47]. In Verma et al's work on plasmonic paired nanostructures, they designed an ANN to model the optical responses (e.g., plasmonic wavelength, sensitivity, etc.)…”

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“…Reproducible and bioreceptor-oriented surface chemistries remain, in addition, an ultimate step to be optimized for each analyte, even for portable SPR devices. The integration of deep- and machine-learning approaches to improve the detection characteristics of SPR is becoming an important and integral part for faster and sustainable sensing [ 25 , 60 , 61 , 62 ]. Some portable plasmonic devices had been reported, such as the smart-phone-based SPRI by Guner at al.…”