Predictive ultrafast laser-induced formation of MoOx using machine learning algorithms

This research introduces an innovative methodology leveraging machine learning algorithms to predict the outcomes of experimental and numerical tests with femtosecond (fs) laser pulses on 500-nm-thick molybdenum films. The machine learning process encompasses several phases, including data acquisition, pre-processing, and prediction. This framework effectively simulates the interaction between fs laser pulses and the surface of molybdenum thin films, enabling precise control over the creation of MoO x phases. The exceptional precision of fs laser pulses in generating molybdenum oxides at localized micrometer scales is a significant advantage. In this study, we explored and evaluated 13 different machine learning methods for predicting oxide formation results. Our numerical results indicate that the extra trees (ET) and gradient boosting (GB) algorithms provide the best performance in terms of mean squared error, mean absolute error, and R-squared values: 48.44, 3.72, and 1.0 for ET and 32.25, 3.72, and 1.0 for GB. Conversely, support vector regression (SVR) and histogram gradient boosting (HGB) performed the worst, with SVR yielding values of 712.48, 15.27, and 0.163 and HGB yielding values of 434.29, 16.37, and 0.548. One of the most significant aspects of this research is that training these algorithms did not require hyperparameter optimization, and the training and validation process only needed 54 experimental samples. To validate this, we used a technique known as leave-one-out cross-validation, which is a robust validation method when the available data is limited. With this research, we aim to demonstrate the capability of machine learning algorithms in applications where data is limited due to the high cost of real experimentation, as is often the case in the field of optics.