Prediction of Gaunt factor by using Support vector regression

Abstract

This research aims to study the possibility of using the Support Vector Regression(SVR) algorithm to predict the values of the Gaunt factor, which is a fundamental element in quantum calculations, especially in describing interactions between electrons in multi electron atoms. This factor is used in complex angular integrals and plays a pivotal role in electron spectral and atomic structure calculations. A predictive model was developed using SVR based on a pre-calculated dataset containing inputs such as angular quantum numbers and interacting orbitals. Several types of kernel functions were tested, and the parameters were tuned to achieve the best predictive performance. The model results showed good accuracy (0.999) and the mean square error MSE (0.003) and in pre dicting the values of the Gaunt factor and also demonstrated the algorithm’s efficiency in representing complex nonlinear relationships between variables. This research con tributes to opening new avenues for accelerating computations in quantum mechanics and confirms the feasibility of interacting machine learning techniques into theoretical sciences, paving the way towards developing more efficient tools for studying complex quantum systems