A Machine Learning-Driven Methodology for the Precise Determination of the Ground State Energy of Helium Atom

Here the ground state energy of helium atom is investigated and also a Machine Learning (ML) model is constructed using Gaussian Process Regression (GPR) algorithm for the same. The parameters free perturbative method in matrix representation approach is used,in which the approximation is improved by adding higher order p-orbital states. The error is reduced to be 1.93%.This allows us to confirm that the accuracy of the energy value will converge with respect to adding higher order states of p-orbital, d-orbital, etc. Since here prediction belongs to regression model, Gaussian Process Regression (GPR) is chosen. With small dataset we extend this work for ML energy prediction model using GPR technique which is used to inter or extrapolate the ground state energy value.Cross validation is also done using R2 evaluation metric.