Direct Scheme Calculation of the Kinetic Energy Functional Derivative Using Machine Learning
We report a direct scheme calculation of kinetic energy functional derivative using Machine Learning. Support Vector Regression and Kernel Ridge Regression techniques were independently employed to estimate the kinetic energy functional and its derivative. Even though the accuracy should have been a decisive factor in modeling a realistic functional, we show that at a certain level it affects the generalizability of the model. By choosing the right regularization term and by considering a reasonable interplay between it and the accuracy, we were able to deduce the functional derivative from a model that was trained to estimate the kinetic energy. Although the derivative calculations demand very high accuracy to account for small variations of the kinetic energy, the developed estimator was capable of capturing these extremely small changes of the electron density. This work pours into highly effective implementation of the orbital-free density functional theory as it employs only direct calculation scheme