Predicting structure-dependent Hubbard U parameters via machine learning

Abstract

DFT+U is a widely used treatment in the density functional theory (DFT) to deal with correlated materials that contain open-shell elements, whereby the quantitative and sometimes even qualitative failures of local and semi-local approximations can be corrected without much computational overhead. However, finding appropriate U parameters for a given system and structure is non-trivial and computationally intensive, because the U value has generally a strong chemical and structural dependence. In this work, we address this issue by building a machine learning (ML) model that enables the prediction of material- and structure-specific U values at nearly no computational cost. Using Mn-O as an example, the ML model is trained by calibrating DFT+U electronic structures with the hybrid functional results of more than 3000 structures. The model allows us to determine an accurate U value (MAE=0.128 eV, R2=0.97) for any given structure. Further analysis reveals that M-O bond lengths are key local structural properties in determining the U value. This approach of the ML U model is universally applicable, to significantly expand and solidify the use of the DFT+U method.

Machine Learning for Chemical Looping: Recent Advances and Prospects

“…Common evaluation indexes for classification models include the confusion matrix, accuracy, error rate, precision, recall ratio, F 1 score, receiver operating characteristic (ROC) curve, area und the curve (AUC), precision–recall (PR) curve, log loss, and text report of classification indexes. Common evaluation indexes in regression include mean absolute error (MAE), − mean-squared error (MSE), − root-mean-squared error (RMSE), , and coefficient of determination ( R 2 ). , Among these metrics, a better fit is indicated by a value closer to 0 for MAE, MSE, and RMSE and a value closer to 1 for R 2 .…”