Supervised deep learning prediction of the formation enthalpy of the full set of configurations in complex phases: the $\sigma-$phase as an example

TL;DR

This study demonstrates that supervised deep learning models can accurately predict the formation enthalpy of complex phases in solid-state chemistry, using a large dataset of $\sigma$-phase compounds, significantly advancing high-throughput materials discovery.

Contribution

The paper introduces a large first-principles dataset and a neural network approach that improves prediction accuracy for complex phase configurations, highlighting the importance of physical descriptors and binary data in training.

Findings

Neural networks outperform traditional regression methods.

Physical descriptors enhance model accuracy.

Binary composition data is crucial for predicting complex configurations.

Abstract

Machine learning (ML) methods are becoming integral to scientific inquiry in numerous disciplines, such as material sciences. In this manuscript, we demonstrate how ML can be used to predict several properties in solid-state chemistry, in particular the heat of formation of a given complex crystallographic phase (here the $\sigma-$phase, $tP30$, $D8_{b}$). Based on an independent and unprecedented large first principles dataset containing about 10,000 $\sigma-$compounds with $n=14$ different elements, we used a supervised learning approach, to predict all the $\sim$500,000 possible configurations within a mean absolute error of 23 meV/at ($\sim$2 kJ.mol$^{-1}$) on the heat of formation and $\sim$0.06 Ang. on the tetragonal cell parameters. We showed that neural network regression algorithms provide a significant improvement in accuracy of the predicted output compared to traditional regression techniques. Adding descriptors having physical nature (atomic radius, number of valence electrons) improves the learning precision. Based on our analysis, the training database composed of the only binary-compositions plays a major role in predicting the higher degree system configurations. Our result opens a broad avenue to efficient high-throughput investigations of the combinatorial binary calculation for multicomponent prediction of a complex phase.