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Machine Learning the Thermodynamic Stability of Crystal structures

Authors: Jonathan Schmidt

Ref.: PhD thesis, Martin-Luther University of Halle-Wittenberg (2022)

Abstract: In recent years machine learning is quickly becoming one of the most valuable tools in solid-state material science. In this cumulative thesis we develop two applications of machine learning to solid-state physics and material science. First, we train machine learning exchange-correlation functionals for density functional theory (DFT). In contrast to earlier works we not only train for the exchange-correlation energy but also use automatic differentiation to train for the correct potential as functional derivative of the neural network. Such neural network functionals can be extremely nonlocal while retaining the same computational scaling of local and semilocal functionals and promise to solve some of the non-locality problems plaguing DFT.

We also develop Crystal-Graph Attention networks (CGAT) for the prediction of thermodynamically stable materials. Previous generations of graph neural networks typically use the atomic positions and the atomic species as input. However, one can only obtain the atomic positions of the relaxed crystal structures during high-throughput searches via DFT calculations. Thus making it impossible to apply these networks directly to such studies. We solve this challenge by replacing the atomic distances with embeddings of the graph distances to create networks suitable for high-throughput studies. To train these networks we accumulate and clean one of the largest datasets of DFT calculations with consistent parameters. Applying the dataset and the new network topology to high-throughput searches we have already discovered more than 14000 materials that are stable relative to the convex hull we started with. Using the hull resulting from our original dataset we perform more than 200k geometry optimizations with the Perdew-Burke-Ernzerhofer functional for solids (PBEsol) and single point calculations with the Strongly Constrained and Appropriately Normed (SCAN) functional to obtain a convex hull and structural information from functionals beyond the PBE. These will allow for a more accurate prediction of stable materials and their properties in the future.