Machine Learning Quantum Mechanics for Materials Science

Nikolaj Rørbæk Knøsgaard

Research output: Book/ReportPh.D. thesis

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Computational materials science plays an important role in the discovery and design of new materials. With accurate and efficient methods for computing the properties of materials it is possible to search through large compositional spaces with the purpose of screening for materials with specific properties. In recent years, the use of machine learning methods in materials science has become increasingly useful. This is a result of the vast amounts of materials data generated using first-principles methods such as density functional theory (DFT), but also the development of new machine learning methods for materials science has had an impact.
Finding good representations or fingerprints of materials as inputs to machine learning models is essential. This thesis presents novel fingerprint methods utilizing additional information from the electronic density and wavefunction obtainable from standard DFT calculations besides the atomic structure. More specifically, the energy decomposed operator matrix elements (ENDOME) fingerprint is constructed using matrix elements of quantum mechanical operators, e.g. the position and momentum operators. Additionally, the radially decomposed projected density of states (RADPDOS) fingerprint is developed using projections of DFT wavefunctions onto atoms and angular orbitals. The presented methods differs from other fingerprints by encoding individual quantum states.
The ENDOME and RAD-PDOS fingerprints of individual states are then applied in a machine learning model. The model predicts the difference in state eigenenergies between a low-fidelity DFT calculation and a high-fidelity G0W0 calculation for 2D materials. The model predicts the G0Wcorrection energies for individual states with a mean absolute error (MAE) of 0.11 eV. This converts to a MAE of 0.15 eV on the G0Wband gap by using the model to compute full G0W0 band structures.
Additionally, the RAD-PDOS fingerprint is used to evaluate the dynamical stability of 2D materials. This is done by training a binary machine learning classification model predicting the stability. The model achieves an excellent receiver operating characteristic with an area under the curve of 0.90, and the model can thus be used to screen materials for dynamic stability without performing expensive phonon calculations.
The dynamical stability is further investigated by developing approximative methods for calculating electron-phonon coupling matrix elements. The methods are based on replacing the DFT effective potential with a potential set up from atomic potentials. With this approximation, the matrix elements are quantitatively similar to the true DFT matrix elements. The approach is further improved by using machine learning to reconstruct the DFT potentials from the atomic potentials, which reduces the error by a factor of ≈ 2.
Original languageEnglish
PublisherDepartment of Physics, Technical University of Denmark
Number of pages147
Publication statusPublished - 2022


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