Bandgap Engineering in the Configurational Space of Solid Solutions via Machine Learning: (Mg,Zn)O Case Study

Abstract

Computer simulations of alloys’ properties often require calculations in a large space of configurations in a supercell of the crystal structure. A common approach is to map density functional theory results into a simplified interaction model using so-called cluster expansions, which are linear on the cluster correlation functions. Alternative descriptors have not been sufficiently explored so far. We show here that a simple descriptor based on the Coulomb matrix eigenspectrum clearly outperforms the cluster expansion for both total energy and bandgap energy predictions in the configurational space of a MgO–ZnO solid solution, a prototypical oxide alloy for bandgap engineering. Bandgap predictions can be further improved by introducing non-linearity via gradient-boosted decision trees or neural networks based on the Coulomb matrix descriptor.

Machine learning of material properties: Predictive and interpretable multilinear models

“…The capabilities and limitations of cluster expansion are known and can be used to predict the accuracy of linear n -grams. For example, in ( 42 ), cluster expansion was shown to perform poorly for the prediction of the mixing energy, E me , of 8043 symmetrically different Zn 8 Mg 24 O 32 structures in a 64 atom supercell. This is a dataset with a fixed composition, multiple space groups, and a very narrow energy range.…”

“…We are able to make this prediction as the physical assumptions present in linear n -grams are known, as is the link to cluster expansion. The test set MAE for cluster expansion in ( 42 ) for the E me was 20 meV per supercell when trained to 6434 structures. However, this corresponds to an R 2 (coefficient of determination) of 0.39 as the energy range is very narrow.…”

“…The comparable accuracy between KRR and a linear model emphasizes the importance of representations for this problem. Although cluster expansion has previously been used for the prediction of the bandgap energies, its use has been limited compared to the wide-spread prediction of formation energies ( 42 , 44 , 45 ). The performance of cluster expansion for bandgap energy prediction has been varied and is dependent on the system studied ( 42 , 44 , 45 ).…”

“…Although cluster expansion has previously been used for the prediction of the bandgap energies, its use has been limited compared to the wide-spread prediction of formation energies ( 42 , 44 , 45 ). The performance of cluster expansion for bandgap energy prediction has been varied and is dependent on the system studied ( 42 , 44 , 45 ). It is yet to be seen whether the addition of cluster-cluster interactions using l 1 regularization and adding the coordination number of the element to identify atoms can allow linear n -grams to accurately predict bandgap energies for a wider range of materials.…”

Using Feature‐Assisted Machine Learning Algorithms to Boost Polarity in Lead‐Free Multicomponent Niobate Alloys for High‐Performance Ferroelectrics

“…However, like for many materials science and engineering problems, the performance (i.e., the error and efficiency) of these classical ML methods is highly sensitive to the size of available data, and usually very large sets of data are needed for accurate and efficient training and prediction. [20,21] In contrast to the aforementioned conventional ML approaches, [22,23] the recently developed sure independence screening sparsifying operator (SISSO) [24] is a very promising method that helps in the identification of the best physically interpretable descriptor of a target property. By searching extensive nonlinear feature spaces generated via a combination of algebraic/functional operations recursively, SISSO is able to extract effective descriptors for even relatively sparse data.…”