Mlatticeabc: Generic Lattice Constant Prediction of Crystal Materials Using Machine Learning

Abstract

Lattice constants such as unit cell edge lengths and plane angles are important parameters of the periodic structures of crystal materials. Predicting crystal lattice constants has wide applications in crystal structure prediction and materials property prediction. Previous work has used machine learning models such as neural networks and support vector machines combined with composition features for lattice constant prediction and has achieved a maximum performance for cubic structures with an average coefficient of determination ( R 2 ) of 0.82. Other models tailored for special materials family of a fixed form such as ABX 3 perovskites can achieve much higher performance due to the homogeneity of the structures. However, these models trained with small data sets are usually not applicable to generic lattice parameter prediction of materials with diverse compositions. Herein, we report MLatticeABC, a random forest machine learning model with a new descriptor set for lattice unit cell edge length ( a , b , c ) prediction which achieves an R 2 score of 0.973 for lattice parameter a of cubic crystals with an average R 2 score of 0.80 for a prediction of all crystal systems. The R 2 scores are between 0.498 and 0.757 over lattice b and c prediction performance of the model, which could be used by just inputting the molecular formula of the crystal material to get the lattice constants. Our results also show significant performance improvement for lattice angle predictions. Source code and trained models can be freely accessed at .

Examining graph neural networks for crystal structures: limitations and opportunities for capturing periodicity

“…Limitations of GNNs for capturing periodicity. Although previous works have suggested that lattice constants of crystal structures are learnable based on only compositions 40,41 , the results in this work show that even with structures as input, CGCNN and ALIGNN cannot capture lattice constants well. In this section, we analyze the possible reasons for such failure and obtain insights for improving GNNs for crystal structures.…”

“…For the dataset used for testing whether CGCNN and ALIGNN can capture human-designed descriptors of crystal structures, since we know that lattice constants of high-symmetry materials are reported to be more learnable than that of low-symmetry materials 40,41 based on compositions, we create a subset of the Materials Project database ("MP dataset") by removing some structures randomly based on their space group number: 𝑃𝑃𝑡𝑡𝑃𝑃𝑏𝑏𝑎𝑎𝑏𝑏𝑖𝑖𝑠𝑠𝑖𝑖𝑔𝑔𝑦𝑦(removed) = Space group number Space group number+15 , where 15 is the space group number of the C2/c group, the last space group in the class of monoclinic Bravais lattice. Consequently, we have a dataset with 47,862 crystal structures biased to materials with low symmetry to test whether CGCNN and ALIGNN can learn human-designed descriptors from crystal structures.…”

Crystal Structure Prediction Using an Age-Fitness Multiobjective Genetic Algorithm and Coordination Number Constraints

“…In many cases, the radius ratio plays an important role. At present, the space group , and lattice constants , of crystal structures can be predicted, and the contact map of a given composition can also be predicted by the deep learning method . With the development of machine learning algorithms, we expect that the various inputs required by our multiobjective genetic algorithm for crystal structure reconstruction can be predicted with high precision, so as to allow our CMCrystalMOO to achieve a high-quality crystal structure prediction with only a given composition.…”

Predicting thrust force during drilling of composite laminates with step drills through the Gaussian process regression

“…GPRs are probabilistic non-parametric models [1]. GPR models could generally work well for relatively small datasets (Koriyama and Kobayashi, 2015;Li et al, 2021;Sheng et al, 2021). We use x i ; y i ð Þ; i ¼ 1; 2; .…”