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Ward et al. Surprisingly, the structural information from the Voronoi tessellation did not improve the results for the training set of 30, materials. This is based on the fact that very few materials with the same composition, but different structure, are present in the dataset. A recent study by Kim et al. The model was trained for different datasets complete open quantum materials database, 80 only the quaternary Heusler compounds, etc. For the prediction of Heusler compounds, it was found that the accuracy of the model also benefited from the inclusion of other prototypes in the training set.
It has to be noted that studies with such large datasets are not feasible with kernel-based methods e. Li et al. Extremely randomized trees proved to be the best classifiers accuracy 0. The errors in this work are difficult to compare to others as the elemental composition space was very limited.
Another work treating the problem of oxide—perovskite stability is ref. Using neural networks based only on the elemental electronegativity and ionic radii, Ye et al.
Unfortunately, their dataset contained only compounds for training, cross-validation, and testing. Ye et al.
By reducing the mixing to the C-site and including additional structural descriptors, Ye et al. If one compares this study to, e. This is easily explained once we notice that ref. In other words, the complexity of the problem differs by more than two orders of magnitude. Up to this point, all component prediction methods presented here relied on first-principle calculations for training data. Owing to the prohibitive computational cost of finite temperature calculations, nearly all of this data correspond to zero temperature and pressure and therefore neglects kinetic effects on the stability.
Recent advances and applications of machine learning in solid-state materials science
Furthermore, metastable compounds, such as diamond, which are stable for all practical purposes and essential for applications, risk to be overlooked. The following methods bypass this problem through the use of experimental training data. The first structure prediction model that relies on experimental information can be traced back to the s. One example that was still relevant until the past decade is the tolerance factor of Goldschmidt, a criterion for the stability of perovskites.
Balachandran et al. The advantage of stability prediction based on experimental data is a higher precision and reliability, as the theoretical distance to the convex hull is a good but far from perfect indicator for stability. Histogram of the distance to the convex hull for perovskites included in the inorganic crystal structure database. Another system with a relatively high number of experimentally known structures are the AB 2 C Heusler compounds. Oliynyk et al. Using basic elemental properties as features, Olynyk et al. Legrain et al. While comparing the results of three ab initio high-throughput studies 37 , , to the machine learning model, they found that the predictions of the high-throughput studies were neither consistent with each other nor with the machine learning model.
The inconsistency between the first-principle studies is due to different publication dates that led to different knowledge about the convex hulls and to slightly differing methodologies. In addition, the machine learning model was able to correctly label several structures for which the ab initio prediction failed.
This demonstrates the possible advantages of experimental training data, when it is available. Zheng et al.
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Transfer learning considers training a model for one problem and then using parts of the model, or the knowledge gained during the first training process, for a second training thereby reducing the data required. An image of the periodic table representation was used in order to take advantage of the great success of convolutional neural networks for image recognition.
The weights of the neural network were then used as starting point for the training of a second convolutional neural network that classified the compositions as stable or unstable according to training data from the inorganic crystal structure database. Hautier et al. These predictions were then validated with ab initio computations. The machine learning part had the task to provide the probability density of different structures coexisting in a system based on the theory developed in ref.
Using this approach, Hautier et al. This resulted in compositions and crystal structures, whose energy was calculated using DFT. To assess the stability, the energies of all decomposition channels that existed in the database were also calculated, resulting in new compounds on the convex hull.
It is clear that component prediction via machine learning can greatly reduce the cost of high-throughput studies through a preselection of materials by at least a factor of ten.
While studies based on experimental data can have some advantage in accuracy, this advantage is limited to crystal structures that are already thoroughly studied, e. For a majority of crystal structures, the number of known experimentally stable systems is extremely small and consequently ab initio data-based studies will definitely prevail over experimental data-based studies. Once again, a major problem is the lack of any benchmark datasets, preventing a quantitative comparison between most approaches.
This is even true for work on the same structural prototype. Considering, for example, perovskites, we notice that three groups predicted distances to the convex hull. In contrast to the previous section, where the desired output of the models was a value quantifying the probability of compositions to condense in one specific structure, models in this chapter are concerned with differentiating multiple crystal structures. Usually this is a far more complex problem, as the theoretical complexity of the structural space dwarfs the complexity of the composition space.
Nevertheless, it is possible to tackle this problem with machine learning methods.
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Early attempts, which predate machine learning, include, e. Some of the first applications of modern machine learning crystal structure prediction can be found in ref. There, Fischer et al. Their method estimates the correlation of the stability of two structures with respect to their composition. The model was trained with data from ref. It has to be mentioned here once again that leave-one-out cross validation is not a good method to evaluate the extrapolation ability of such models. Olynyk et al. In order to reduce the complexity of the problem, only the seven most common binary prototype structures were considered.
A dataset of compounds was divided into three sets, for feature selection, for optimization of the PLS-DA and SVMs, and for validation. The SVMs performed better with an average false positive rate of 5. It has to be noted that these values differ significantly depending on the crystal system that one tries to predict see Fig.
This approach was adapted by Olynyk et al.
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Reducing the number of features via cluster resolution, from an initial features to , resulted in a sensitivity of Predicted probability for ZnS-type left and CsCl-type structures right for the support vector machine model with 31 features. As crystal structure prediction is only the first step in the rational design process, combining stability determination with property design is necessary. First, SVMs were used to classify them into perovskites and non-perovskites, followed by a prediction of the Curie temperature of those classified as perovskites.
Once a candidate was experimentally synthesized, it was added to the training set and the process was repeated. Graser et al. As expected, the recall improved with increasing cutoff number. The confusion table see Fig. Confusion matrix for cutoff size of a perfect confusion matrix is diagonal. Park et al. All the others methods discussed up to now used the chemical composition, or data derived from the chemical composition, and structure as descriptors.
In contrast, Park et al. Because the three-dimensional electron density is contracted into a 1D diffraction pattern, the symmetry of the crystal is often not fully determined from the diffraction pattern alone, especially for low-symmetry structures. While software for indexing and determining the space group exists, it requires substantial expertise and human input to obtain the correct results.