Machine Learning to Predict Quasicrystals from Chemical Compositions

Abstract

Quasicrystals have emerged as the third class of solid‐state materials, distinguished from periodic crystals and amorphous solids, which have long‐range order without periodicity exhibiting rotational symmetries that are disallowed for periodic crystals in most cases. To date, more than one hundred stable quasicrystals have been reported, leading to the discovery of many new and exciting phenomena. However, the pace of the discovery of new quasicrystals has lowered in recent years, largely owing to the lack of clear guiding principles for the synthesis of new quasicrystals. Here, it is shown that the discovery of new quasicrystals can be accelerated with a simple machine‐learning workflow. With a list of the chemical compositions of known stable quasicrystals, approximant crystals, and ordinary crystals, a prediction model is trained to solve the three‐class classification task and its predictability compared to the observed phase diagrams of ternary aluminum systems is evaluated. The validation experiments strongly support the superior predictive power of machine learning, with the overall prediction accuracy of the phase prediction task reaching ≈0.728. Furthermore, analyzing the input–output relationships black‐boxed into the model, nontrivial empirical equations interpretable by humans that describe conditions necessary for stable quasicrystal formation are identified.

Studying Complex Evolution of Hyperelastic Materials under External Field Stimuli using Artificial Neural Networks with Spatiotemporal Features in a Small‐Scale Dataset

“…On the one hand, high-precision DL models often require datasets with large sample sizes to supply sufficient information for their training. [9,10] Current material design methods based on DL mainly rely on large-scale open-source theoretical calculation databases [11,12] or advanced simulation tools [1,[13][14][15][16] to obtain sufficiently large datasets, which originate from highly idealized molecular or structural models and differ from datasets based on actual experimental measurements. The distortion of these datasets is then also naturally inherited by the DL models that are trained on them.…”

Functional Output Regression for Machine Learning in Materials Science

“…Recently, there has been a growing trend to use machine-learning techniques to accelerate the process of designing and creating new materials in various domains of material science. Conventionally, machine-learning models are used to rapidly perform high-throughput virtual screening across millions or billions of candidate materials that span an enormous search space. − In general, a model describes physicochemical, electronic, thermodynamic, or mechanical properties as a function of the input materials, which are given in various forms, such as small- or macro-molecules, crystalline systems, chemical or raw material compositions, and their mixtures. To put the task into a machine-learning framework, such a non-numeric variable needs to be transformed into a fixed-length numeric vector called a descriptor , which represents the compositional or structural features of the given material. − Under the supervision of given data, a model is trained to learn the mapping from the vectorized features to their respective properties.…”

“…A class of descriptors, referred to as molecular fingerprints, has long been studied in chemical informatics, which converts a chemical structure or molecular graph into an integer-valued vector according to the presence or absence or the number of occurrences of a particular chemical fragment, in which hundreds or thousands of fragments are considered. − Another type of molecular descriptor employs a quantitative representation of the topological or physicochemical features of a molecular system. − Chemical composition can be considered as a set variable consisting of a variable number of element species and their contents. There are a large volume of previous studies on the representation of such compositional features. − A crystal structure is typically vectorized by encoding the local structural environments of each atom and the neighboring relations of constituent atoms in a unit cell. − , In recent years, there has also been an increasing trend in treating a material structure as a graph and in modeling its properties using graph neural networks (NNs). − A natural representation of the chemical structure is created on a labeled graph. A periodic configuration of atoms in a crystalline system can also be translated into a graph called a crystal graph, which represents the coordination of constituent atoms in infinitely arranged unit cells .…”

Prediction of Phase Diagrams and Associated Phase Structural Properties

“…Riding the wave of machine learning, the number of attempts to predict phase diagrams using data-driven approaches has increased significantly. However, because of the complexity of generating sufficiently high-quality data, the majority of these works focused on systems consisting of a relatively small number of elements, such as two-species oxides , or other oxides consisting of <10 species. , Other works applied machine learning to cementite, high-pressure water, lipides, single-substance phase diagrams, the prediction of phases of block copolymers, of magnetic and superconducting phase diagrams, thin films, disordered alloys, the discovery of new quasi-crystal materials, of high entropy alloys, , and of quantum phases . Machine learning is also used for the development of classification methods that provide direct physical insights into phase diagrams, and for transforming the computational and physical laboratory infrastructural landscapes used to create materials data in the first place .…”