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Prediction of stable crystal structures at given pressure-temperature conditions, based only on the knowledge of the chemical composition, is a central problem of condensed matter physics. This extremely challenging problem is often termed…
The calculation of crystal structure from X-ray diffraction data requires that the phases of the ``structure factors'' (Fourier coefficients) determined by scattering be deduced from the absolute values of those structure factors. Motivated…
Crystalline materials are widely used in technological applications, yet their discovery remains a significant challenge. As their properties are driven by structure, crystal structure prediction (CSP) methods play a central role in…
Diffraction is the most common method to solve for unknown or partially known crystal structures. However, it remains a challenge to determine the crystal structure of a new material that may have nanoscale size or heterogeneities. Here we…
The prediction of energetically stable crystal structures formed by a given chemical composition is a central problem in solid-state physics. In principle, the crystalline state of assembled atoms can be determined by optimizing the energy…
Representing crystal structures of materials to facilitate determining them via neural networks is crucial for enabling machine-learning applications involving crystal structure estimation. Among these applications, the inverse design of…
Graphs are one of the most important data structures for representing pairwise relations between objects. Specifically, a graph embedded in a Euclidean space is essential to solving real problems, such as physical simulations. A crucial…
Predicting properties of crystals from their structures is a fundamental yet challenging task in materials science. Unlike molecules, crystal structures exhibit infinite periodic arrangements of atoms, requiring methods capable of capturing…
Generative models have achieved impressive results in many domains including image and text generation. In the natural sciences, generative models have led to rapid progress in automated drug discovery. Many of the current methods focus on…
Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide…
Crystal structure design is important for the discovery of new highly functional materials because crystal structure strongly influences material properties. Crystal structures are composed of space-filling polyhedra, which affect material…
Graph convolutional neural networks (GCNNs) have become a machine learning workhorse for screening the chemical space of crystalline materials in fields such as catalysis and energy storage, by predicting properties from structures.…
Crystalline materials, with symmetrical and periodic structures, exhibit a wide spectrum of properties and have been widely used in numerous applications across electronics, energy, and beyond. For crystalline materials discovery,…
The technique known as 4D-STEM has recently emerged as a powerful tool for the local characterization of crystalline structures in materials, such as cathode materials for Li-ion batteries or perovskite materials for photovoltaics. However,…
Crystal structure prediction has been a subject of topical interest, but remains a substantial challenge, especially for complex structures as it deals with the global minimization of the extremely rugged high-dimensional potential energy…
Machine Learning models have emerged as a powerful tool for fast and accurate prediction of different crystalline properties. Exiting state-of-the-art models rely on a single modality of crystal data i.e. crystal graph structure, where they…
Procedural material graphs are a compact, parameteric, and resolution-independent representation that are a popular choice for material authoring. However, designing procedural materials requires significant expertise and publicly…
The recently proposed crystal graph convolutional neural network (CGCNN) offers a highly versatile and accurate machine learning (ML) framework by learning material properties directly from graph-like representations of crystal structures…
This monograph introduces key concepts and problems in the new research area of Periodic Geometry and Topology for materials applications.Periodic structures such as solid crystalline materials or textiles were previously classified in…
Graph Transformers have garnered significant attention for learning graph-structured data, thanks to their superb ability to capture long-range dependencies among nodes. However, the quadratic space and time complexity hinders the…