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Crystal structure optimization is fundamental to materials modeling but remains computationally expensive when performed with density-functional theory (DFT). Machine-learning (ML) approaches offer substantial acceleration, yet existing…
We develop a rigorous framework for modelling the geometry equilibration of crystalline defects. We formulate the equilibration of crystal defects as a variational problems on a discrete energy space and establish qualitatively sharp…
We introduce and evaluate a set of feature vector representations of crystal structures for machine learning (ML) models of formation energies of solids. ML models of atomization energies of organic molecules have been successful using a…
Detecting structures at the particle scale within plastically deformed crystalline materials allows a better understanding of the occurring phenomena. While previous approaches mostly relied on applying hand-chosen criteria on different…
A nonlocal phase-field crystal (NPFC) model is presented as a nonlocal counterpart of the local phase-field crystal (LPFC) model and a special case of the structural PFC (XPFC) derived from classical field theory for crystal growth and…
Durable interest in developing a framework for the detailed structure of glassy materials has produced numerous structural descriptors that trade off between general applicability and interpretability. However, none approach the combination…
A fundamental problem in applying machine learning techniques for chemical problems is to find suitable representations for molecular and crystal structures. While the structure representations based on atom connectivities are prevalent for…
Properties of crystalline materials are closely linked to microstructure arising from the spatial arrangement, orientation, and phase of nanocrystals. Rapid characterization of crystalline microstructure can accelerate the identification of…
Although superspace formalism has become the standard approach for the analysis of structurally modulated crystals, it has remained during the last thirty years almost unexplored as a practical tool to deal with magnetic incommensurate…
Computational prediction of stable crystal structures has a profound impact on the large-scale discovery of novel functional materials. However, predicting the crystal structure solely from a material's composition or formula is a promising…
3D Gaussian splatting (3D-GS) has recently revolutionized novel view synthesis in the simultaneous localization and mapping (SLAM) problem. However, most existing algorithms fail to fully capture the underlying structure, resulting in…
We present a novel approach to generate a fingerprint for crystalline materials that balances efficiency for machine processing and human interpretability, allowing its application in both machine learning inference and understanding of…
Symmetry plays a fundamental role in understanding natural phenomena and mathematical structures. This work develops a comprehensive theory for studying the persistent symmetries and degree of asymmetry of finite point configurations over…
We prove a general version of the crystalline equivalence principle which gives an equivalence of categories between a category of TQFTs defined on a generic space with $G$-symmetry, and a category of TQFTs with internal symmetry. We give a…
We present a generic construction of finite realisations of amalgamation patterns. An amalgamation pattern is specified by a finite collection of finite template structures together with a collection of partial isomorphisms between them. A…
Generative design marks a significant data-driven advancement in the exploration of novel inorganic materials, which entails learning the symmetry equivalent to the crystal structure prediction (CSP) task and subsequent learning of their…
Molecular and polymeric crystals show a wide range of functional properties that arise from the interplay between the atomic-scale structure of their constituent molecules and the organization of these molecules within the crystal lattice…
Novel materials drive advancements in fields ranging from energy storage to electronics, with crystal structure characterization forming a crucial yet challenging step in materials discovery. In this work, we introduce \emph{deCIFer}, an…
Accurately predicting experimentally realizable 3D molecular crystal structures from their 2D chemical graphs is a long-standing open challenge in computational chemistry called crystal structure prediction (CSP). Efficiently solving this…
The discovery of new functional and stable materials is a big challenge due to its complexity. This work aims at the generation of new crystal structures with desired properties, such as chemical stability and specified chemical…