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As datasets used in scientific applications become more complex, studying the geometry and topology of data has become an increasingly prevalent part of the data analysis process. This can be seen for example with the growing interest in…

Algebraic Geometry · Mathematics 2024-03-22 Ezzeddine El Sai , Parker Gara , Markus J. Pflaum

Though symmetry-based indicators formulae are powerful in diagnosing topological states with a gapped band structure at/between any high-symmetry points, it fails in diagnosing topological degeneracies when the compatibility condition is…

Materials Science · Physics 2021-07-15 Tiantian Zhang , Shuichi Murakami

Machine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large dataset…

Materials Science · Physics 2020-05-06 Conrad W. Rosenbrock , Eric R. Homer , Gábor Csányi , Gus L. W. Hart

The thermoelectric performance of materials exhibits complex nonlinear dependencies on both elemental types and their proportions, rendering traditional trial-and-error approaches inefficient and time-consuming for material discovery. In…

Materials Science · Physics 2025-04-14 Yuxuan Zeng , Wenhao Xie , Wei Cao , Tan Peng , Yue Hou , Ziyu Wang , Jing Shi

Recent advancements in machine learning (ML) for materials have demonstrated that "simple" materials representations (e.g., the chemical formula alone without structural information) can sometimes achieve competitive property prediction…

Materials Science · Physics 2025-01-31 Raul Ortega-Ochoa , Alán Aspuru-Guzik , Tejs Vegge , Tonio Buonassisi

First-principles computations are the driving force behind numerous discoveries of hydride-based superconductors, mostly at high pressures, during the last decade. Machine-learning (ML) approaches can further accelerate the future…

Superconductivity · Physics 2023-06-01 Huan Tran , Tuoc N. Vu

High-throughput computational materials design promises to greatly accelerate the process of discovering new materials and compounds, and of optimizing their properties. The large databases of structures and properties that result from…

Chemical Physics · Physics 2016-11-22 Sandip De , Felix Musil , Teresa Ingram , Carsten Baldauf , Michele Ceriotti

Machine learning can accelerate materials discovery. Models perform impressively on many benchmarks. However, strong benchmark performance does not imply that a model learned chemistry. I test a concrete alternative hypothesis: that…

Chemical Physics · Physics 2026-02-23 Kevin Maik Jablonka

High-entropy alloys are solid solutions of multiple principal elements, capable of reaching composition and feature regimes inaccessible for dilute materials. Discovering those with valuable properties, however, relies on serendipity, as…

The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering…

Mesoscale and Nanoscale Physics · Physics 2025-08-08 Amit Goft , Eric Akkermans

Conventional metals, insulators, and semimetals are constrained by fundamental limitations in terms of their thermoelectric performance. Topological materials offer certain features that allow them to circumvent these constraints, and…

Materials Science · Physics 2026-03-26 Brian Skinner , Poulomi Chakraborty , Joshua Scales , Joseph P. Heremans

Metamaterials exhibit materials response deviation from conventional elasticity. This phenomenon is captured by the generalized elasticity as a result of extending the theory at the expense of introducing additional parameters. These…

Computational Engineering, Finance, and Science · Computer Science 2021-06-10 Bilen Emek Abali , Emilio Barchiesi

We present a level-set based topology optimization algorithm for design optimization problems involving an arbitrary number of different materials, where the evolution of a design is solely guided by topological derivatives. Our method can…

Optimization and Control · Mathematics 2020-06-24 Peter Gangl

Machine Learning (ML) has offered innovative perspectives for accelerating the discovery of new functional materials, leveraging the increasing availability of material databases. Despite the promising advances, data-driven methods face…

Topological materials can host edge and corner states that are protected from disorder and material imperfections. In particular, the topological edge states of mechanical structures present unmatched opportunities for achieving robust…

Materials Science · Physics 2023-04-12 Marcelo Guzman , Xiaofei Guo , Corentin Coulais , David Carpentier , Denis Bartolo

Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surface states that show up due to a topological character of the bulk wave functions. This review presents a pedagogical account on…

Materials Science · Physics 2013-09-04 Yoichi Ando

Over the last few years, crystalline topology has been used in photonic crystals to realize edge- and corner-localized states that enhance light-matter interactions for potential device applications. However, the band-theoretic approaches…

Optics · Physics 2024-02-23 Alexander Cerjan , Terry A. Loring , Hermann Schulz-Baldes

Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and…

Materials Science · Physics 2018-01-24 Andrea Grisafi , David M. Wilkins , Gábor Csányi , Michele Ceriotti

Quantifying the correlation between the complex structures of amorphous materials and their physical properties has been a long-standing problem in materials science. In amorphous Si, a representative covalent amorphous solid, the presence…

Materials Science · Physics 2022-06-29 Emi Minamitani , Takuma Shiga , Makoto Kashiwagi , Ippei Obayashi

Studying materials informatics from a data mining perspective can be beneficial for manufacturing and other industrial engineering applications. Predictive data mining technique and machine learning algorithm are combined to design a…

Databases · Computer Science 2012-09-20 Doreswamy , Hemanth K. S
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