Related papers: Persistence is All You Need -- A Topological Lens …
We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…
Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to…
Accelerating materials development requires quantitative linkages between processing, microstructure, and properties. In this work, we introduce a framework for mapping microstructure onto a low-dimensional material manifold that is…
Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines…
Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams…
In quality control, microstructures are investigated rigorously to ensure structural integrity, exclude the presence of critical volume defects, and validate the formation of the target microstructure. For quenched,…
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…
The Materials Project crystal structure database has been searched for materials possessing layered motifs in their crystal structures using a topology-scaling algorithm. The algorithm identifies and measures the sizes of bonded atomic…
Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems' persistence involves different…
Quantitative structure-property relationships are crucial for the understanding and prediction of the physical properties of complex materials. For fluid flow in porous materials, characterizing the geometry of the pore microstructure…
Microstructure reconstruction has been an essential part of computational material engineering to reveal the relationship between microstructures and material properties. However, finding a general solution for microstructure…
Classification of features in a scene typically requires conversion of the incoming photonic field into the electronic domain. Recently, an alternative approach has emerged whereby passive structured materials can perform classification…
A key feature of mechanical structures ranging from crumple zones in cars to padding in packaging is their ability to provide protection by absorbing mechanical energy. Designing structures to efficiently meet these needs has profound…
A main goal of data-driven materials research is to find optimal low-dimensional descriptors, allowing us to predict a physical property, and to interpret them in a human-understandable way. In this work, we advance methods to identify…
Superconductivity has been the focus of enormous research effort since its discovery more than a century ago. Yet, some features of this unique phenomenon remain poorly understood; prime among these is the connection between…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
To leverage advancements in machine learning for metallic materials design and property prediction, it is crucial to develop a data-reduced representation of metal microstructures that surpasses the limitations of current physics-based…
Such modern applications of topology as data analysis and digital image analysis have to deal with noise and other uncertainty. In this environment, topological spaces often appear equipped with a real valued function. Persistence is a…
Topological descriptors, such as the Euler characteristic function and the persistence diagram, have grown increasingly popular for representing complex data. Recent work showed that a carefully chosen set of these descriptors encodes all…
The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…