Related papers: Persistence is All You Need -- A Topological Lens …
Phase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative way. In recent years, a number of novel topological metrics for microstructures…
Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding…
Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
Tomography is a widely used tool for analyzing microstructures in three dimensions (3D). The analysis, however, faces difficulty because the constituent materials produce similar grey-scale values. Sometimes, this prompts the image…
Understanding the decision-making processes of large language models is critical given their widespread applications. To achieve this, we aim to connect a formal mathematical framework - zigzag persistence from topological data analysis -…
Machine learning has emerged as an attractive alternative to experiments and simulations for predicting material properties. Usually, such an approach relies on specific domain knowledge for feature design: each learning target requires…
Quantifying the relationship between geometric descriptors of microstructure and effective properties like permeability is essential for understanding and improving the behavior of porous materials. In this paper, we employ a previously…
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…
A dataset of 35,608 materials with their topological properties is constructed by combining the density functional theory (DFT) results of Materiae and the Topological Materials Database. Thanks to this, machine-learning approaches are…
Traditional member-based two-step design approaches included in current structural codes for steel structures, as well as more recent system-based direct-design alternatives, require building rigorous structural reliability frameworks for…
Technological advances are in part enabled by the development of novel manufacturing processes that give rise to new materials or material property improvements. Development and evaluation of new manufacturing methodologies is labor-,…
Machine learning has emerged as a powerful approach in materials discovery. Its major challenge is selecting features that create interpretable representations of materials, useful across multiple prediction tasks. We introduce an…
Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this…
Adhesion is a fundamental phenomenon that plays a role in many engineering and biological applications. This paper concerns the use of machine learning to characterize the effective adhesive properties when a thin film is peeled from a…
An image based prediction of the effective heat conductivity for highly heterogeneous microstructured materials is presented. The synthetic materials under consideration show different inclusion morphology, orientation, volume fraction and…
In most applications of nanoporous materials the pore structure is as important as the chemical composition as a determinant of performance. For example, one can alter performance in applications like carbon capture or methane storage by…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
The structural characterization is an essential task in the study of porous materials. To achieve reliable results, it requires to evaluate images with hundreds of pores. Current methods require large time amounts and are subjected to human…
Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…