Related papers: Persistent homology-based descriptor for machine-l…

Machine Learning (ML) has the potential to accelerate discovery of new materials and shed light on useful properties of existing materials. A key difficulty when applying ML in Materials Science is that experimental datasets of material…

3-D shape is important to chemistry, but how important? Machine learning works best when the inputs are simple and match the problem well. Chemistry datasets tend to be very small compared to those generally used in machine learning so we…

We address the problem of estimating topological features from data in high dimensional Euclidean spaces under the manifold assumption. Our approach is based on the computation of persistent homology of the space of data points endowed with…

Recent studies have actively employed persistent homology (PH), a topological data analysis technique, to analyze the topological information in time series data. Many successful studies have utilized graph representations of time series…

In semiconductor manufacturing, wafer map defect pattern provides critical information for facility maintenance and yield management, so the classification of defect patterns is one of the most important tasks in the manufacturing process.…

In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…

Persistent Homology (PH) allows tracking homology features like loops, holes and their higher-dimensional analogs, along with a single-parameter family of nested spaces. Currently, computing descriptors for complex data characterized by…

Accurate predictions of the failure progression of structural materials is critical for preventing failure-induced accidents. Despite considerable mechanics modeling-based efforts, accurate prediction remains a challenging task in…

Artificial intelligence-assisted drug design is revolutionizing the pharmaceutical industry. Effective molecular features are crucial for accurate machine learning predictions, and advanced mathematics plays a key role in designing these…

Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…

Persistent homology (PH) is an approach to topological data analysis (TDA) that computes multi-scale topologically invariant properties of high-dimensional data that are robust to noise. While PH has revealed useful patterns across various…

We explore the use of Physics Informed Neural Networks to analyse nonlinear Hamiltonian Dynamical Systems with a first integral of motion. In this work, we propose an architecture which combines existing Hamiltonian Neural Network…

Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…

Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…

Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…

In recent times, the use of machine learning in materials design and discovery has aided to accelerate the discovery of innovative materials with extraordinary properties, which otherwise would have been driven by a laborious and…

In this paper we introduce a statistic, the persistent homology transform (PHT), to model surfaces in $\mathbb{R}^3$ and shapes in $\mathbb{R}^2$. This statistic is a collection of persistence diagrams - multiscale topological summaries…

The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…

Multiparameter persistent homology has been largely neglected as an input to machine learning algorithms. We consider the use of lattice-based convolutional neural network layers as a tool for the analysis of features arising from…

Persistent homology (PH) studies the topology of data across multiple scales by building nested collections of topological spaces called filtrations, computing homology and returning an algebraic object that can be vizualised as a…