Related papers: Topological, or Non-topological? A Deep Learning B…

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…

We introduce a method for training neural networks to perform image or volume segmentation in which prior knowledge about the topology of the segmented object can be explicitly provided and then incorporated into the training process. By…

Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…

The landscape of condensed matter physics is facing an unprecedented data surge driven by high-throughput ab initio workflows and rapidly expanding experimental datasets. Traditional first-principles methods such as Density Functional…

Graphs have a superior ability to represent relational data, like chemical compounds, proteins, and social networks. Hence, graph-level learning, which takes a set of graphs as input, has been applied to many tasks including comparison,…

Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks…

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…

We propose PLLay, a novel topological layer for general deep learning models based on persistence landscapes, in which we can efficiently exploit the underlying topological features of the input data structure. In this work, we show…

Deep Learning has been shown to learn efficient representations for structured data such as image, text or audio. In this chapter, we present neural network architectures that are able to learn efficient representations of molecules and…

In this paper, we study the problem of using representation learning to assist information diffusion prediction on graphs. In particular, we aim at estimating the probability of an inactive node to be activated next in a cascade. Despite…

Persistent Homology (PH) offers stable, multi-scale descriptors of intrinsic shape structure by capturing connected components, loops, and voids that persist across scales, providing invariants that complement purely geometric…

Graph neural networks are currently leading the performance charts in learning-based molecule property prediction and classification. Computational chemistry has, therefore, become the a prominent testbed for generic graph neural networks,…

Structural information of phylogenetic tree topologies plays an important role in phylogenetic inference. However, finding appropriate topological structures for specific phylogenetic inference tasks often requires significant design effort…

This survey provides a comprehensive exploration of applications of Topological Data Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology and Mapper, we delve into the intricate structures and behaviors…

High-quality training data is the foundation of machine learning and artificial intelligence, shaping how models learn and perform. Although much is known about what types of data are effective for training, the impact of the data's…

Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these…

This paper proposes a new topology optimization method that applies a convolutional neural network (CNN), which is one deep learning technique for topology optimization problems. Using this method, we acquire a structure with a little…

Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been…

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…

For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…