Frontiers | A Survey of Topological Machine Learning Methods
May 25, 2021 · In this paper, we review the state of the art of a nascent field we refer to as “topological machine learning,” i.e., the successful symbiosis of topology-based methods and machine learning algorithms, such as deep neural networks. We identify common threads, current applications, and future challenges. 1. Introduction.
machine learning - In what ways is the term "topology" applied to ...
Dec 13, 2021 · In local search problems or sometimes in optimization for machine learning, the "topology" of a problem corresponds to the change in the function you're optimizing as you move between adjacent states. If the change is sharp, you have a "rugged topology".
Topological deep learning - Wikipedia
Topological deep learning (TDL)[1][2][3][4][5][6] is a research field that extends deep learning to handle complex, non-Euclidean data structures. Traditional deep learning models, such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs), excel in processing data on regular grids and sequences.
Topology Applied to Machine Learning: From Global to Local
May 13, 2021 · Applied topology is designed to measure the shape of data—but what is shape? Early examples in applied topology found low-dimensional structures in high-dimensional datasets, such as the three circle and Klein bottle models for grayscale natural image patches.
Topology optimization via machine learning and deep learning: a …
Jul 13, 2023 · Topology optimization (TO) is a method of deriving an optimal design that satisfies a given load and boundary conditions within a design domain. This method enables effective design without initial design, but has been limited in use due to high computational costs.
On AI for Topology Optimisation with Ole Sigmund - CDFAM
Advancements in AI and Topology Optimization? In our last discussion in 2022 , you mentioned that AI seemed to be a dead-end for topology optimization based on the findings in your co-authored paper “ On the use of artificial neural networks in topology optimization .”
Machine learning for topology optimization: Physics-based …
Aug 1, 2022 · To reduce this computational cost, we propose an artificial intelligence approach to drastically accelerate topology optimization without sacrificing its accuracy. The resulting AI-driven topology optimization can fully capture the underlying physics of the problem.
Topology optimization (TO) is a method of deriving an optimal design that satisfies a given load and boundary conditions within a design domain. This method enables effective design without initial design, but has been limited in use due to high computational costs.
An Artificial Intelligence–Assisted Design Method for Topology ... - MDPI
Sep 28, 2021 · This paper proposes an AI-assisted design method for topology optimization, which does not require any optimized data. An artificial neural network—the predictor—provides the designs on the basis of boundary conditions and degree of filling as input data.
Topology in Real-World Machine Learning and Data Analysis
Topology is concerned with understanding the global shape and structure of objects. When applied to data, topological methods provide a natural complement to conventional machine learning approaches, which tend to rely on local properties of the data.
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