Related papers: Data-driven topology design with persistent homolo…

The search ability of an Evolutionary Algorithm (EA) depends on the variation among the individuals in the population [3, 4, 8]. Maintaining an optimal level of diversity in the EA population is imperative to ensure that progress of the EA…

Topology optimization (TO) serves as a widely applied structural design approach to tackle various engineering problems. Nevertheless, sensitivity-based TO methods usually struggle with solving strongly nonlinear optimization problems. By…

The search ability of an Evolutionary Algorithm (EA) depends on the variation among the individuals in the population. Maintaining an optimal level of diversity in the EA population is imperative to ensure that progress of the EA search is…

Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of…

Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence…

The main goal of diversity optimization is to find a diverse set of solutions which satisfy some lower bound on their fitness. Evolutionary algorithms (EAs) are often used for such tasks, since they are naturally designed to optimize…

Topological data analysis (TDA) is a rapidly evolving field in applied mathematics and data science that leverages tools from topology to uncover robust, shape-driven insights in complex datasets. The main workhorse is persistent homology,…

Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…

In this paper, we propose a sensitivity-free and multi-objective structural design methodology called data-driven topology design. It is schemed to obtain high-performance material distributions from initially given material distributions…

Topology optimization (TO) has been widely adopted in engineering design; however, it is prone to being trapped in local optima, particularly in strongly nonlinear problems. Sensitivity-free data-driven topology design (DDTD) offers a…

In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…

We propose a method for learning topology-preserving data representations (dimensionality reduction). The method aims to provide topological similarity between the data manifold and its latent representation via enforcing the similarity in…

Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…

Evolutionary optimization is a generic population-based metaheuristic that can be adapted to solve a wide variety of optimization problems and has proven very effective for combinatorial optimization problems. However, the potential of this…

Recently, there has been an explosion in statistical learning literature to represent data using topological principles to capture structure and relationships. We propose a topological data analysis (TDA)-based framework, named Topological…

Population diversity plays a key role in evolutionary algorithms that enables global exploration and avoids premature convergence. This is especially more crucial in dynamic optimization in which diversity can ensure that the population…

Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features in high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. In particular,…

Two fundamental challenges face generative models in engineering applications: the acquisition of high-performing, diverse datasets, and the adherence to precise constraints in generated designs. We propose a novel approach combining…

Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase…

Evolutionary algorithms (EAs) are promising approaches for non-differentiable or strongly multimodal topology optimization problems, but they often suffer from the curse of dimensionality, generally leading to low-resolution optimized…