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Industry 4.0 is changing fundamentally the way data is collected, stored and analyzed in industrial processes. While this change enables novel application such as flexible manufacturing of highly customized products, the real-time control…
Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach which can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent…
The study of topology is strictly speaking, a topic in pure mathematics. However in only a few years, Topological Data Analysis (TDA), which refers to methods of utilizing topological features in data (such as connected components, tunnels,…
A time-delay embedding (TDE), grounded in the framework of Takens's Theorem, provides a mechanism to represent and analyze the inherent dynamics of time-series data. Recently, topological data analysis (TDA) methods have been applied to…
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…
Topological Data Analysis (TDA), an emerging field in investment sciences, harnesses mathematical methods to extract data features based on shape, offering a promising alternative to classical portfolio selection methodologies. We utilize…
Time series forecasting is a critical task across domains such as energy, finance, and meteorology, where accurate predictions enable informed decision-making. While transformer-based and large-parameter models have recently achieved…
The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…
With increasingly more computation being shifted to the edge of the network, monitoring of critical infrastructures, such as intermediate processing nodes in autonomous driving, is further complicated due to the typically…
Short-term precipitation forecasting is essential for planning of human activities in multiple scales, ranging from individuals' planning, urban management to flood prevention. Yet the short-term atmospheric dynamics are highly nonlinear…
Time series forecasting models have diverse real world applications (e.g., from electricity metrics to software workload). Latest foundational models trained for time series forecasting show strengths (e.g., for long sequences and in…
Multi-objective evolutionary algorithms (MOEAs) have become essential tools for solving multi-objective optimization problems (MOPs), making their running time analysis crucial for assessing algorithmic efficiency and guiding practical…
Energy system models require a large amount of technical and economic data, the quality of which significantly influences the reliability of the results. Some of the variables on the important data source ENTSO-E transparency platform, such…
We develop a framework for analyzing multivariate time series using topological data analysis (TDA) methods. The proposed methodology involves converting the multivariate time series to point cloud data, calculating Wasserstein distances…
Topological Data Analysis (TDA) provides a pipeline to extract quantitative topological descriptors from structured objects. This enables the definition of topological loss functions, which assert to what extent a given object exhibits some…
Weather prediction is a quintessential problem involving the forecasting of a complex, nonlinear, and chaotic high-dimensional dynamical system. This work introduces an efficient reduced-order modeling (ROM) framework for short-range…
The objective of this study is to establish a gradient-free topology optimization framework that facilitates more global solution searches to avoid entrapping in undesirable local optima, especially in problems with strong non-linearity.…
Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such…
Age of Information (AoI) is a crucial metric for quantifying information freshness in real-time systems where the sampling rate of data packets is time-varying. Evaluating AoI under such conditions is challenging, as system states become…
Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…