Related papers: Topological flow data analysis for transient flow …
This study aims to extract and characterize structures in fully developed pipe flow at a friction Reynolds number of $\text{Re}_\tau = 12\,400$. To do so, we employ data-driven wavelet decomposition (DDWD) [D.~Floryan and M.~D.~Graham, PNAS…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we introduce a statistical protocol that reduces TDA's memory…
We introduce a widely applicable tensor network-based framework for developing reduced order models describing wall-bounded fluid flows. As a paradigmatic example, we consider the incompressible Navier-Stokes equations and the lid-driven…
We apply supervised machine learning techniques to a number of regression problems in fluid dynamics. Four machine learning architectures are examined in terms of their characteristics, accuracy, computational cost, and robustness for…
In recent decades, hypergraphs and their analysis through Topological Data Analysis (TDA) have emerged as powerful tools for understanding complex data structures. Various methods have been developed to construct hypergraphs -- referred to…
We present a novel topological framework for analyzing functional brain signals using time-frequency analysis. By integrating persistent homology with time-frequency representations, we capture multi-scale topological features that…
Topological data analysis (TDA) approaches are becoming increasingly popular for studying the dependence patterns in multivariate time series data. In particular, various dependence patterns in brain networks may be linked to specific tasks…
Topological Data Analysis (TDA) is a rapidly growing field, which studies methods for learning underlying topological structures present in complex data representations. TDA methods have found recent success in extracting useful geometric…
Time series anomaly detection is a challenging problem due to the complex temporal dependencies and the limited label data. Although some algorithms including both traditional and deep models have been proposed, most of them mainly focus on…
Mobile devices and the Internet of Things (IoT) devices nowadays generate a large amount of heterogeneous spatial-temporal data. It remains a challenging problem to model the spatial-temporal dynamics under privacy concern. Federated…
Transition prediction is an important aspect of aerodynamic design because of its impact on skin friction and potential coupling with flow separation characteristics. Traditionally, the modeling of transition has relied on correlation-based…
The growth of computational resources in the past decades has expanded the application of Computational Fluid Dynamics (CFD) from the traditional fields of aerodynamics and hydrodynamics to a number of new areas. Examples range from the…
Based on experimental traffic data obtained from German and US highways, we propose a novel two-dimensional first-order macroscopic traffic flow model. The goal is to reproduce a detailed description of traffic dynamics for the real road…
The lid-driven cavity flow is a well-known benchmark problem for the validation of new numerical methods and techniques. In experimental and numerical studies with viscoelastic fluids in such lid-driven flows, purely-elastic instabilities…
Streaming Dynamic Mode Decomposition (sDMD) (Hemati et al., Phys. Fluids 26(2014)) is a low-storage version of Dynamic Mode Decomposition (DMD) (Schmid, J. Fluid Mech. 656 (2010)), a data-driven method to extract spatio-temporal flow…
The statistical properties of the local topology of two-dimensional turbulence are investigated using an electromagnetically forced soap film. The local topology of the incompressible 2D flow is characterized by the Jacobian determinant…
Spatial networks are ubiquitous in social, geographical, physical, and biological applications. To understand the large-scale structure of networks, it is important to develop methods that allow one to directly probe the effects of space on…
In a novel application of the tools of topological data analysis (TDA) to nonperturbative quantum gravity, we introduce a new class of observables that allows us to assess whether quantum spacetime really resembles a ``quantum foam" near…
Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge. Neural controlled differential equations provide a principled framework for such tasks, yet their performance is highly…