Related papers: Visualization of Unsteady Flow Using Heat Kernel S…
Many scientific and engineering problems involving multi-physics span a wide range of scales. Understanding the interactions across these scales is essential for fully comprehending such complex problems. However, visualizing multivariate,…
Understanding turbulence is the key to our comprehension of many natural and technological flow processes. At the heart of this phenomenon lies its intricate multi-scale nature, describing the coupling between different-sized eddies in…
The tasks of identifying separation structures and clusters in flow data are fundamental to flow visualization. Significant work has been devoted to these tasks in flow represented by vector fields, but there are unique challenges in…
We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall's shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these…
This paper extends the possibility to examine the underlying curvature of data through the lens of topology by using the Betti curves, tools of Persistent Homology, as key topological descriptors, building on the clique topology approach.…
Classical shape descriptors such as Heat Kernel Signature (HKS), Wave Kernel Signature (WKS), and Signature of Histograms of OrienTations (SHOT), while widely used in shape analysis, exhibit sensitivity to mesh connectivity, sampling…
We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics…
Advances in computational science offer a principled pipeline for predictive modeling of cardiovascular flows and aspire to provide a valuable tool for monitoring, diagnostics and surgical planning. Such models can be nowadays deployed on…
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
Deep learning has been employed to identify flow characteristics from Computational Fluid Dynamics (CFD) databases to assist the researcher to better understand the flow field, to optimize the geometry design and to select the correct CFD…
A kernel based method is proposed for the construction of signature (defining) functions of subsets of $\mathbb{R}^d$. The subsets can range from full dimensional manifolds (open subsets) to point clouds (a finite number of points) and…
Understanding protein dynamics are essential for deciphering protein functional mechanisms and developing molecular therapies. However, the complex high-dimensional dynamics and interatomic interactions of biological processes pose…
We analyze the asymptotic behaviour of the heat kernel defined by a stochastically perturbed geodesic flow on the cotangent bundle of a Riemannian manifold for small time and small diffusion parameter. This extends WKB-type methods to a…
The numerical simulation of fluid flow through a complex geometry with heat transfer is of strong interest for many applications, such as oil-filled power transformers. A fundamental challenge here is that high resolution is necessary to…
We present the derivation of a new unidirectional model for We present the derivation of a new unidirectional model for unsteady mixed flows in non uniform closed water pipes. We introduce a local reference frame to take into account the…
The signature of a path is an essential object in the theory of rough paths. The signature representation of the data stream can recover standard statistics, e.g. the moments of the data stream. The classification of random walks indicates…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
The work is devoted to the development and computational implementation of the homogenization method for modeling unsteady flows of a viscous incompressible fluid in periodic porous media taking into account memory effects. At the…
Advancements in computational fluid mechanics have largely relied on Newtonian frameworks, particularly through the direct simulation of Navier-Stokes equations. In this work, we propose an alternative computational framework that employs…
Computational Fluid Dynamics (CFD) simulations are a very important tool for many industrial applications, such as aerodynamic optimization of engineering designs like cars shapes, airplanes parts etc. The output of such simulations, in…