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Sparse autoencoders have become a standard tool for uncovering interpretable latent representations in neural networks. Yet salient concepts often span manifolds that current linear methods cannot capture without post hoc analysis. This…
We perform a three-dimensional, short-wavelength stability analysis on the numerically simulated two-dimensional flow past a circular cylinder for Reynolds numbers in the range $50\le Re\le300$; here, $Re = U_{\infty}D/\nu$ with $U_\infty$,…
Vortex Shedding Dynamics in the Laminar Wake of Cones Michel Provansal1 and Peter A. Monkewitz1,2 1 IRPHE Aix-Marseille Universit\'{e}s FRANCE 2LMF, EPFL, SWITZERLAND Experiments on two cones of different taper ratios have been performed in…
We aim to reconstruct the latent space dynamics of high dimensional, quasi-stationary systems using model order reduction via the spectral proper orthogonal decomposition (SPOD). The proposed method is based on three fundamental steps: in…
We analyzed the performance of Convolutional Autoencoders in generating reduced-order representations the temperature field of 2D Rayleigh-B\'enard flows at $Pr=1$ and Rayleigh numbers extending from $10^6$ to $10^8$, capturing the range…
A novel data-driven modal decomposition of fluid flow is proposed comprising key features of POD and DMD. The first mode is the normalized real or imaginary part of the DMD mode which minimizes the time-averaged residual. The N-th mode is…
Wall-bounded turbulence is relevant for many engineering and natural science applications, yet there are still aspects of its underlying physics that are not fully understood, particularly at high Reynolds numbers. In this study, we…
High-dimensional data are ubiquitous, with examples ranging from natural images to scientific datasets, and often reside near low-dimensional manifolds. Leveraging this geometric structure is vital for downstream tasks, including signal…
We consider the ability of deep neural networks to represent data that lies near a low-dimensional manifold in a high-dimensional space. We show that deep networks can efficiently extract the intrinsic, low-dimensional coordinates of such…
Time-dependent flow fields are typically generated by a computational fluid dynamics (CFD) method, which is an extremely time-consuming process. However, the latent relationship between the flow fields is governed by the Navier-Stokes…
The linear stability of rectilinear compressible vortex sheets is studied for two-dimensional isentropic elastic flows. This problem has a free boundary and the boundary is characteristic. A necessary and sufficient condition is obtained…
We experimentally investigate the wake dynamics of a square cylinder rising through quiescent water over a range of Froude numbers ($\mathrm{Fr}$). Time-resolved Particle Image Velocimetry provides velocity and vorticity fields that enable…
We introduce a variational manifold of simple tensor network states for the study of a family of constrained models that describe spin-1/2 systems as realized by Rydberg atom arrays. Our manifold permits analytical calculation via…
The stable operation of autonomous off-grid photovoltaic systems requires solar forecasting algorithms that respect atmospheric thermodynamics. Contemporary deep learning models consistently exhibit critical anomalies, primarily severe…
Wake and force characteristics of an oscillating cylinder in inline steady currents are investigated numerically over a wide parameter space of dimensionless oscillation amplitude ($A^* = 0.01 - 0.50$) and wavelength ($\lambda^* = 0.4 -…
The fluidic pinball is a geometrically simple flow configuration with three rotating cylinders on the vertex of an equilateral triangle. Yet, it remains physically rich enough to host a range of interacting frequencies and to allow testing…
Nonlinear embedding manifold learning methods provide invaluable visual insights into the structure of high-dimensional data. However, due to a complicated nonconvex objective function, these methods can easily get stuck in local minima and…
The unsteady variations in the near wake of a moving cylinder induce lift and drag forces on it, which are customarily normalized and expressed in terms of nondimensional lift and drag coefficients. While there are already several wake…
The vortex unsteadiness around a hemisphere-cylinder body at AOAs of 10 to 80 deg was studied using Large Eddy Simulation (LES) and Dynamic Mode Decomposition (DMD). The Reynolds number (Re) based on the cylinder diameter of the body is…
Graph theoretical approaches have been proven to be effective in the characterization of connected systems, as well as in quantifying their dysfunction due to perturbation. In this paper, we show the advantage of a non-Euclidean…