Related papers: Multi-Point Gradient Estimation in Turbulence

Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has…

We simulate the head-on collision between vortex rings with circulation Reynolds numbers of 4000 using an adaptive, multiresolution solver based on the lattice Green's function. The simulation fidelity is established with integral metrics…

Integrated gradients is prevalent within machine learning to address the black-box problem of neural networks. The explanations given by integrated gradients depend on a choice of base-point. The choice of base-point is not a priori obvious…

We investigate two-point velocity-gradient correlation functions in homogeneous isotropic turbulence using exact relations and direct numerical simulations. The second-order gradient correlation is shown to be exactly related to the…

We suggest simple implementable modifications of conditional gradient and gradient projection methods for smooth convex optimization problems in Hilbert spaces. Usually, the custom methods attain only weak convergence. We prove strong…

A novel approach is presented to recover an image degraded by atmospheric turbulence. Given a sequence of frames affected by turbulence, we construct a variational model to characterize the static image. The optimization problem is solved…

The problem of classifying turbulent environments from partial observation is key for some theoretical and applied fields, from engineering to earth observation and astrophysics, e.g. to precondition searching of optimal control policies in…

An appealing property of the natural gradient is that it is invariant to arbitrary differentiable reparameterizations of the model. However, this invariance property requires infinitesimal steps and is lost in practical implementations with…

Cook's [J. Roy. Statist. Soc. Ser. B 48 (1986) 133--169] local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model. However, no rigorous…

Nonlinear initial value turbulence simulations often exhibit large temporal variations in their dynamics. Quantifying the temporal uncertainty of turbulence simulation outputs is an important component of validating the simulation results…

An old theorem, due to Graustein, asserts that the average curvature of a plane oval is attained at least at four points. We present a proof by way of wave propagation and extend this result to the spherical and hyperbolic geometries - in…

Point cloud is often regarded as a discrete sampling of Riemannian manifold and plays a pivotal role in the 3D image interpretation. Particularly, rotation perturbation, an unexpected small change in rotation caused by various factors (like…

For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is…

The statistics obtained from turbulent flow simulations are generally uncertain due to finite time averaging. The techniques available in the literature to accurately estimate these uncertainties typically only work in an offline mode, that…

In this paper, we propose a novel approach for saliency detection for seismic applications using 3D-FFT local spectra and multi-dimensional plane projections. We develop a projection scheme by dividing a 3D-FFT local spectrum of a data…

In this work, we propose a novel technique to generate shapes from point cloud data. A point cloud can be viewed as samples from a distribution of 3D points whose density is concentrated near the surface of the shape. Point cloud generation…

This paper introduces a novel approach for image and video orientation estimation by leveraging depth distribution in natural images. The proposed method estimates the orientation based on the depth distribution across different quadrants…

The impact of gradient noise on training deep models is widely acknowledged but not well understood. In this context, we study the distribution of gradients during training. We introduce a method, Gradient Clustering, to minimize the…

An innovative orbit determination method which makes use of gravity gradients for Low-Earth-Orbiting satellites is proposed. The measurement principle of gravity gradiometry is briefly reviewed and the sources of measurement error are…

Atmospheric turbulence, a common phenomenon in daily life, is primarily caused by the uneven heating of the Earth's surface. This phenomenon results in distorted and blurred acquired images or videos and can significantly impact downstream…