Related papers: Quartic Gradient Flow
We present a semi-Lagrangian characteristic mapping method for the incompressible Euler equations on a rotating sphere. The numerical method uses a spatio-temporal discretization of the inverse flow map generated by the Eulerian velocity as…
Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning models efficiently. First-order methods such as gradient descent are usually the methods of choice for training machine…
An extended range of energy stable flux reconstruction schemes, developed using a summation-by-parts approach, is presented on quadrilateral elements for various sets of polynomial bases. For the maximal order bases, a new set of correction…
More than 150 years after their invention by Hamilton, quaternions are now widely used in the aerospace and computer animation industries to track the paths of moving objects undergoing three-axis rotations. It is shown here that they…
Based on the characteristics of the multi-scale and similarity at different scales in turbulent flow, we propose a scale decomposition for solving the turbulence problem of incompressible Newtonian fluid. The solution domain is decomposed…
The propagation of internal gravity waves in stratified media, such as those found in ocean basins and lakes, leads to the development of geometrical patterns called "attractors". These structures accumulate much of the wave energy and make…
This paper proposes a novel analysis for the Scaffold algorithm, a popular method for dealing with data heterogeneity in federated learning. While its convergence in deterministic settings--where local control variates mitigate client…
In this paper, we introduce the Quasi-Quadratic Gradient (QQG), a novel search direction designed to accelerate the BFGS method within the quasi-Newton framework. By defining the QQG as the product of the inverse Hessian approximation and…
Evolution of sphalerons in a class of quartic Klein-Gordon models are studied under a growing perturbation. Sphalerons are unstable lump-like solutions that arise from a saddle point between true and false vacua in the energy functional.…
In this paper we consider solving saddle point problems using two variants of Gradient Descent-Ascent algorithms, Extra-gradient (EG) and Optimistic Gradient Descent Ascent (OGDA) methods. We show that both of these algorithms admit a…
Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open…
A saddle-node bifurcation cascade is studied in the logistic equation, whose bifurcation points follow an expression formally identical to the one given by Feigenbaum for period doubling cascade. The Feigenbaum equation is generalized…
In this work, we introduce two algorithmic frameworks, named Bregman extragradient method and Bregman extrapolation method, for solving saddle point problems. The proposed frameworks not only include the well-known extragradient and…
We obtained a new solution of Schrodinger equation by the method of Euclidean approach (Wick rotation). This is a wave motion which is fluctuating.
We establish the existence of saddle points for a free boundary problem describing the two-dimensional free surface of a ferrofluid which undergoes normal field instability (also known as Rosensweig instability). The starting point consists…
Viscous hydrodynamics serves as a successful mesoscopic description of the Quark-Gluon Plasma produced in relativistic heavy-ion collisions. In order to investigate, how such an effective description emerges from the underlying microscopic…
Based on machine learning techniques, we propose a novel method to estimate flow fields using only floating sensor locations. This method does not require either ground-truth velocity fields or governing equations for fluid flows, which is…
We present an analysis of the quantum fluctuations around the electroweak sphaleron and calculate the associated determinant which gives the 1--loop correction to the sphaleron transition rate. The calculation differs in various technical…
Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…
Quantum algorithms are built enabling to find Poincar\'e recurrence times and periodic orbits of classical dynamical systems. It is shown that exponential gain compared to classical algorithms can be reached for a restricted class of…