Related papers: Gradient Flow Structure of a Multidimensional Nonl…
Tseytlin has recently proposed that an action functional exists whose gradient generates to all orders in perturbation theory the Renormalization Group (RG) flow of the target space metric in the worldsheet sigma model. The gradient is…
We prove that the standard gradient flow in parameter space that underlies many training algorithms in deep learning can be continuously deformed into an adapted gradient flow which yields (constrained) Euclidean gradient flow in output…
The construction of a generalized (higher-order) nonlinear thermo-hydrodynamics, based on a nonequilibrium ensemble formalism has been presented in the preceding article. The working of such theory is illustrated in the present one. We…
We compute the full set of second-order inertial corrections to the instantaneous force and torque acting on a small spherical rigid particle moving unsteadily in a general steady linear flow. This is achieved by using matched asymptotic…
New one-leg multistep time discretizations of nonlinear evolution equations are investigated. The main features of the scheme are the preservation of the nonnegativity and the entropy-dissipation structure of the diffusive equations. The…
We prove that the Gini coefficient of economic inequality is a Lyapunov functional for a class of nonlinear, nonlocal integro-differential equations arising at the intersection of mathematics, economics, and statistical physics. Next, a…
We study nonequilibrium thermodynamic properties of a driven one-dimensional quantum fluid by combining nonlinear Luttinger liquid theory with the quantum kinetic equation. In particular, we derive an entropy production consistent with the…
We find an explicit form of entropy solutions to a Riemann problem for a degenerate nonlinear parabolic equation with piecewise constant velocity and diffusion coefficients. It is demonstrated that this solution corresponds to the minimum…
Reduced-order models have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably…
Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate shape-dependent orientational dynamics,…
In finite dimension, the long-time and metastable behavior of a gradient flow perturbated by a small Brownian noise is well understood. A similar situation arises when a Wasserstein gradient flow over a space of probability measure is…
We use the distances introduced in a previous joint paper to exhibit the gradient flow structure of some drift-diffusion equations for a wide class of entropy functionals. Functional inequalities obtained by the comparison of the entropy…
In the paper of Uwano [Czech. J. of Phys., vol.56, pp.1311-1316 (2006)], a gradient system is found on the space of density matrices endowed with the quantum SLD Fisher metric (to be referred to as the quantum information space) that…
We establish both global existence and decay properties for solutions with small data for a general class of coupled system of tensorial quasilinear hyperbolic wave equations in three space dimensions, that covers the dynamical Einstein…
We consider the gradient flow structure of the porous medium equations with non-negative constant Dirichlet boundary conditions. We construct weak solutions to the equations via the minimizing movement scheme by considering an entropy…
A simple model to handle the flow of people in emergency evacuation situations is considered: at every point x, the velocity U(x) that individuals at x would like to realize is given. Yet, the incompressibility constraint prevents this…
The scarcity of labeled data is a long-standing challenge for many machine learning tasks. We propose our gradient flow method to leverage the existing dataset (i.e., source) to generate new samples that are close to the dataset of interest…
We develop a general mathematical framework to analyze scaling regimes and derive explicit analytic solutions for gradient flow (GF) in large learning problems. Our key innovation is a formal power series expansion of the loss evolution,…
The solution of potential-driven steady-state flow in large networks is required in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear equations depends…
The gradient flow is the evolution of fields and physical quantities along a dimensionful parameter~$t$, the flow time. We give a simple argument that relates this gradient flow and the Wilsonian renormalization group (RG) flow. We then…