Related papers: Gradient Bounds for Kolmogorov Type Diffusions
The propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion coefficients is studied. Using coordinate changes, WKB approximations, and multiple scales analysis, we provide an analytic framework that…
We develop a generalized gradient expansion of the inhomogeneous dynamical mean-field theory method for determining properties of ultracold atoms in a trap. This approach goes beyond the well-known local density approximation and at higher…
Communication overhead is the key challenge for distributed training. Gradient compression is a widely used approach to reduce communication traffic. When combining with parallel communication mechanism method like pipeline, gradient…
On the basis of perturbed Kolmogorov backward equations and path integral representation, we unify the derivations of the linear response theory and transient fluctuation theorems for continuous diffusion processes from a backward point of…
Recent studies have shown that fractional calculus is an effective alternative mathematical tool in various scientific fields. However, some investigations indicate that results established in differential and integral calculus do not…
Recent developments in generative modeling have utilized score-based methods coupled with stochastic differential equations to sample from complex probability distributions. However, these and other performant sampling methods generally…
Mathematical physics problems are often formulated using differential oprators of vector analysis - invariant operators of first order, namely, divergence, gradient and rotor operators. In approximate solution of such problems it is natural…
The method of preliminary group classification is rigorously defined, enhanced and related to the theory of group classification of differential equations. Typical weaknesses in papers on this method are discussed and strategies to overcome…
A simple finite element formulation of the outlet gradient boundary condition is presented in the general context of convective-diffusive transport processes. Basically, the method is based on an upstream evaluation of the dependent…
We formulate and compute a class of mean-field information dynamics for reaction-diffusion equations. Given a class of nonlinear reaction-diffusion equations and entropy type Lyapunov functionals, we study their gradient flows formulations…
We give a geometric perspective on the algebra of Drinfeld modular forms for congruence subgroups $\Gamma\leq \GL_2(\bbF_q[T]).$ In particular, we describe an isomorphism between the section ring of a line bundle on the stacky modular curve…
Semi-analytical methods, based on Eulerian perturbation theory, are a promising tool to follow the time evolution of cosmological perturbations at small redshifts and at mildly nonlinear scales. All these schemes are based on two…
This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The…
We study regularity and numerical methods for two-sided fractional diffusion equations with a lower-order term. We show that the regularity of the solution in weighted Sobolev spaces can be greatly improved compared to that in standard…
We introduce the Space-Time Markov Chain Approximation (STMCA) for a general diffusion process on a finite metric graph $\Gamma$. The STMCA is a doubly asymmetric (in both time and space) random walk defined on a subdivisions of $\Gamma$,…
This article extends the preprint "Characterizing Agent-Based Model Dynamics via $\epsilon$-Machines and Kolmogorov-Style Complexity" by introducing diffusion models as orthogonal and complementary tools for characterizing the output of…
A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential equations, generated by…
We propose a new classification scheme for diffusion processes for which the backward Kolmogorov equation is solvable in analytically closed form by reduction to hypergeometric equations of the Gaussian or confluent type. The construction…
Molecular dynamics simulations have been performed to investigate in detail collective modes spectra of two-dimensional Coulomb fluids in a wide range of coupling. The obtained dispersion relations are compared with theoretical approaches…
We formulate gradient flow dynamics generated by two natural actions of the quantum metric for an isolated set of Bloch bands. Specializing to two spatial dimensions, we derive Bogomolny-type lower bounds that relate these actions to the…