相关论文: Space-time coupled evolution equations and their s…

The evolution of states of a spatial ecological model is studied. The model describes an infinite population of point entities placed in $\mathbb{R}^d$ which reproduce themselves at distant points (disperse) and die with rate that includes…

We investigate the long-time behavior of exact solutions and numerical approximations of linear stochastic evolution equations defined on the sphere. We focus on three classical models arising in mathematical physics: the stochastic wave…

Evolutionary algorithms (EAs) serve as powerful black-box optimizers inspired by biological evolution. However, most existing EAs predominantly focus on heuristic operators such as crossover and mutation, while usually overlooking…

From the underlying Master equations we derive one-dimensional stochastic processes that describe generalized ensemble simulations as well as tempering (simulated and parallel) simulations. The representations obtained are either in the…

The properties of nonlinear PDEs that generate filtered solutions are explored with particular attention given to the constraints on the residual term. The analysis is carried out for nonlinear PDEs with an emphasis on evolution problems…

This paper focuses on inverse problems to identify parameters by incorporating information from measurements. These generally ill-posed problems are formulated here in a probabilistic setting based on Bayes's theorem because it leads to a…

We prove local in time well-posedness in Sobolev spaces of the Cauchy problem for semi-linear p-evolution equations of the first order with real principal part, but complex valued coefficients for the lower order terms, assuming decay…

This article is devoted to the existence and uniqueness of pathwise solutions to stochastic evolution equations, driven by a H\"older continuous function with H\"older exponent in $(1/2,1)$, and with nontrivial multiplicative noise. As a…

In this article we provide a method for establishing operator-type error estimates between solutions to rapidly oscillating evolutionary equations and their homogenised counter parts. This method is exemplified by applications to the wave,…

We examine a class of stochastic differential inclusions involving multiscale effects designed to solve a class of generalized variational inequalities. This class of problems contains constrained convex non-smooth optimization problems,…

We expand our group classification of quasilinear evolution equations (Acta Appl.Math., v.69, 2001) to the case of general evolution equation in one spatial variable. This enables obtaining several new classes of evolution equations with…

It was recently demonstrated that time-dependent PDE problems can numerically be solved with a fully pseudospectral scheme, i.e. using spectral expansions with respect to both spatial and time directions (Hennig and Ansorg, 2009 [15]). This…

A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…

We study a new class of McKean-Vlasov stochastic differential equations (SDEs), possibly with common noise, applying the theory of time-inhomogeneous polynomial processes. The drift and volatility coefficients of these SDEs depend on the…

An alternative approach - nonequilibrium evolution thermodynamics, is compared with classical Landau approach. A statistical justification of the approach is carried out with help of probability distribution function on an example of a…

We present a deep learning emulator for stochastic and chaotic spatio-temporal systems, explicitly conditioned on the parameter values of the underlying partial differential equations (PDEs). Our approach involves pre-training the model on…

Modeling nonlinear spatiotemporal dynamical systems has primarily relied on partial differential equations (PDEs). However, the explicit formulation of PDEs for many underexplored processes, such as climate systems, biochemical reaction and…

We study the time evolution of correlation functions in closed quantum systems for nonequilibrium ensembles of initial conditions. For a scalar quantum field theory we show that generic time-reversal invariant evolutions approach…

We present a method for the identification of continuous, spatiotemporal dynamics from experimental data. We use a model in the form of a partial differential equation and formulate an optimization problem for its estimation from data. The…

In this article we present a way of treating stochastic partial differential equations with multiplicative noise by rewriting them as stochastically perturbed evolutionary equations in the sense of \cite{picardbook}, where a general…