Recent breakthroughs in computing power have made it feasible to use machine learning
and deep learning to advance scientific computing in many fields, including fluid mechanics …

Advancements in computing power have recently made it possible to utilize machine
learning and deep learning to push scientific computing forward in a range of disciplines …

Now in its second edition, this book gives a systematic and self-contained presentation of
basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and …

This book is devoted to the asymptotic properties of solutions of stochastic evolution
equations in infinite dimensional spaces. It is divided into three parts: Markovian dynamical …

In this paper, we generalize the notion of an attractor for the stochastic dynamical system
introduced in [7]. We prove that the stochastic attractor satisfies most of the properties …

In this chapter we will apply the general theory developed in Chapter 2 to solve various
stochastic partial differential equations (SPDEs). In fact, as pointed out in Chapter 1, our …

We consider two strictly related models: a solid on solid interface growth model and the
weakly asymmetric exclusion process, both on the one dimensional lattice. It has been …

The main objective of this book is to give an overview of the theory of Hamilton–Jacobi–
Bellman (HJB) partial differential equations (PDEs) in infinite-dimensional Hilbert spaces …

We study, in one space dimension, the heat equation with a random potential that is a white
noise in space and time. This equation is a linearized model for the evolution of a scalar field …

Kolmogorov Equations for Stochastic PDEs gives an introduction to stochastic partial
differential equations, such as reaction-diffusion, Burgers and 2D Navier-Stokes equations …