Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning

Monte Carlo Solutions to specific PDEs

Energy Study of Monte Carlo and Quasi-Monte Carlo Algorithms for Solving Integral Equations

In the past few years the development of exascale computing technology necessitated to obtain an estimate for the energy consumption when large-scale problems are solved with different high-performance computing (HPC) systems. In this paper we study the energy efficiency of a class of Monte Carlo (MC) and Quasi-Monte Carlo (QMC) algorithms for a given integral equation using hybrid HPC systems....

Monte Carlo methods for stochastic PDEs

It is well known that boundary value problems with random parameters are very interesting models which become more and more popular in many fields of science and technology, especially in problems where the data are highly irregular, for instance, like in the case of turbulent transport in atmosphere and ocean [8], [11], [15], flows in porous medium [2], [7], or evaluation of elastic properties...

Introduction To Monte Carlo Algorithms

In these lectures, given in ’96 summer schools in Beg-Rohu (France) and Budapest, I discuss the fundamental principles of thermodynamic and dynamic Monte Carlo methods in a simple light-weight fashion. The keywords are Markov chains, Sampling, Detailed Balance, A Priori Probabilities, Rejections, Ergodicity, “Faster than the clock algorithms”. The emphasis is on Orientation, which is difficult ...

Bayesian Estimation by Sequential Monte Carlo Sampling: Application to High-dimensional Nonlinear Dynamic Systems

Modern industrial enterprises have invested significant resources for collecting and distributing data, with the expectation that it will enhance profitability via better decision making. Due to the complexity of these problems, existing approaches tend to make convenient, but invalid assumptions so that tractable solution may be found. For example, for estimation in nonlinear dynamic systems, ...