Fabio Nobile: Multilevel Monte Carlo methods for random differential equations (Part II)
Автор: Hausdorff Center for Mathematics
Загружено: 2026-01-23
Просмотров: 12
In this series of lectures we focus on random differential problems which may arise for instance when studying physical systems governed by partial differential equations with uncertainty in the model parameters described by means of random variables, or when studying dynamical systems subject to random fluctuations, described by stochastic differential equations. We will first introduce the Monte Carlo method, combined with a suitable discretization of the underlying differential equation, to compute expectations of output quantities of interest (QoIs) or of the whole solution, and investigate the interplay between the discretization error and the Monte Carlo error. We then introduce the Multilevel Monte Carlo paradigm, analyze its properties and practical implementation aspects, extend its formulation for computations of moments or other statistics of the QoIs. We will also discuss the related Multifidelity Monte Carlo approach. In the second part of the course we present how Multilevel Monte Carlo techniques can be used in some applications, such as PDE constrained optimization under uncertainty or sequential data assimilation.
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