Multilevel Monte Carlo

Darcy flow in random porous medium

AMCS 301 Numerical methods for random partial differential equations: hierarchical approximation and machine learning approaches

A course on modern numerical methods for random partial differential equations
Illustration weak approximation SDE

AMCS 336 Numerical Methods for Stochastic Differential Equations with connections to Machine Learning

The goal of this course is to give basic knowledge of stochastic differential equations and their numerical solution, useful for scientific and engineering modeling, guided by some problems in applications in financial mathematics, material science, geophysical flow problems, turbulent diffusion, control theory, and Monte Carlo methods.

PhD Student Abdul Lateef Haji Ali to Present 'Monte Carlo Methods' Talk at University of Basel

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KAUST

In this talk, I explore the application of single level and multilevel Monte Carlo methods for computing key quantities in a stochastic particle system within the mean-field framework.

Bayesian Optimal Experimental Design Using Multilevel Monte Carlo By Chaouki ben Issaid (Master Student of Prof. Raul Tempone, KAUST)

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B1 R4214

Experimental design can be vital when experiments are resource exhaustive and time-consuming. In this work, we carry out experimental design in the Bayesian framework. To measure the amount of information, which can be extracted from the data in an experiment, we use the expected information gain as the utility function, which specifically is the expected logarithmic ratio between the posterior and prior distributions.

Multilevel Monte Carlo Acceleration of Seismic Wave Propagation under Uncertainty

1 min read ·
We interpret uncertainty in a model for seismic wave propagation by treating the model parameters as random variables and apply the Multilevel Monte Carlo method to reduce the cost of approximating expected values of selected, physically relevant, quantities of interest (QoI) with respect to the random variables.