Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations
Graph Chatbot
Chattez avec Graph Search
Posez n’importe quelle question sur les cours, conférences, exercices, recherches, actualités, etc. de l’EPFL ou essayez les exemples de questions ci-dessous.
AVERTISSEMENT : Le chatbot Graph n'est pas programmé pour fournir des réponses explicites ou catégoriques à vos questions. Il transforme plutôt vos questions en demandes API qui sont distribuées aux différents services informatiques officiellement administrés par l'EPFL. Son but est uniquement de collecter et de recommander des références pertinentes à des contenus que vous pouvez explorer pour vous aider à répondre à vos questions.
Because of their robustness, efficiency and non-intrusiveness, Monte Carlo methods are probably the most popular approach in uncertainty quantification to computing expected values of quantities of interest (QoIs). Multilevel Monte Carlo (MLMC) methods sig ...
Self-affine rough interfaces are ubiquitous in experimental systems, and display characteristic scaling properties as a signature of the nature of disorder in their supporting medium, i.e. of the statistical features of its heterogeneities. Different metho ...
Temporal point-processes are often used for mathematical modeling of sequences of discrete events with asynchronous timestamps. We focus on a class of temporal point-process models called multivariate Wold processes (MWP). These processes are well suited t ...
A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a random forcing term, ...
In this work, we present, analyze, and implement a class of Multi-Level Markov chain Monte Carlo (ML-MCMC) algorithms based on independent Metropolis-Hastings proposals for Bayesian inverse problems. In this context, the likelihood function involves solvin ...
Multiscale problems, such as modelling flows through porous media or predicting the mechanical properties of composite materials, are of great interest in many scientific areas. Analytical models describing these phenomena are rarely available, and one mus ...
Mathematical models involving multiple scales are essential for the description of physical systems. In particular, these models are important for the simulation of time-dependent phenomena, such as the heat flow, where the Laplacian contains mixed and ind ...
Stabilized Runge–Kutta (aka Chebyshev) methods are especially efficient for the numerical solution of large systems of stiff differential equations because they are fully explicit; hence, they are inherently parallel and easily accommodate nonlinearity. Fo ...
This thesis is devoted to the derivation of a posteriori error estimates for the numerical approximation of fluids flows separated by a free surface. Based on these estimates, error indicators are introduced and adaptive algorithms are proposed to solve th ...
Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In this work, we show ...
