Multiscale Methods: Averaging and Homogenization

By Grigorios A. Pavliotis, Andrew M. Stuart. 2008

997 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/84e399076873c284674936f983acebfa9263e4b4

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Citations in the corpus

Large Deviations and Importance Sampling for Systems of Slow-Fast Motion (2012, methodology): “This can be derived via standard homogenization theory [6, 31].”
Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging (2009, background): “2, it is known (we refer the reader, for instance, to [99] or to Theorem 14 of section 3 of Chapter II of [108] or to [92]) that x converges towards xt defined as the solution to the ODE”
Deep relaxation: partial differential equations for optimizing deep neural networks (2017, methodology): “Derivation of local entropy via homogenization of SDEs.”
Smooth approximation of stochastic differential equations (2014, background): “] In applications, smooth processesWn that approximate Brownian motion arise naturally from differential equations as follows [18, 21, 36, 42, 43].”
Predicting the Behavior of Techno-Social Systems (2009, methodology): “Thus, we have to develop appropriate formalisms and techniques, as researchers studying multi-scale physical systems (fluids, solids, distribution of masses in the universe, etc.) have done in the past ( 33 ).”
Stochastic models of intracellular transport (2013, methodology): “(3.23) The basic idea of the homogenization method is to represent the diffusive behavior of a tracer on two different spatial scales (Pavliotis and Stuart, 2008; Torquato, 2002): one involving a macroscopic slow variable x and the other a microscopic fast variable y ≡ x/ so that u is periodic with…”
Stochastic climate theory and modeling (2015, unknown): “[125] Pavliotis, G.”
A Micro-Macro Parareal Algorithm: Application to Singularly Perturbed Ordinary Differential Equations (2012, methodology): “Many methods have been proposed to obtain such macroscopic models, either analytically (see e.g. [34] for a recent overview) or numerically.”
Strong and weak orders in averaging for SPDEs (2012, methodology): “Convergence in law or in probability of X ε to X in the space C([0, T ], H) can be shown by different techniques: by using a Khasminskii technique based on a subdivision of the interval [0, T ](see [19,15]); a Poisson equation (see [18]); the method of perturbed test functions and of a martingale pr”