Equation-free: The computer-aided analysis of complex multiscale systems

By Ioannis G. Kevrekidis, C. Gear, Gerhard Hummer. 2004

408 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/8297c024234b000162cfa54e13929dc5c3c260ee

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In Computational Theory and Mathematics

In Computer Networks and Communications

In Environmental Engineering

Citations in the corpus

Bridging the scales in nano engineering and science (2006, methodology): “In this section we review several informationpassing bridging technique including: the Force field calibration method, which constructs effective interatomic potentials and eliminates the need for explicitly tracing the evolution of electronic structure; the Generalized Mathematical Homogenization (”
Multiresolution Dynamic Mode Decomposition (2015, methodology): “The mathematical architecture advocated here is an alternative to the equation-free, multi-scale modeling method proposed by Kevrekidis and co-workers [12, 13].”
Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Planck Operators (2005, methodology): “Finally, these eigenvectors may be used to design better search and da t collection protocols [29].”
Agent-based models in translational systems biology (2009, neutral): “55”
Diffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems (2008, methodology): “Specifically, following the equation-free coarse molecular dynamics approach [31, 32, 33], we propose to explore the effective free energy and diffusion coefficients as a function of the diffusion map coordinates by a series of multiple short simulations appropriately initialized at given values of ”
Plug-and-play inference for disease dynamics: measles in large and small populations as a case study (2009, methodology): “(ii) In the analysis of complex systems, methods that are based solely on simulations from computer codes representing a model have been called equation-free (Kevrekidis et al. 2004).”
Strong convergence of projective integration schemes for singularly perturbed stochastic differential systems (2006, methodology): “This has motivated the development of algorithms such as projective and coarse projective integration [14, 15, 16] within the so-called equation-free framework [17, 18].”