Journal ArticleDOI
Equation-free: The computer-aided analysis of complex multiscale systems
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Over the last few years with several collaborators, a mathematically inspired, computational enabling technology is developed and validated that allows the modeler to perform macroscopic tasks acting on the microscopic models directly, and can lead to experimental protocols for the equation-free exploration of complex system dynamics.Abstract:
The best available descriptions of systems often come at a fine level (atomistic, stochastic, microscopic, agent based), whereas the questions asked and the tasks required by the modeler (prediction, parametric analysis, optimization, and control) are at a much coarser, macroscopic level. Traditional modeling approaches start by deriving macroscopic evolution equations from microscopic models, and then bringing an arsenal of computational tools to bear on these macroscopic descriptions. Over the last few years with several collaborators, we have developed and validated a mathematically inspired, computational enabling technology that allows the modeler to perform macroscopic tasks acting on the microscopic models directly. We call this the “equation-free” approach, since it circumvents the step of obtaining accurate macroscopic descriptions. The backbone of this approach is the design of computational “experiments”. In traditional numerical analysis, the main code “pings“ a subroutine containing the model, and uses the returned information (time derivatives, etc.) to perform computer-assisted analysis. In our approach the same main code “pings“ a subroutine that runs an ensemble of appropriately initialized computational experiments from which the same quantities are estimated. Traditional continuum numerical algorithms can, thus, be viewed as protocols for experimental design (where “experiment“ means a computational experiment set up, and performed with a model at a different level of description). Ultimately, what makes it all possible is the ability to initialize computational experiments at will. Short bursts of appropriately initialized computational experimentation -through matrix-free numerical analysis, and systems theory tools like estimationbridge microscopic simulation with macroscopic modeling. If enough control authority exists to initialize laboratory experiments “at will” this computational enabling technology can lead to experimental protocols for the equation-free exploration of complex system dynamics.read more
Citations
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Journal ArticleDOI
Adaptive generalized mathematical homogenization framework for nanostructured materials
Jacob Fish,Aiqin Li,Fazel Yavari +2 more
TL;DR: In this article, an adaptive generalized mathematical homogenization (AGMH) framework for modeling nanostructured materials with evolving defects at a finite temperature is presented, where a molecular dynamics model is employed in the vicinity of defects whereas constitutive equation-free continuum model is used away from the defects.
Journal ArticleDOI
Data-driven model reduction of agent-based systems using the Koopman generator.
Jan-Hendrik Niemann,Jan-Hendrik Niemann,Stefan Klus,Stefan Klus,Christof Schütte,Christof Schütte +5 more
TL;DR: This paper shows how Koopman operator theory can be used to derive reduced models of agent-based systems using only simulation data, and demonstrates that the obtained reduced systems are in good agreement with the analytical results, provided that the numbers of agents is sufficiently large.
Book ChapterDOI
Discrete Element Modeling for Multiscale Simulation of Aggregation Processes
Alexander Reinhold,Heiko Briesen +1 more
TL;DR: The first steps of combining the favorable predictive capability of the discrete element method and the computational efficiency of the population balance approach are presented in this paper, where aggregation due to gravitational settling and shear induced aggregation are implemented and discussed as case studies.
Proceedings Article
Ant Colony Systems and the Calibration of Multi-Agent Simulations: a New Approach
Benoît Calvez,Guillaume Hutzler +1 more
TL;DR: The aim of the work is to provide tools for the calibration of agent-based models, which consists inding the optimal set of parameters for a given criterion, for example that the model achieves a specic function optimally or that the results of the simulation are as close as possible to experimental data.
Error control and analysis in coarse-graining of stochastic lattice dynamics
TL;DR: Analytical and numerical evidence is provided that the hierarchy of the coarse models is built in a systematic way that allows for the error control of quantities that may also depend on the path.
References
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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
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A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
J. Guckenheimer,P. J. Holmes +1 more
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
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