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

摘要: The best available descriptions of systems often come at a fine level (atomistic, stochastic, microscopic, agent based), whereas the questions asked and tasks required by modeler (prediction, parametric analysis, optimization, control) are much coarser, macroscopic level. Traditional modeling approaches start deriving evolution equations from microscopic models, then bringing an arsenal computational tools to bear on these descriptions. Over last few years with several collaborators, we have developed validated mathematically inspired, enabling technology that allows perform acting models directly. We call this “equation-free” approach, since it circumvents step obtaining accurate backbone approach is design “experiments”. In traditional numerical main code “pings“ subroutine containing model, uses returned information (time derivatives, etc.) computer-assisted analysis. our same runs ensemble appropriately initialized experiments which quantities estimated. continuum algorithms can, thus, be viewed as protocols for experimental (where “experiment“ means experiment set up, performed model different description). Ultimately, what makes all possible ability initialize will. Short bursts experimentation -through matrix-free theory like estimationbridge simulation modeling. If enough control authority exists laboratory “at will” can lead equation-free exploration complex system dynamics.