@book{39291,
  keywords = {dynamics, bifurcation-analysis, integration, optimal prediction, simulators, coarse stability},
  author = {Kevrekidis},
  title = {Equation-free modeling for complex systems},
  abstract = { In current modeling, the best available descriptions of a system are often given at a fine level (atomistic, stochastic, microscopic, individual-based) even though the questions asked and the tasks required by the modeler (prediction, parametric analysis, optimization and control) are at a much coarser, averaged, macroscopic level. Traditional modeling approaches first derive macroscopic evolution equations from the microscopic models and then bring an arsenal of mathematical and algorithmic tools to bear on these macroscopic descriptions. Over the last few years, and 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 because it circumvents the step of obtaining accurate macroscopic descriptions. We argue that the basis of this approach is the design of (computational) experiments. Traditional continuum numerical algorithms can 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 the equation free approach 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 variance reduction and estimation-bridge microscopic simulation with macroscopic modeling. Remarkably, if there is enough control authority to initialize laboratory experiments "at will, " this computational enabling technology can become a set of experimental protocols for the equation-free exploration of complex system dynamics. },
  year = {2005},
  publisher = {Natl Academies Press},
  address = {Washington},
  isbn = {0-309-09547-6},
  language = {English},
}