An Equation-free Approach to Complex System Modeling

In current modeling , the best available descriptions of a system often come at a fine level (atomistic, stochastic, microscopic, individual-based) while the questions asked and the tasks required by the modeler are at a much coarser, averaged, macroscopic level.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.

This the ``equation-free” approach circumvents the derivation of accurate macroscopic descriptions; instead, it uses traditional continuum numerical methods as protocols for the design of short (computational) experiments with the fine scale code.Ultimately, what makes this connection of microscopic simulation with macroscopic modeling possible, is the ability to initialize computational experiments at will.

I will illustrate the approach with coarse-graining examples that arise in modeling complex biological systems, and discuss some connections with modern data analysis techniques.

Ioannis Kevrekidis, Princeton University

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