Inhalt des Dokuments
Equation-free modeling of complex systems
Held by Prof. Ioannis G. Kevrekidis (Chemical Engineering, PACM and Mathematics, Princeton University, USA)
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 (prediction, parametric analysis, optimization and control) are at a much coarser, averaged, macroscopic level. Traditional modeling approaches start by first deriving macroscopic evolution equations from the microscopic models, and then bringing our 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, since it circumvents the step of obtaining accurate macroscopic descriptions.
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 variance reduction and estimation - bridges microscopic simulation with macroscopic modeling.
I will discuss linking this modeling approach with uncertainty quantification algorithms. If time permits, I will also discuss the use of data-mining for the computer-assisted discovery of good coarse-grained descriptors of complex systems.