Equation-Free Modeling and Computation for Complex/Multiscale Systems

Speaker: Dr. Yannis Kevrekidis,
Princeton University"Equation-Free Modeling and Computation for Complex/Multiscale Systems"In current modeling practice for complex/multiscale systems, the best available descriptions 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. We will argue that the backbone of this approach is the design of (computational) experiments. Traditional continuum numerical algorithms can thus 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 variance reduction and estimation- bridge microscopic simulation with macroscopic modeling. I will also discuss some recent developments in data mining algorithms, exploring large complex data sets to find good "reduction coordinates".

Location: Kaprielian Hall (KAP) - 209

Audiences: Everyone Is Invited

Contact: Evangeline Reyes