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SUMMARY:Equation-free modeling and computation for complex/multiscale syst
 ems - Yannis  Kevrekidis\,   Princeton
DTSTART:20070309T160000Z
DTEND:20070309T170000Z
UID:TALK6781@talks.cam.ac.uk
CONTACT:Nigel Peake
DESCRIPTION:In current modeling practice for complex reacting systems\, th
 e best available descriptions often come at a fine level\n(atomistic\, sto
 chastic\, microscopic\, individual-based) while the questions asked and th
 e tasks required by the modeler\n(prediction\, parametric analysis\, optim
 ization and control) are at a much coarser\, averaged\, macroscopic level.
  Traditional modeling approaches start by first deriving macroscopic evolu
 tion equations from the microscopic\nmodels\, and then bringing our arsena
 l of mathematical and algorithmic tools to bear on these macroscopic descr
 iptions.\nOver the last few years\, and with several collaborators\, we ha
 ve\ndeveloped and validated a mathematically inspired\, computational enab
 ling technology that allows the modeler to\nperform macroscopic tasks acti
 ng on the microscopic models directly.\nWe call this the ``equation-free
 ” approach\, since it circumvents the\nstep of obtaining accurate macros
 copic descriptions. We will argue that the backbone of this approach is th
 e design of\n(computational) experiments. Traditional continuum numerical 
 algorithms can thus viewed as\nprotocols for experimental design (where 
 “experiment” means a computational experiment set up and\nperformed wi
 th a model at a different level of description).\nUltimately\, what makes 
 it all possible is the ability to initialize computational experiments at 
 will.\nShort bursts of appropriately initialized computational experimenta
 tion ­through matrix-free\nnumerical analysis and systems theory tools li
 ke variance reduction and estimation- bridges\nmicroscopic simulation with
  macroscopic modeling.\nI will also discuss some recent developments in da
 ta mining algorithms\, exploring large complex data sets to find good "red
 uction coordinates". 
LOCATION:MR2\, Centre for Mathematical Sciences
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