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CATEGORIES:Fluid Mechanics (DAMTP)
SUMMARY:Equation-free modeling and computation for complex
/multiscale systems - Yannis Kevrekidis\, Princ
eton
DTSTART;TZID=Europe/London:20070309T160000
DTEND;TZID=Europe/London:20070309T170000
UID:TALK6781AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/6781
DESCRIPTION:In current modeling practice for complex reacting
systems\, the best available descriptions often co
me at a fine level\n(atomistic\, stochastic\, micr
oscopic\, individual-based) while the questions as
ked and the tasks required by the modeler\n(predic
tion\, parametric analysis\, optimization and cont
rol) are at a much coarser\, averaged\, macroscopi
c level. Traditional modeling approaches start by
first deriving macroscopic evolution equations fro
m the microscopic\nmodels\, and then bringing our
arsenal of mathematical and algorithmic tools to b
ear on these macroscopic descriptions.\nOver the l
ast few years\, and with several collaborators\, w
e have\ndeveloped and validated a mathematically i
nspired\, computational enabling technology that a
llows the modeler to\nperform macroscopic tasks ac
ting on the microscopic models directly.\nWe call
this the ``equation-free” approach\, since it circ
umvents the\nstep of obtaining accurate macroscopi
c descriptions. We will argue that the backbone of
this approach is the design of\n(computational) e
xperiments. Traditional continuum numerical algori
thms can thus viewed as\nprotocols for experimenta
l design (where “experiment” means a computational
experiment set up and\nperformed with a model at
a different level of description).\nUltimately\, w
hat makes it all possible is the ability to initia
lize computational experiments at will.\nShort bur
sts of appropriately initialized computational exp
erimentation through matrix-free\nnumerical analy
sis and systems theory tools like variance reducti
on and estimation- bridges\nmicroscopic simulation
with macroscopic modeling.\nI will also discuss s
ome recent developments in data mining algorithms\
, exploring large complex data sets to find good "
reduction coordinates".
LOCATION:MR2\, Centre for Mathematical Sciences
CONTACT:Nigel Peake
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