PHYSICS AND ASTRONOMY
MATH DEPARTMENT
Science at the Edge
Friday, November 21, 2008
11:30a
1400 Biomedical & Physical Sciences Bldg
Refreshments at 11:15a in 1400 BPS Bldg
Yannis Kevrekidis
Princeton University
Department of Chemical Engineering
“Equation-free modeling and computation for
complex systems”
In current modeling practice
for complex systems, and in biologically inspired models in particular, the
best available description 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.
Traditionally 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.
I will argue that the
backbone of this approach is the design of (computational) experiments.
In traditional numerical analysis, the main code “pings” a
subroutine containing the model, and uses the return information (time
derivatives, function evaluations, functional derivatives) to perform
computer-assisted analysis. In our approach the same main code
“pings” a subroutine that sets up a short ensemble of appropriately
initialized computational experiments from which the same quantities are
estimated (rather than evaluated). Traditional continuum numerical
algorithms can thus be 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-bridges 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”.
**If you would like
to meet with this speaker, contact Keith Promislow directly at [log in to unmask]">[log in to unmask], and let him know what times you are
available. The speaker is available at the following times on Nov. 21:
9am – 11am and 2pm – 5pm. *****
Kim Crosslan
Undergraduate Secretary
Dept. Physics & Astronomy
Michigan State University
1312 Biomedical & Physical Sciences
East Lansing, MI 48824
517-884-5531
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