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Abstract :
Starting from two orthogonal concepts of understanding, namely
from quite general basic principles or from simplified models capturing
the
essence of a problem, I will describe the crucial importance of
coarse-graining from the point of view of any applied scientist or
engineer.
Coarse-graining, in turn, naturally leads to stochastic equations.
A very
general form of the theory of coarse-graining dynamics will be presented
within a modern formalism of nonequilibrium thermodynamics. This formalism,
called GENERIC, leads to a variety of serious and important challenges
in the
theory and numerics of stochastic differential equations. Moreover,
the
abstract formulation of reversible and irreversible dynamics within
the
GENERIC framework leads to a number of both fundamental questions related
to
geometry and practical numerical problems related to space-time
discretizations of model equations.