In recent years, multiscale, multi-physics
modeling has attracted a lot of attention by the scientific community.
Put it bluntly, this can be considered as an effort to stamp out
the empirical aspects in the modeling process and replace them by more
rigorous approaches based on first principles.
Such an effort, if successful, will fundamentally change the way we
think about modeling as well as the role of mathematics in modeling.

However, many fundamental mathematical issues have to be addressed
before such an effort becomes truly successful.
Examples of such issues include the general formulation of microscopic
models, the connection between differentl laws
of physics and the microscopic foundation of continuum theory.
In this lecture, I will discuss some of these issues and the progresses
made so far.