1. Introduction
Scientific research in the 21st century is
characterized by research problems of increasing complexity amidst a
data revolution. An ever-growing number of scientific research problems
are now focused on systems and processes that are complex not only in
terms of their underlying mechanisms and governing principles but also
by virtue of the high-dimensional and heterogeneous data worlds that
they live in. Modeling, simulation, and high-performance computing,
alongside experiments, are indispensable for tackling such problems —
numerous success stories have been published across diverse fields.
Nonetheless, the unabated increases in complexity and data-intensiveness
of modern research problems are now posing three evolving challenges for
training a new generation of researchers to have the right tools to
navigate the emerging challenges. First, many contemporary problems are
now defined over multiple length and time scales (i.e., they are
multiscale) and also by multiple distinct, yet intricately coupled,
physical, chemical and/or biological processes (they are multiphysics).
Solving multiscale-multiphysics problems through multiscale modeling
(MSM) methods requires the construction of highly sophisticated
algorithms at different scales, the rigorous coupling of the scales, and
laborious algorithmic implementation using message passing on parallel
high-performance computing (HPC) platforms. Second, the associated
increases in data types, data intensiveness, and the types of questions
asked, now require more sophisticated approaches for data analysis,
including machine learning (ML) techniques, which are becoming
indispensable in many applications. Third, MSM and ML approaches have
evolved independently, and therefore, the art of combining them is very
much an emerging paradigm. This review article describes the convergence
of several advances in the scientific literature that has made the field
of MSM what it is today and provides a perspective of its future, hoping
that it would benefit current and potential researchers navigate and
advance the field of MSM.