2. Governing equations for multiphysics modeling
While the considerations above and the motivation to combine MSM and ML
can benefit several disciplines, it is particularly relevant for
chemical, biomolecular, and biological engineers. In our disciplines,
the fundamentals (namely, thermodynamics, kinetics, transport, controls)
have always emphasized molecular to process length and timescales. These
core subjects are rooted in their own foundations, each with its
premise, and a set of governing equations are discipline dependent.
Statistical mechanics drives much of molecular-scale interactions,
quantum mechanics drives catalytic mechanisms, mesoscopic scale relevant
to advanced functional materials, energy, or cellular processes are
constrained by the laws of transport physics, and foundations of process
control and optimizations are rooted in applied mathematics, in
particular, in the formal analysis of stability, robustness,
evolvability, stochastic effects or noise propagation, and sensitivity
analysis [1-4]. In this section, we attempt to provide a unified
description of the underlying governing equations in multiphysics
modeling. In section 3, we summarize how the foundations and the
governing equations have translated into methods and algorithms for
multiphysics modeling and simulations. In section 4, we discuss HPC, and
in sections 5 and 6 we discuss the current and future prospects of MSM.
We end with some conclusions in section 7. We begin by outlining a
summary of historical developments of governing equations and
foundations for multiphysics modeling in Table 1.