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.