Modern science faces fundamental methodological dilemmas when dealing with complex systems. This paper proposes a solution at the meta-theoretical level: the theory of composite model systems, which elevates the research focus from individual models to the structural relationships among them. The core contribution is clarifying a crucial distinction between the product state manifold and the constrained submanifold, showing that the physical evolution of the system is entirely confined to this constrained submanifold. This leads to a reformulation of system dynamics using differential-algebraic equations (DAEs), with stability analysis performed on the tangent bundle of the constrained submanifold. The framework provides a unified mathematical language for multi-physics coupling and initiates a new paradigm: meta-modeling, the modeling of modeling activity itself.
Wang et al. (Sun,) studied this question.