The utility of homomorphism concepts in simulation: building families of models from base-lumped model pairs

In this tutorial review paper we explain the concept of homomorphism and identify some principles that justify homomorphism construction based on the homogeneity of structure and coupling in systems with multiple components. We discuss some simple examples to show how these underlying justifying conditions can arise. Examples include brain simulation, combat attrition, and the greatly reduced computational complexity represented by Pascal’s triangle. Homomorphism is also shown to be fundamental for constructing approximate low-resolution models. Models that simplify complex time-demanding simulation models are often used as surrogate or metamodels in system optimization. However, such models are fitted typically to computationally derived response surfaces and not structurally related directly to the originals using homomorphisms as described here. Along these lines, we show how homomorphism plays an essential role in a novel approach being developed to strongly control tree expansion in state space explorations of stochastic system simulation.