The role of approximate morphisms in multiresolution modeling: Can we relax the strict lumpability requirements?

To become the core development methodology of major defense-related simulation projects, multiresolution modeling needs more advances in basic theory and practice. In this note, we illustrate an approach to addressing issues relating to approximate morphisms (structure/behavior preservation relations) between pairs of models. Such issues include metrics for departure from strict lumpability, tying approximate satisfaction of structural conditions to the resulting behavioral error, and how to enhance the probability of creating good approximate morphisms by humans and artificial modelers.