Mathematical Foundations for Modeling and Simulation

A tractable scientific basis is needed for M&S modeling, specification, abstraction, refinement, composition, and decomposition. While the component composition, abstraction, and refinement work of others will provide valuable insights, M&S fundamentals for physical systems must be applicable to the lowest level of knowledge about those systems. Starting with objects, components, or systems (such as the approaches from the software engineering and systems engineering literature) is too high a level. In addition, none of the published theory addresses the situational requirements issues of M&S in conjunction with the fundamental composition, abstraction, and refinement issues. As a result, M&S development, integration, and evolution are often ad hoc, based on ambiguous specifications. Additional theoretical and practical work is needed to support M&S. This paper provides an overview description of several fundamental M&S issues and outlines a recommended M&S foundations research agenda to address these issues.