Mathematical approaches for complexity/predictivity trade-offs in complex system models : LDRD final report.

Goldsby, Michael E. ; Mayo, Jackson R. ; Bhattacharyya, Arnab (Massachusetts Institute of Technology, Cambridge, MA) ; Armstrong, Robert C. ; Vanderveen, Keith

关键词: 97;    ACCURACY;    MATHEMATICAL MODELS;    RENORMALIZATION;    FORECASTING;    BEHAVIOR Complex variables.;    Mathematical Sciences-Complex Analysis;   

DOI  :  10.2172/942063
RP-ID  :  SAND2008-6041
PID  :  OSTI ID: 942063
Others  :  TRN: US200902%%8

学科分类：社会科学、人文和艺术（综合）

美国|英语

来源: SciTech Connect

【 摘 要 】

The goal of this research was to examine foundational methods, both computational and theoretical, that can improve the veracity of entity-based complex system models and increase confidence in their predictions for emergent behavior. The strategy was to seek insight and guidance from simplified yet realistic models, such as cellular automata and Boolean networks, whose properties can be generalized to production entity-based simulations. We have explored the usefulness of renormalization-group methods for finding reduced models of such idealized complex systems. We have prototyped representative models that are both tractable and relevant to Sandia mission applications, and quantified the effect of computational renormalization on the predictive accuracy of these models, finding good predictivity from renormalized versions of cellular automata and Boolean networks. Furthermore, we have theoretically analyzed the robustness properties of certain Boolean networks, relevant for characterizing organic behavior, and obtained precise mathematical constraints on systems that are robust to failures. In combination, our results provide important guidance for more rigorous construction of entity-based models, which currently are often devised in an ad-hoc manner. Our results can also help in designing complex systems with the goal of predictable behavior, e.g., for cybersecurity.