Increasingly, the engineering of complex systems requires consideration of an intricate web of components and their interaction in diverse social and technical environments. Simulation can assist in designing and testing socio-technical systems by allowing the potential space of outcomes to be explored under given designs. Agent-based models have been developed as a method for building models of complex systems, with great success. Agents may be designed to represent system components and to specify the interactions between them in an incredible level of detail. While popular, the full potential of the methodology to support engineering of complex systems has not been reached, however, because of a set of key challenges. First, there exists a relative lack of robust methods for calibrating agent-based models to theory. Second, there is a paucity of reliable approaches for extracting coarse-grained, system level information as it emerges in agent-based simulations. Third, there is a dearth of schemes for handling uncertainty in the application of agent-based rules to system behavior. Fourth, computation of agent-based models is inefficient when agents are numerous in volume and richly-specified in behavior. Together, these impediments constrain the ability of agent-based modeling to enable prediction, to support decisions, and to facilitate the design, control, and optimization of complex systems. The main objective of this project is to broaden the extensibility of agent-based modeling beyond these constraints. This will be achieved by developing novel computational methods to fuse agent-based modeling, uncertainty measurement and quantification, and mathematics for pattern-extraction.
This project will expand the capabilities of agent-based modeling in supporting the design, engineering, and testing of complex systems. Our initial focus is to develop a prototype scheme that can be applied to complex socio-behavioral systems, but the project is of potential relevance across a diverse array of substantive areas. Indeed, one of our central aims is to provide the glue that can bridge diverse schemes for agent-based simulation across application areas. This could be incredibly useful in reconciling agent-based modeling into a larger ?ecology? of mathematical modeling and computation, fundamentally expanding the range of questions that can be posed and systems that can be explored in simulation, while better linking simulation to real-world dynamics.
This project addressed some fundamental issues related to complex systems. In particular, research under this project provided insight into the significance of uncertainty to the predictive power of common dynamical system models. It also provided mathematical and computational methodology to explore the effect of community feedback on the behavior of individual interacting agents. Finally, the research developed new methodology to characterize ecological systems at different scales that are appropriate for their management, both against natural hazards and as they interface with human habitats. More specifically, Markov chains have been treated as random dynamical systems with uncertain transition probabilties. This deceptively simple perspective permits the application of a ubiquitous building block of dynamical systems (Markov Chains) to highly complex problems with the understanding that uncertainties in the model and its data can be quantified and used to determine the confidence in inferences and decisions predicated on the model. An immediate result of this approach is a methodology capable of mitigating risks associated with model-based prediction and decision. With regards to modeling interacting agents, this research has contributed to fundamental understanding of and capabilities for anticipating the behavior of the collective of interacting agents from knowledge of the behavior of an individual. The challenge has typically been the fact that dynamics for the collective is unknown, while dynamics for individual agents can be synthesized from their psychological profiles. The approach developed under this grant explores the applicability of equation-free methods to characterize and predict the evolution of a collective, from knowledge of agents behavior. Applications of this methodology to the problem of urban sprawl has been demonstrated. Finally, concerning ecological systems, the present research develops new mathematical and algorithmic approaches for describing these systems on several distinct scales that may be more suitable for different types of decisions. In particular, forests as dynamical systems, are considered. The characterization of the evolution of tree densities with time was considered, taking into account evolutionary traits such as competition for sunlight and food. The evolution of the forest, considered at different spatial scales, was considered, allowing for predictions that are relevant to the management of ecological diversity, wildfires and forest-city interfaces.
