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Agent-based modeling has grown in popularity over the last decade. It has been used to investigate bacterial chemotaxis signaling pathways, population ecology, social, economic, and political systems, modeling
of natural organic matter and microbes in the soil, software engineering, neural networks, engineering design, business and commerce and many other areas.
The central idea of an agent-based model (ABM) is to view
some of the physical entities in the domain to be modeled as, i.e., autonomous entities interacting based on physical laws ("agent laws") that govern their individual behaviors. Consequently, the changes
over time modeled in an ABM are the states of each individual agent (different from equation-based models, where overall states of a domain and their changes over time are modeled). In computer simulations, ABMs
are implemented as software objects, where agent laws are encoded in computational procedures that operate on the agent representation and update its state over time. A run of the simulated ABM then consists of
instantiating agents in a prespecified simulated environment according to a predetermined initial configuration and updating the agents' and environmental states for a certain number of times. Simulation states
can be visualized, recorded, and subsequently analyzed, which often leads to new insights in the studied domain that would not have been possible with other modeling techniques.
We believe that agent-based
methods are best-suited for multi-scale modeling for at least six reasons:
(1) ABM can simulate heterogeneous discrete or discontinuous behaviors, which are required for multi-scale models (i.e. each agent's
attributes and properties may uniquely differ from all others).
(2) Even within a given level, ABMs accommodate extreme heterogeneity better than equation-based models that tend to approximate the distributions
of agent properties with averages which may miss important phenomena triggered by entities at the "tails of the distribution".
(3) ABMs are intuitive and easy to understand since ABM simulations have
direct representations of actual physical entities.
(4) ABM simulations can reveal emergent behaviors that might be hidden by top-down equation based modeling (e.g., the evolution of a complex biological system
may display path dependence due to sensitive dependence to initial conditions or unstable behavior caused by amplified feedback).
(5) Single-scale ABMs can be extended to multiple scales by defining agents that
are comprised of component agents, which is a natural and realistic approach to the challenge of spanning the scales (i.e., aggregation of lower level agents into a higher level agent, along with downward feedback
relationships).
Most importantly, (6) ABM techniques can be applied without prior knowledge
of the effects of the interactions among agents as long as the behavior of individual agents can be specified in terms of agent laws. This is crucial for the development of novel multi-scale models, where causal effects across levels are not known.
Currently, almost all reported applications of ABM are at a single scale. The few exceptions that model 2 levels are not based on any systematic theory of multi-scale models. We will remedy the
limitations of current ABMs by developing a novel theoretical framework for multi-scale ABMs. It will provide a formal definition of multi-scale agent-based models that consists of environments at different
scales/levels and their agents that interact within and across levels.
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