Modelling Dr Andy Evans Modelling Examples Cellular Automata

Modelling Dr Andy Evans

Modelling Examples: Cellular Automata Agent-based models The modelling process

What are models? Hypothetical or Theoretical statement of how a system works, ignoring “accidental” influences. Physical recreation of the same using scaled objects and applying the same processes. Computer recreation of the same using virtual objects and applying virtual processes.

Why model? Prediction: Future Past (backcasting) Testing our knowledge is complete. Emergence (how simple processes give us complicated patterns) Holding our knowledge in a framework.

Virtual model types Analytical models Mathematical equation. Logical Logic models; fuzzy logic; etc. Iterative models Finite element models; agent-based models Statistical models Regression equations; Bayesian nets; etc.

Verisimilitude Abstract models: Simplified objects Subset of processes Thought experiments Verify that core processes are appropriate Alternative is to try and model everything accurately. Is this possible in systems that don’t have closure?

Model scale Aggregate models Regression Disaggregate models Range from area processing to individual-based Individual elements Finite-element models Agent-based models

Individual level modelling Aggregate representation was good when it all had to be done in our heads. Now we have power for individual representation, i. e. as we understand the world. We struggle to understand emergence – how simple rules of individuals end up in complicated system behaviour.

Emergence May seem subjective (how to do recognise “complicated”, why worry about other scales? ) But subjective aggregate elements have a big effect (e. g. inflation rates affect interest rates) Systems of small scale elements that combine to make large scale systems in unclear ways are called complex. Individual-level models are a useful way of exploring complexity.