Modeling Techniques for Self-Organizing Systems

Modeling Techniques for Self-Organizing Systems - Group 1

In general: Three methodologies for designing (self-organizing) systems.

• Bottom up modeling
  • System consists of units
  • Modeling structure and dynamics of units (agents), topology, and interaction
    • Model I/O behavior of agents
      • Transfer function
      • Local rule set
    • Topology
      • Network, connections between agents
      • Spatial environment, e.g. 2d grid, defining a continuous neighborhood
    • Interaction between agents
      • Transfer function linear or non-linear
  • Advantage: straightforward implementation
  • Disadvatage: Emergenct properties cannot been foreseen from local rules
  • Examples:
    • Conway's Game of Life e(Cellular Automaton
    • Micro economics

• Top down modeling
  • Model entire system from observations
  • Observe time series and predict behavior by finding regularities in pattern's using for instance:
    • Markov Models
    • Neural Networks
  • Advantage: Covers emergence and goal orientation
  • Disadvantage: Analyzing system as black box, difficult to verify obtained system model
  • Example:
    • Chart Analysis in stock market

• Recursive bootstrapping
  • Cyclic adaptation of both models
  • Increase understanding in each iteration

Modeling the Structure, Dynamics and Quantification - Group 2

Looked at modeling the topology and connections between agents.

Techniques for dynamic processes (microscopic rules of behaviour) and their strengths/weaknesses regarding robustness:

• Cellular Automaton
  • Easy to form, broad range of patterns
  • But: Dependence on synchronization

• Evolutionary Algorithms
  • Genetic Algorithms
    • Efficient search through high dimensional state
    • However: Need to specify a "fitness landscape" a priori (need to know what to find a good solution to)
    • History dependence (converges to different solutions)
    • Good, but no optimal solutions
    • Discussion mentioned that this may be more design than modeling (since it designs the solution)

• UML (Modelling specification language)
• Finite State Machines / Hidden Marcov Models
  • Flexible
  • Model at the system level (macroscopic)

• Control Theory
  • Real-Time, but has some centralized, global requirements
• Agent-based approaches
  • Local synch. algorithms
  • Local geometric constructions
  • Game theory (high complexity once N>2)
  • Swarm behaviour / intelligence (scalable, but has limited modeling capabilities)

Group Work - Group 4

• Modeling Techniques
  • Use differential/difference equations to model Self Organizing Systems that correlate at some point e.g. for synchronization
    • Lyapunov-Exponent – evaluate how different start points change the systems evolution through a phase space
    • Sensitivity to the initial conditions of the differential equations
  • (Hidden) Markov models
• Properties
  • Emergent properties are often not easy to measure/understand
  • Sensitivity to the initial conditions of the differential equations might help with adaptivness
  • Adaptivness/goal-orientedness: in Markov models we can remove some nodes and re-evalute. Can give us an idea about effectiveness etc.
• Limitations/Potentials
  • “classical methods” are well researched and evaluated but not specifically tailored towards SOS
  • very hard to measure