GoldSim 2006 User Conference

1

Abstracting Complex Models Into Simpler
Ones Presented by Ian Miller
GoldSim User Conference San Francisco, CA October
25-26, 2007
2
Woonawowo Island- the Model

• The model we played with yesterday was greatly
  simplified. How did it get that way?
• Was the simplified model adequate?

3
Darcys Law for Groundwater Flow

• Q k i A
• Q flow in pathway
• k hydraulic conductivity
• i gradient of hydraulic head
• A pathway cross sectional area
• This is an extremely simplified model.
• Which is extremely useful.
• In what ways is it an abstraction or
  simplification?

4
What makes a model complex?

• Depth
• Breadth
• Nonlinearity
• Coupling

5
What makes a model complex?

• Depth
• Its hierarchical, but there are too many levels.
• Breadth
• It isnt hierarchical.
• (Or, it is largely hierarchical, but
  unfortunately there are some links between low
  level components).
• Nonlinearity
• It has complex functional relationships.
• Coupling
• f(A, B, C, ). Needs an iterative solution.

6
How simplified should it be?
Any fool can make things bigger, more complex,
and more violent. It takes a touch of genius --
and a lot of courage -- to move in the opposite
direction. - Albert Einstein

• What is the goal of the model?
• To support a decision?
• To gain insight?
• To demonstrate understanding of the system (e.g.
  to a regulator)
• Make sure that the model is not too simplified to
  meet the goals!
• But sometimes, being too complex may also result
  in missing the goals!

7
Approximation

• All models are approximations of reality.
• Generally, a more simplified model will be a
  poorer approximation.
• How can you defend your degree of simplification?
• Compare your models results to reality.
• Compare to a more complex model.
• Estimate bounds to the degree of approximation,
  and add these as random variables in your Monte
  Carlo model.

8
How can you simplify a models

• Overall complexity?
• Choose simpler representations of functional
  relationships. E.g. the law of gravity, Darcys
  Law.
• Ignore or simplify components that have a minor
  effect on model results.
• Depth?
• Progressively more simplified at greater depth.
• Breadth?
• Remove unimportant subsystems.
• Nonlinearity?
• Use linear approximations.
• Coupling?
• Use previous time step values.

9
Identify State Variables and Functions

• Dynamic components (state variables)
• Reduce the number of variables.
• Function components
• Use approximations (see next slide).

10
Simplification of functions

• Run a separate analysis first, then
• Fit polynomials
• Capture as Lookup Tables
• Known as response surfaces.
• Can be 1, 2, or 3-dimensional.

11
The rest of this morning will continue this theme
of model simplification.