1. GoldSim 2007 User Conference Slide 1 San Francisco GoldSim User Conference San Francisco, CA October 25-26, 2007 Abstracting Complex Models Into Simpler Ones Presented by Ian Miller

2. GoldSim 2007 User Conference Slide 2 San Francisco 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. GoldSim 2007 User Conference Slide 3 San Francisco Darcy’s 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. GoldSim 2007 User Conference Slide 4 San Francisco What makes a model complex? Depth Breadth Nonlinearity Coupling

5. GoldSim 2007 User Conference Slide 5 San Francisco What makes a model complex? Depth –It’s hierarchical, but there are too many levels. Breadth –It isn’t 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. GoldSim 2007 User Conference Slide 6 San Francisco How simplified should it be? 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! “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

7. GoldSim 2007 User Conference Slide 7 San Francisco 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 model’s 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. GoldSim 2007 User Conference Slide 8 San Francisco How can you simplify a model’s Overall complexity? –Choose simpler representations of functional relationships. E.g. the law of gravity, Darcy’s 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. GoldSim 2007 User Conference Slide 9 San Francisco Identify State Variables and Functions Dynamic components (state variables) –Reduce the number of variables. Function components –Use approximations (see next slide).

10. GoldSim 2007 User Conference Slide 10 San Francisco 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. GoldSim 2007 User Conference Slide 11 San Francisco The rest of this morning will continue this theme of model simplification. …