REPLY Who wants to share models (SD6876)

[SDMAIL j-d]

Posted by  j-d <jaideep at optimlator.com>

In reply to Martin's description of modeling of the Chilean economy, I
had done similar work using the Limits to Growth (LTG) model. As I
understand it, LTG was done collaboratively by different authors
working on population (Dana Meadows), agriculture, resources, capital,
and pollution. So there were 5 submodels so to speak. I had extended
the model to North (US, Canada, Europe) and South (China, India,
Brazil etc.) regions of countries to understand the dynamics of their
inter-relations over time as resources get tighter and regions compete
or cooperate in different ways (trying to model what Lester Brown and
the WorldWatch Institute people had been saying for years and which
seems to be coming to passnow , with the rising oil prices and so on).
All of this was in the context of dynamic games (which involve
multi-player optimization and are not just simulations).

My impressions are as follows: understanding even a simple nonlinear
model through simulations is difficult indeed (for example,
population, capital models are pretty complicated - resources model
was almost trivial and made LTG model kind of unbalanced, in my view -
but that is okay - it is still a great piece f modeling work).
Splitting the model into sub-models and really going through the
simulations described in the book Dynamics of Growth (DOG) in a Finite
World built my understanding of the various sub-models (did I say I
was working solo on this) - the submodels had exogenous inputs
(constants or functions) as their "links" to other submodels, so one
could basically plug-and-pray the sub-models in stead of the exogenous
inputs. For example, population as an exogenous logistic function may
be replaced by the output from a population model, all with cohorts
and internal dynamics as described in DOG. So you could link
population and agriculture models this way, and build your
understanding of linked pop-ag model using simulations. You could
affect population internal dynamics by agricultural parts linking back
to population model, which is when things become a little hairy. They
become really complicated when 10 sub-models are connected - a clear
understanding of internals of each sub-model plus the effect of
different links between submodels is needed. In a real-world
situation, generally you have domain experts for each submodel and I
agree that a complete understanding of everything by everyone is
difficult if not impossible.

To optimize policies, using optimal control or dynamic game theory,
was very hard for the full linked models (CPU requirements plus the
sheer complexity and opaqueness of the model), so I simplified from 10
to I think 2 or 4 submodels for this kind of analyses. Bottomline
learning for me from this whole exercise was that in complex,
nonlinear systems, even discounting the possibilities of chaotic
systems, optimization and simulation have limitations, and a mental
exercise using many simulations, while trying to optimize one or more
policies, can cause deeper intuition and more effective policies. It
is similar to katas or patterns in martial arts practice, where katas
function as libraries of accumulated wisdom, and they are practiced by
all students (and even masters), similar to simulation exercises we
give our students, and then optimization happens when we tweak the
katas or models to suit our real-world problems. I had called this
practice "optimlation" at that time :-)

I hope all of the above makes sense -

Best regards

Jaideep Mukherjee, Ph. D.
Posted by  j-d <jaideep at optimlator.com>
posting date  Mon, 7 Apr 2008 17:23:20 -0500