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Alternative Approaches for Integration of Models
Elena Rovenskaya IIASA Advanced Systems Analysis Program


Sometimes multi-model approach is
necessary...



Paradigm shifts by Kuhn: successive change of one model by another, rather than integration of different paradigms


Progress of science: from single- to multi-model approach
Some examples from natural science...
· theory of light: from vibration of ether to wave-particle duality · laws of motion: from
Newton's
dynamics
to
SchrЖdinger 's
and
Heisenberg's
formalism
In social and environmental sciences appreciation of the multi-model approach is to be obtained


Example: multi-model approach for sustainable forest management

Orange area is the Pareto area for the PPA model, blue area is the Pareto area for the model with no feedback (IIASA project on optimization of forest management)

The relationship between economic benefit and ecological value is rather different in two models


Evolution of modeling paradigm
single-model approach multi-model approach

Belief in one model

Comparison of models

Integration of models


Models integration: formalization
Model 1 Input Model 2 Output 2 Output 1 Synthetic signal based on output 1 and output 2

· Output 1 and output 2 represent the model results for the

same real quantity · Output 1 does not coincide with output 2 · Output 1 and output 2 can be either deterministic or

stochastic, either scalar or vector, either finite or infinite
dimensional variable


Basing on the past approach
· Approximate the past history by
two
models'
outcomes
and extrapolate the obtained approximation into the future

, Arg min x C1 x1 C2 x2
* 1 * 2 C1 ,C
2

x C x C x
* 11

* 22


Example
· Nordhaus's DICE-model (nonlinear!) as a generator of "real"
data
with
the
terminal
GDP
as
a
model's
output
· Two one-dimensional linear models of the global GDP

The blue, red and green bars represent relative errors in terminal GDP for 50 testing controls in case the learning database consists of 10, 50 and 100 controls correspondingly (IIASA project on integration of models)


Distribution-based approach
· Compare
the
distributions
of
models'
outputs
with
the
joint
distribution => in case the joint distribution has lower variance, use its expectation

Lower variance => compatible models

Higher variance => incompatible models


Example
· Integration of the Landscape Ecosystems Approach (LEA) and Stochastic Modeling Approach (SMA) of net primary production of the Russian forest-tundra

The blue and red curves show the NPP distributions (in grams of carbon per square meter per year) given by LEA and SMA, respectively. The green curve shows the integrated distribution formed using the posterior integration analysis technique (IIASA YSSP project on integration of models)


"Calculus
of
models"
· Objects: models · Actions: linking
(IAM),
integration,
approximation,...


THANK YOU FOR YOUR ATTENTION! I welcome your comments, suggestions,
ideas...
rovenska@iiasa.ac.at