describing the same system have been built, an average of the output of the
different models can be better than any single prediction. It’s therefore
immensely valuable to have an ensemble of models, each designed somewhat
differently. But what’s the best way to put their predictions together into a single
best estimate? The most straightforward is to just average them, but sometimes,
one model is known to be better than another much of the time. In that case, it
may be that weighting the output of the models according to quality would
produce a better prediction. But mathematical scientists don’t yet know the best
ways to combine the forecasts of different models, so a huge amount of work
remains to be done in this area.
The importance of ensembles also points to the need for the sameproblem to be modeled in different ways. Mathematicians are working to build
and understand entire new classes of models for this purpose. Infectious
disease, for example, can be studied using network models, in which each
individual is modeled as a node in a network and the people they have contact
with (and might spread disease to) are connected to them by an edge. Network
models have the potential to be very powerful, but their application to the
understanding of complex adaptive systems is sufficiently new that their
theoretical underpinning requires further development. Studying complex
systems from multiple perspectives, using different modeling paradigms, helps
deal with their inherent difficulty.
The economy points to another kind of model that needs to be built.Economic concerns are essential to almost all sustainability issues, but our
current ability to forecast the economy is very limited. Current economic models
entirely ignore its complex adaptive nature; instead they imagine the economy as
a fundamentally unchanging structure that stays in equilibrium. The complete
failure of such models to predict the 2008 economic collapse points out their
deep limitations. A bubble is essentially a positive feedback loop that is carried to
its limits, and these static models are by their fundamental design incapable of
predicting them. So, new models of the economy, using the principles of complex
adaptive systems, need to be built. Then these models need to be linked to
models of the environment.