change of pH in the oceans requires sophisticated new ocean surveillance systems and
concomitant methods of machine learning and data analysis. We need to understand
what physical, chemical, and biological oceanographic data are most relevant to getting
early warning of anomalies in pH levels in oceans and what statistical/machine learning
methods will help us attain such early warning. Finally, models of temporal change of pH
in oceans carry great uncertainty. How do we lessen such uncertainty?
Research Challenge for the Mathematical Sciences: Develop mathematical
models of changes in quality of fresh water resulting from agriculture and the challenges
for agriculture resulting from changes in quality and quantity of available fresh water; find
models that will enable us to understand the interconnection between human systems
and the acidification of the oceans; find ways to utilize sophisticated methods of
statistical science, machine learning, and the use of remote sensing to get early warning
of changes in quality and health of our bodies of water.
Example 7: Energy as a Contributor to Human Well-being: Electric Power Grids
Our models of the interplay among natural and human systems will require us to
identify factors that underlie “human well-being.” One of these is the availability of a
sufficiently reliable, sufficiently “inexpensive” source of power for the machines that
make our lives easier and allow us to sustain the complex societies that have come to
depend upon power supplies. The design of “sustainable” energy systems is the focus of
study of another working group. However, here we mention mathematical challenges
underlying energy systems that reflect some of the mathematical themes our group has
identified.
Today’s decision makers in fields ranging from engineering to medicine to security
have available to them remarkable new technologies, huge amounts of information, and
the ability to share information at unprecedented speeds and quantities. These tools and
resources will enable better decisions if we can surmount concomitant challenges: The
massive amounts of data available are often incomplete or unreliable or distributed and
there is great uncertainty in them; interoperating/distributed decision makers and
decision-making devices need to be coordinated; many sources of data need to be fused
to formulate a good decision, often in a remarkably short time; decisions must be made
in dynamic environments based on partial information; there is heightened risk due to
extreme consequences of poor decisions; decision makers must understand complex,
multi-disciplinary problems. In the face of these new opportunities and challenges, the
new field of “algorithmic decision theory” (Rossi and Tsoukias 2009, Roberts 2008) aims
to exploit algorithmic methods to improve the performance of decision makers (human or
automated). There is a long tradition of algorithmic methods in logistics and planning
dating at least to World War II, leading to the field of operations research. However,
algorithms to speed up and improve real-time decision making are much less common.
Advances in algorithmic decision theory are particularly needed to deal with
problems of the electric power grid.^3 Today’s electric power systems have grown up
incrementally and haphazardly – they were not designed from scratch; they form
complex systems that are in constant change (loads change, breakers go out; there are
unexpected disturbances; they are at the mercy of uncontrollable influences such as
(^3) Much of the discussion in the rest of Example 7 is based on a presentation by Gilbert Bindewald of the
U.S. Department of Energy to the SIAM Science Policy Committee on October 28, 2009.