sectors, mathematicians are too often treated as junior partners, “the technical
consultants” instead of the science drivers. This needs to change.
In the following discussion of mathematical areas of research we identified Three
Cross-Cutting Themes: a) Uncertainty, b) Multiscale and Mixed Methods, and c) Model
Evaluations.
Uncertainty
The stochasticity of energy supply and demand and the need to reduce environment
impact and increase energy independence demand the development of new
mathematical tools to
- deal with uncertainty;
- address how multiple time and spatial scales enter in this quantification;
- treat coarse-grained and fine-grained uncertainties;
- deal with heavy tailed distributions and the associated measures of risk;
- build models to describe rare but disruptive (natural) events;
- solve complex design and control problems in the area of stochastic optimization to
include:
o long term policy models;
o the power/smart grid (conservation, control, engineering);
o energy storage;
o market mechanisms and agent based models in the portfolio of tools used to
control green house gas emissions, discussed below.
Multiscale and Mixed Modeling
In this area new initiatives are needed to
- continue and enhance the development of theories of Partial Differential
Equations (PDEs) and Stochastic Partial Differential Equations (SPDEs) for
specific purposes such as microstructural optimization, sustainable technologies,
and the design of new materials for energy conversion (batteries, fuel cells, etc.); - develop mixed models for climate, ocean, macro/micro economics;
- design and study networks (edges + nodes; e.g. power grid, transportation, etc.)
at different scales; - create new statistical models to accommodate stochastic factors;
- design and manage sensor technologies to collect data more efficiently.
Model Evaluation
One of the major issues is the validation/invalidation of models, especially in the
absence of a ground truth.
Clearly, one needs new tools in PDEs/SPDEs to validate the simulated design of novel
energy high-impact materials and physical devices, complex models, climate, economy,
atmospheric, ocean. Can we use historical back testing for this purpose? Also, how
should we design and implement assessment/metrics?