Describe the model much more precisely.

[cshjin]

Literally, describe the project much more precisely. In which perspective? What are assumptions? What objectives? What constrains.

[cshjin]

Wait for feedback from others.

[cshjin]

An outline and some questions:

Applied mathematics & power / grid system

• mathematical modeling,
• numerical analysis of differential equations,
• optimization theory,
• mesh generation for complex geometries,
• adaptive algorithms,
• other important mathematical areas

Problems are to be met:

• Can we predict the operating characteristics of a clean coal power plant?
• How stable is the plasma containment in tokamak?
• How quickly is climate change occurring and what are the uncertainties in the predicted time scales?
• How quickly can an introduced bio-weapon contaminate the agricultural environment in the US?
• How do we modify models of the atmosphere and clouds to incorporate newly collected data of possibly of new types?
• How quickly can the United States recover if part of the power grid became inoperable?
• What are optimal locations and communication protocols for sensing devices in a remote-sensing network?
• How can new materials be designed with a specified desirable set of properties?
• How to understand complex systems?

Areas that are not adequately developed:

• development and analysis of methods to model large stochastic systems
• techniques for decomposing complex systems into systems of canonical subsystems
• sensitivity analysis, uncertainty quantification, risk analysis, optimization and inversion
• breaking problems down into simpler components cannot be the only mathematical approach
• development of modeling, simulation and analysis tools that deal with the full complex systems
• enhance the theory and tools for data-model fusion for complex systems

Three main themes:

Predictive modeling and simulation of complex systems

• Develop analytical and computational approaches needed to understand and model the behavior of complex multiphysics, and multiscale phenomena.
• Enhance the theory and tools for complex multiscale, multicomponent models when observational or experimental data are incorporated in an essential way.
• Develop new approaches for efficient modeling of large stochastic systems
• Develop mathematical techniques for decomposing complex systems into systems of canonical subsystems and modeling their behavior

Mathematical analysis of the behavior of complex systems

• Develop sound, computationally feasible strategies and methods for the collection, organization, statistical analysis and use of data associated with complex systems.
• Advance the theory and tools for sensitivity analysis to address the challenges posed by complex multiscale, multicomponent models
• Significantly advance the theory and tools for quantifying the effects of uncertainty and numerical simulation error on predictions using complex models and when fitting complex models to observations

Using models of complex systems to inform policy makers

• Significantly advance the mathematics that supports risk analysis techniques for policy-making involving complex systems that include natural and engineered components, and economic, security and policy consequences.
• Develop techniques for formulating, analyzing and solving challenging optimization problems arising in complex natural and engineered systems.
• Develop techniques for addressing the mathematical and computational difficulties of inverse problems associated with complex systems.

Criteria:

Reliability

Energy efficiency

Sustainability