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# Mathematics and Statistics Colloquium

Date/Time/Room: Monday (10/25/2004) at 3:00pm in 304 Pickard Hall

Speaker: Craig C. Douglas
University of Kentucky
Professor, Departments of Computer Science and Mechanical Engineering
Associate Director, Center for Computational Sciences
and
Yale University
Senior Research Scientist, Department of Computer Science

### "Dynamic Data-Driven Application Simulations (DDDAS)"

Abstract: DDDAS is a new paradigm in which data dynamically controls almost all aspects of long term simulations. Rather than run many simulations using static data as initial conditions, a very small number of simulations are run with additional data injected as it becomes available. Most candidate problems for the DDDAS paradigm involve solving a nonlinear time dependent partial differential equation of the form F(x+∆x(t)) = 0 by iteratively choosing a new approximate solution x based on the time dependent perturbation ∆x(t).

In practice, the data streaming in may have errors and therefore may not be completely accurate or reliable (for example, in reservoir data sets, a 15% error in the data is common). As a result, perhaps one does not need to solve the nonlinear equation precisely at each step. This can expedite the execution

At each iterative step, the following three issues may need to be addressed:
• Incomplete solves of a sequence of related models must be understood.
• The effects of perturbations, either in the data and/or the model, need to be resolved and kept within acceptable limits.
• Nontraditional convergence issues have to be understood and resolved. Consequently, there will be a high premium on developing quick approximate direction choices, such as, lower rank updates and continuation methods, and understanding their behavior are important issues. Fault tolerant algorithms have a premium.
The dynamic data is used to determine
• Whether or not a warm restart is necessary due to unacceptable errors building up in parts of the domain.
• If a rollback in time is required.
• If the simulation is running with acceptable errors. Ideally, there does not have to be a human in the control loop throughout a simulation.
Using the data appropriately lets the physical and mathematical models, the discretization, and the scales of interesting parts of the computations become parameters that can be changed during the course of the simulation. In addition, error propagation is of particular interest in nonlinear time dependent simulations.

DDDAS offers interesting computational and mathematically unsolved problems, such as, how do you analyze the properties of a generalized PDE when you do not know either where or what the local boundary conditions are at any given moment in the simulation in advance?

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