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The emergence of the computational Grid and the potential for seamless aggregation, integration and interactions has made it possible to conceive a new generation of realistic, scientific and engineering simulations of complex physical phenomena. The inherently heterogeneous and dynamic nature of these application and the Grid presents significant runtime management challenges. In this paper we extend the PRAGMA framework to enable self adapting, self optimizing runtime management of dynamically adaptive applications. Specifically, we present the design, prototype implementation and initial evaluation of policies and mechanisms that enable PRAGMA to autonomically manage, adapt and optimize structured adaptive mesh refinement applications (SAMR) based on current system and application state and predictive models for system behavior and application performance. We use the 3-D adaptive Richtmyer-Meshkov compressible fluid dynamics application and Beowulf clusters at Rutgers University, University of Arizona, and NERSC to develop our performance models, and define and evaluate our adaptation policies. In our prototype, the predictive performance models capture computational and communicational loads and, along with current system state, adjust processors capacities at runtime to enable the application to adapt and optimize its performance.