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We describe, devise, and augment dynamic data-driven application simulations (DDDAS). DDDAS offers interesting computational and mathematically unsolved problems. In this paper, we discuss how to update the solution as well as input parameters involved in the simulation based on local measurements. The updates are performed in time. We test our method on various synthetic examples.

Multiscale Interpolation, Backward in Time Error Analysis for Data-Driven Contaminant Simulation