Least squares shadowing sensitivity analysis of a modified Kuramoto-Sivashinsky equation

Computational methods for sensitivity analysis are invaluable tools for scientists and engineers investigating a wide range of physical phenomena. However, many of these methods fail when applied to chaotic systems, such as the Kuramoto–Sivashinsky (K–S) equation, which models a number of different chaotic systems found in nature. The following paper discusses the application of a new sensitivity analysis method developed by the authors to a modified K–S equation. We find that least squares shadowing sensitivity analysis computes accurate gradients for solutions corresponding to a wide range of system parameters.
United States. Air Force Office of Scientific Research (AFSOR Award F11B-T06-0007)
United States. National Aeronautics and Space Administration (NASA Award NNH11ZEA001N)
United States. Department of Defense (NDSEG fellowship)