2018/07/15 by Angxiu Ni, Ni, Angxiu · 1 citation
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Chaotic Dynamics (nlin.CD) #Computational Fluid Dynamics and Aerodynamics #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1807.05568
openalex publication_date 2018/07/15 · openalex created_date 2018/08/03 · openalex updated_date 2026/08/01
For hyperbolic diffeomorphisms, we define adjoint shadowing directions as a bounded inhomogeneous adjoint solution whose initial condition has zero component in the unstable adjoint direction. For hyperbolic flows, we define adjoint shadowing directions similarly, with the additional requirement that the average of its inner-product with the trajectory direction is zero. In both cases, we show unique existence of adjoint shadowing directions, and how they can be used for adjoint sensitivity analysis. Our work set a theoretical foundation for efficient adjoint sensitivity methods for long-time-averaged objectives such as NILSAS.