Related papers: Multiple Shooting Shadowing for Sensitivity Analys…
The following paper discusses the application of a multigrid-in-time scheme to Least Squares Shadowing (LSS), a novel sensitivity analysis method for chaotic dynamical systems. While traditional sensitivity analysis methods break down for…
This paper develops the non-intrusive formulation of the Least-squares shadowing (LSS) method, for computing the sensitivity of long-time averaged objectives in chaotic dynamical systems. This non-intrusive formulation constrains the…
Computational methods for sensitivity analysis are invaluable tools for aerodynamics research and engineering design. However, traditional sensitivity analysis methods break down when applied to long-time averaged quantities in turbulent…
The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged…
Adjoint-based sensitivity analysis methods are powerful tools for engineers who use flow simulations for design. However, the conventional adjoint method breaks down for scale-resolving simulations like large-eddy simulation (LES) or direct…
The sensitivity of long-time averages of a hyperbolic chaotic system to parameter perturbations can be determined using the shadowing direction, the uniformly-bounded-in-time solution of the sensitivity equations. Although its existence is…
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…
This paper develops a variant of the Least Squares Shadowing (LSS) method, which has successfully computed the derivative for several chaotic ODEs and PDEs. The development in this paper aims to simplify Least Squares Shadowing method by…
Chaotic dynamical systems such as turbulent flows are characterized by an exponential divergence of infinitesimal perturbations to initial conditions. Therefore, conventional adjoint/tangent sensitivity analysis methods that are successful…
We present the Finite Difference Non-Intrusive Least Squares Shadowing (FD-NILSS) algorithm for computing sensitivities of long-time averaged quantities in chaotic dynamical systems. FD-NILSS does not require tangent solvers, and can be…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…
Chaotic dynamical systems are characterized by the sensitive dependence of trajectories on initial conditions. Conventional sensitivity analysis of time-averaged functionals yields unbounded sensitivities when the simulation is chaotic. The…
It is well-known that linearized perturbation methods for sensitivity analysis, such as tangent or adjoint equation-based, finite difference and automatic differentiation are not suitable for turbulent flows. The reason is that turbulent…
Modeling dynamical systems plays a crucial role in capturing and understanding complex physical phenomena. When physical models are not sufficiently accurate or hardly describable by analytical formulas, one can use generic function…
In this computational paper, we perform sensitivity analysis of long-time (or ensemble) averages in the chaotic regime using the shadowing algorithm. We introduce automatic differentiation to eliminate the tangent/adjoint equation solvers…
We develop the NILSAS algorithm, which performs adjoint sensitivity analysis of chaotic systems via computing the adjoint shadowing direction. NILSAS constrains its minimization to the adjoint unstable subspace, and can be implemented with…
Deducing the states of spatiotemporally chaotic systems (SCSs) as they evolve in time is crucial for various applications. However, it is a dramatic challenge for generally achieving so due to the complexity of non-periodic dynamics and the…
This paper uses compressible flow simulation to analyze the hyperbolicity, shadowing directions, and sensitivities of a weakly turbulent three dimensional cylinder flow at Reynolds number 525 and Mach number 0.1. By computing the first 40…
A common goal in the study of high dimensional and complex system is to model the system by a low order representation. In this letter we propose a general approach for assessing the quality of a reduced order model for high dimensional…
Underground energy storage, which includes storage of hydrogen, compressed air, and CO2, requires careful monitoring to track potential leakage pathways, a situation where time-lapse seismic imaging alone may be inadequate. A recently…