Gradient-based optimization of chaotic acoustics is challenging for a threefold reason:(i) first-
order perturbations grow exponentially in time;(ii) the statistics of the solution may have a …

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 …

Unstable periodic orbits (UPOs) are a valuable tool for studying chaotic dynamical systems,
as they allow one to distill their dynamical structure. We consider here the Lorenz 1963 …

The sensitivity of time averages in a chaotic system to an infinitesimal parameter
perturbation grows exponentially with the averaging time. However, long-term averages or …

We present a frequency-domain method for computing the sensitivities of time-averaged
quantities of chaotic systems with respect to input parameters. Such sensitivities cannot be …

Long-time averages of outputs from chaotic dynamical systems exhibit high-frequency
oscillations in parameter space, which makes gradient-based optimization impractical. We …

We present a computable reformulation of Ruelle's linear response formula for chaotic
systems. The new formula, called Space-Split Sensitivity or S3, achieves an error …

An assumption of smooth response to small parameter changes, of statistics or long-time
averages of a chaotic system, is generally made in the field of sensitivity analysis, and the …

Dynamical systems often exhibit limit cycle oscillations (LCOs), self-sustaining oscillations of
limited amplitude. LCOs can be supercritical or subcritical. The supercritical response is …

We propose a preconditioner that can accelerate the rate of convergence of the Multiple
Shooting Shadowing (MSS) method [1]. This recently proposed method can be used to …