Related papers: Adjoint chaos via cumulant truncation

The tight-coupling approximation (TCA) used to describe the early dynamics of the baryons-photons system is systematically built to higher orders in the inverse of the interaction rate. This expansion can be either used to grasp the…

We propose a simple method to estimate the parameters involved in discrete dynamical systems from time series. The method is based on the concept of controlling chaos by constant feedback. The major advantages of the method are that it…

The accuracy of simulation-based forecasting in chaotic systems is heavily dependent on high-quality estimates of the system state at the time the forecast is initialized. Data assimilation methods are used to infer these initial conditions…

We present a method to describe driven-dissipative multi-mode systems by considering a truncated hierarchy of equations for the correlation functions. We consider two hierarchy truncation schemes with a global cutoff on the correlation…

Whereas the importance of transient dynamics to the functionality and management of complex systems has been increasingly recognized, most of the studies are based on models. Yet in realistic situations the models are often unknown and what…

Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal…

Lagrangian stochastic models are widely used to predict and analyze turbulent dispersion in complex environments, such as in various terrestrial and marine canopy flows. However, due to a lack of empirical data, it is still not understood…

Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based…

A new efficient ensemble prediction strategy is developed for a general turbulent model framework with emphasis on the nonlinear interactions between large and small scale variables. The high computational cost in running large ensemble…

We introduce a simple, stochastic, a-posteriori, turbulence closure model based on a reduced subgrid scale term. This subgrid scale term is tailor-made to capture the statistics of a small set of spatially-integrate quantities of interest…

Mechanical systems exhibit complex dynamical behavior from harmonic oscillations to chaotic motion. The dynamics undergo qualitative changes due to changes to internal system parameters like stiffness and changes to external forcing.…

Many geophysical and astrophysical phenomena are driven by turbulent fluid dynamics, containing behaviors separated by tens of orders of magnitude in scale. While direct simulations have made large strides toward understanding geophysical…

This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…

Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to…

Verification, validation and uncertainty quantification (VVUQ) have become a common practice in thermal-hydraulics analysis. An important step in the uncertainty analysis is the sensitivity analysis of various uncertain input parameters.…

We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite- time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered…

The influence-matrix formalism provides an alternative route to the classical simulation of quantum dynamics. Because influence matrices retain information only about the effective bath seen by local observables, they are expected to be…

An exact solution of the transient dynamics for a sequential associative memory model is discussed through both the path-integral method and the statistical neurodynamics. Although the path-integral method has the ability to give an exact…

Due to the deterministic nature of chaotic systems, fluctuations in their trajectories arise solely from the choice of initial conditions. Some of these dynamical fluctuations may lead to extremely unlikely scenarios. Understanding the…

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…