Related papers: Computational assessment of smooth and rough param…
SRB measures are limiting stationary distributions describing the statistical behavior of chaotic dynamical systems. Directional derivatives of SRB measure densities conditioned on unstable manifolds are critical in the sensitivity analysis…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence of chaos, the rigorous computation of these quantities is certainly possible, but…
We investigate the statistical properties of a piecewise smooth dynamical system by studying directly the action of the transfer operator on appropriate spaces of distributions. We accomplish such a program in the case of two-dimensional…
In this study, we introduce a sensitivity analysis methodology for stochastic systems in chemistry, where dynamics are often governed by random processes. Our approach is based on gradient estimation via finite differences, averaging…
Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or…
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…
Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…
Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from…
Accurate approximations of the change of system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing…
We study the robustness of system estimation to parametric perturbations in system dynamics and initial conditions. We define the problem of sensitivity-based parametric uncertainty quantification in dynamical system estimation. The main…
We analyze an approach aiming at determining statistical properties of spectra of time-periodic quantum chaotic system based on the parameter dynamics of their quasienergies. In particular we show that application of the methods of…
It is well known that chaotic dynamic systems (such as three-body system, turbulent flow and so on) have the sensitive dependance on initial conditions (SDIC). Unfortunately, numerical noises (such as truncation error and round-off error)…
We study the problem of parameter estimation for a univariate discretely observed ergodic diffusion process given as a solution to a stochastic differential equation. The estimation procedure we propose consists of two steps. In the first…
Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view. In this work, we present a numerical investigation of a novel approach, known as the space-split sensitivity or S3 algorithm. The S3…
Stable distributions are an important class of infinitely-divisible probability distributions, of which two special cases are the Cauchy distribution and the normal distribution. Aside from a few special cases, the density function for…
We present the numerical estimation of noise parameter induced in the dynamics of the variables by random particle interactions involved in the stochastic chemical oscillator and use it as order parameter to detect the transition from…
In this paper, we investigate the impact of numerical instability on the reliability of sampling, density evaluation, and evidence lower bound (ELBO) estimation in variational flows. We first empirically demonstrate that common flows can…
We discuss the possibility of applying some standard statistical methods (the least square method, the maximum likelihood method, the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional…
We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding…