相关论文: A Novel Approach for Estimating Largest Lyapunov E…

We study the effect of regime switches on finite size Lyapunov exponents (FSLEs) in determining the error growth rates and predictability of multiscale systems. We consider a dynamical system involving slow and fast regimes and switches…

In the context of the analysis of the chaotic properties of homogeneous and isotropic turbulence, direct numerical simulations are used to study the fluctuations of the finite time Lyapunov exponent (FTLE) and its relation to Reynolds…

Covariant Lyapunov vectors characterize the directions along which perturbations in dynamical systems grow. They have also been studied as predictors of critical transitions and extreme events. For many applications like, for example,…

Lyapunov exponents (LEs) are key indicators of chaos in dynamical systems. In general relativity the classical definition of LE meets difficulty because it is not coordinate invariant and spacetime coordinates lose their physical meaning as…

The largest Lyapunov exponent is widely used to diagnose chaos in gravitational dynamics, but in mixed phase spaces and finite-N systems it does not always provide a complete description of orbital complexity and phase-space transport.…

Designing stabilizing controllers is a fundamental challenge in autonomous systems, particularly for high-dimensional, nonlinear systems that can hardly be accurately modeled with differential equations. The Lyapunov theory offers a…

Finite-time Lyapunov exponents of generic chaotic dynamical systems fluctuate in time. These fluctuations are due to the different degree of stability across the accessible phase-space. A recent numerical study of spatially-extended systems…

Predictive multiplicity and chaotic dynamics represent two fundamental challenges in machine learning that have evolved independently despite their conceptual connections. We bridge this gap by introducing horizon-constrained Rashomon sets,…

The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to…

By tracking the divergence of two initially close trajectories in phase space in an Eulerian approach to forced turbulence, the relation between the maximal Lyapunov exponent $\lambda$, and the Reynolds number $Re$ is measured using direct…

We propose an interpretable AI-assisted reliability diagnostic framework for parameterized root-finding schemes based on kNN-LLE proxy stability profiling and multi-horizon early prediction. The approach augments a numerical solver with a…

A major line of contemporary research on complex networks is based on the development of statistical models that specify the local motifs associated with macro-structural properties observed in actual networks. This statistical approach…

We study weighted Tikhonov regularization for large-scale linear discrete ill-posed problems with random noise. Under a polynomial upper-bound assumption on the generalized eigenvalues of the discrete forward operator, we derive stochastic…

We study the dynamics of systems with different time scales, when access only to the slow variables is allowed. We use the concept of Finite Size Lyapunov Exponent (FSLE) and consider both the case when the equations of motion for the slow…

The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…

A variety of pruning methods have been introduced for over-parameterized Recurrent Neural Networks to improve efficiency in terms of power consumption and storage utilization. These advances motivate a new paradigm, termed `hyperpruning',…

The maximum Lyapunov exponent (referred to the mean half-period of phase libration) of the motion in the chaotic layer of a nonlinear resonance subject to symmetric periodic perturbation, in the limit of infinitely high frequency of the…

Every student in statistics or data science learns early on that when the sample size largely exceeds the number of variables, fitting a logistic model produces estimates that are approximately unbiased. Every student also learns that there…

We study a network whose rich spatiotemporal dynamics have recently been shown to enable dynamics-based computation, including logic gates, short-term memory, and simple encryption. The network's time dynamics can be exactly solved through…

Delay differential equations (DDEs) are infinite-dimensional systems, so even a scalar, unforced nonlinear DDE can exhibit chaos. Lyapunov exponents are indicators of chaos and can be computed by comparing the evolution of infinitesimally…