Related papers: A Novel Approach for Estimating Largest Lyapunov E…

We consider the problem of estimating the number of distinct elements in a large data set (or, equivalently, the support size of the distribution induced by the data set) from a random sample of its elements. The problem occurs in many…

Training large deep neural networks is resource intensive. This study investigates whether Lyapunov exponents can accelerate this process by aiding in the selection of hyperparameters. To study this I formulate an optimization problem using…

Violent relaxation (VR) is often regarded as the mechanism leading stellar systems to collisionless meta equilibrium via rapid changes in the collective potential. We investigate the role of chaotic instabilities on single particle orbits…

Recently there has been a great deal of interest surrounding the calibration of quantum sensors using machine learning techniques. In this work, we explore the use of regression to infer a machine-learned point estimate of an unknown…

We consider parameter estimation in finite hidden state space Markov models with time-dependent inhomogeneous noise, where the inhomogeneity vanishes sufficiently fast. Based on the concept of asymptotic mean stationary processes we prove…

This paper focuses on relaxing the excitation conditions for the adaptive control of uncertain nonlinear systems. By adopting the spectral decomposition technique, a linear regression equation (LRE) is constructed to quantitatively collect…

Discovering governing equations that describe complex chaotic systems remains a fundamental challenge in physics and neuroscience. Here, we introduce the PEM-UDE method, which combines the prediction-error method with universal differential…

Various phonemes are considered in terms of nonlinear dynamics. Phase portraits of the signals in the embedded space, correlation dimension estimate and the largest Lyapunov exponent are analyzed. It is shown that the speech signals have…

In this paper, we propose a novel Gaussian process-based moving horizon estimation (MHE) framework for unknown nonlinear systems. On the one hand, we approximate the system dynamics by the posterior means of the learned Gaussian processes…

Data-driven weather forecast based on machine learning (ML) has experienced rapid development and demonstrated superior performance in the global medium-range forecast compared to traditional physics-based dynamical models. However, most of…

For a non-generic, yet dense subset of $C^1$ expanding Markov maps of the interval we prove the existence of uncountably many Lyapunov optimizing measures which are ergodic, fully supported and have positive entropy. These measures are…

This paper presents a distributed Lyapunov-based control framework for achieving both complete and phase synchronization in a class of leader-follower multi-agent systems composed of identical chaotic agents. The proposed approach…

The forthcoming Hyper-Kamiokande experiment requires substantially larger Monte Carlo datasets than previous experiments to satisfy stringent systematic-uncertainty requirements. While traditional maximum-likelihood reconstruction provides…

In this paper, we introduce the first machine learning framework for predicting optimal processing times in Single-Level Tree Network (SLTN) architectures for the Divisible Load Theory (DLT) paradigm. Using a feedforward neural network(FNN)…

This work is to investigate the (top) Lyapunov exponent for a class of Hamiltonian systems under small non-Gaussian L\'evy noise. In a suitable moving frame, the linearisation of such a system can be regarded as a small perturbation of a…

Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…

Conditions for the emergence of a statistical relationship between $T_r$, the chaotic transport (recurrence) time, and $T_L$, the local Lyapunov time (the inverse of the numerically measured largest Lyapunov characteristic exponent), are…

We introduce a data-driven learning framework that assimilates two powerful ideas: ideal large eddy simulation (LES) from turbulence closure modeling and neural stochastic differential equations (SDE) for stochastic modeling. The ideal LES…

Deep neural networks (DNNs) often produce overconfident out-of-distribution predictions, motivating Bayesian uncertainty quantification. The Linearized Laplace Approximation (LLA) achieves this by linearizing the DNN and applying Laplace…

Inspired by chaotic firing of neurons in the brain, we propose ChaosNet -- a novel chaos based artificial neural network architecture for classification tasks. ChaosNet is built using layers of neurons, each of which is a 1D chaotic map…