Related papers: Constructing low-dimensional ordinary differential…

Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…

In this research work, let us focus on the construction of numerical scheme based on radial basis functions finite difference (RBF-FD) method combined with the Laplace transform for the solution of fractional order dispersive wave…

Physical laws governing population dynamics are generally expressed as differential equations. Research in recent decades has incorporated fractional-order (non-integer) derivatives into differential models of natural phenomena, such as…

We infer both microscopic and macroscopic behaviors of a three-dimensional chaotic fluid flow using reservoir computing. In our procedure of the inference, we assume no prior knowledge of a physical process of a fluid flow except that its…

We present a framework for constructing physics and causally constrained neural models of turbulent dynamical systems from data. We first formulate a finite-time flow map with strict energy-preserving nonlinearities for stable modeling of…

We present a nonparametric way to retrieve a system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long term predictions. We demonstrate the…

This paper proposes stochastic models for the analysis of ocean surface trajectories obtained from freely-drifting satellite-tracked instruments. The proposed time series models are used to summarise large multivariate datasets and infer…

In this paper, based on real-time nonlinear receding horizon control methodology, a novel approach is developed for parameter estimation of time invariant and time varying nonlinear dynamical systems in chaotic environments. Here, the…

A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…

Surrogate testing techniques have been used widely to investigate the presence of dynamical nonlinearities, an essential ingredient of deterministic chaotic processes. Traditional surrogate testing subscribes to statistical hypothesis…

Approximation of scattered geometric data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This method is useful for…

Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…

In this note we prove that a fractional stochastic delay differential equation which satisfies natural regularity conditions generates a continuous random dynamical system on a subspace of a H\"older space which is separable.

Two recent papers on prediction of chaotic systems, one on multi-view embedding1 , and the second on prediction in projection2 provide empirical evidence to support particular prediction methods for chaotic systems. Multi-view embedding1 is…

We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the…

Forecasting nonlinear time series with multi-scale temporal structures remains a central challenge in complex systems modeling. We present a novel reservoir computing framework that combines delay embedding with random Fourier feature (RFF)…

Functional data analysis offers a diverse toolkit of statistical methods tailored for analyzing samples of real-valued random functions. Recently, samples of time-varying random objects, such as time-varying networks, have been increasingly…

From the integer quantum Hall effect, to swimming at low Reynolds number, geometric phases arise in the description of many different physical systems. In many of these systems the temporal evolution prescribed by the geometric phase can be…

In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…

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…