Related papers: Nonlinear chaos in temperature time series: Part I…
Time series forecasting has become an increasingly popular research area due to its critical applications in various real-world domains such as traffic management, weather prediction, and financial analysis. Despite significant…
Low-frequency simulations of a one-layer model with lateral buoyancy variations (i.e., thermodynamically active) have revealed circulatory motions resembling quite closely submesoscale observations in the surface ocean rather than…
This paper provides a framework to strong time periodic solutions of quasilinear evolution equations. The novelty of this approach is that zero is allowed to be a spectral value of the underlying linearized operator. This approach is then…
This article is devoted to the mathematical study of a new Navier-Stokes-alpha model with a nonlinear filter equation. For a given indicator function, this filter equation was first considered by W. Layton, G. Rebholz, and C. Trenchea to…
Modern design, control, and optimization often requires simulation of highly nonlinear models, leading to prohibitive computational costs. These costs can be amortized by evaluating a cheap surrogate of the full model. Here we present a…
In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is a unnormalized probability density function of the filter…
In this contribution we discuss the occurrence of first-order transitions in temperature in various short-range lattice models with a rotation symmetry. Such transitions turn out to be widespread under the condition that the interaction…
A semi-explicit formula of solution to the boundary layer system for thermal layer derived from the compressible Navier-Stokes equations with the non-slip boundary condition when the viscosity coefficients vanish is given, in particular in…
We consider the Stokes-Boussinesq (and the stationary Navier-Stokes-Boussinesq) equations in a slanted, i.e. not aligned with the gravity's direction, 3d channel and with an arbitrary Rayleigh number. For the front-like initial data and…
Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial datasets. However, the large number of observations in modern datasets makes fitting such models computationally intractable with…
The ability to forecast far into the future is highly beneficial to many applications, including but not limited to climatology, energy consumption, and logistics. However, due to noise or measurement error, it is questionable how far into…
This paper is concerned with the large-time behavior of solutions to the initial and initial boundary value problems with large initial data for the compressible Navier-Stokes system describing the one-dimensional motion of a viscous…
Considering one-dimensional nonminimally-coupled lattice gauge theories, a class of nonlocal one-dimensional systems is presented, which exhibits a phase transition. It is shown that the transition has a latent heat, and, therefore, is a…
We consider the limitations of two techniques for detecting nonlinearity in time series. The first technique compares the original time series to an ensemble of surrogate time series that are constructed to mimic the linear properties of…
The applicability of machine learning for predicting chaotic dynamics relies heavily upon the data used in the training stage. Chaotic time series obtained by numerically solving ordinary differential equations embed a complicated noise of…
We introduce a class of semiparametric time series models by assuming a quasi-likelihood approach driven by a latent factor process. More specifically, given the latent process, we only specify the conditional mean and variance of the time…
Post-processing typically takes the outputs of a Numerical Weather Prediction (NWP) model and applies linear statistical techniques to produce improve localized forecasts, by including additional observations, or determining systematic…
The modelling of small-scale processes is a major source of error in climate models, hindering the accuracy of low-cost models which must approximate such processes through parameterization. Red noise is essential to many operational…
In the context of filtering chaotic dynamical systems it is well-known that partial observations, if sufficiently informative, can be used to control the inherent uncertainty due to chaos. The purpose of this paper is to investigate, both…
This paper proposes strategies to detect time reversibility in stationary stochastic processes by using the properties of mixed causal and noncausal models. It shows that they can also be used for non-stationary processes when the trend…