Related papers: Nonlinear chaos in temperature time series: Part I…
In this paper a new concept, namely the critical predictable time $T_c$, is introduced to give a more precise description of computed chaotic solutions of nonlinear differential equations: it is suggested that computed chaotic solutions are…
The 3DVAR filter is prototypical of methods used to combine observed data with a dynamical system, online, in order to improve estimation of the state of the system. Such methods are used for high dimensional data assimilation problems,…
A new comprehensive approach to nonlinear time series analysis and modeling is developed in the present paper. We introduce novel data-specific mid-distribution based Legendre Polynomial (LP) like nonlinear transformations of the original…
Long-term time series forecasting (LTSF) is a challenging task that has been investigated in various domains such as finance investment, health care, traffic, and weather forecasting. In recent years, Linear-based LTSF models showed better…
We study a unitary time evolution of a symmetry-broken state in a form of a charge density wave in a finite system of interacting hard-core bosons, which can be mapped onto the XXZ Heisenberg chain. Moreover, we introduce a…
We consider a three-dimensional domain occupied by a homogeneous, incompressible, non-Newtonian, heat-conducting fluid with prescribed nonuniform temperature on the boundary and no-slip boundary conditions for the velocity. No external body…
We produce new reconstructions of Northern Hemisphere annually averaged temperature anomalies back to 1000 AD, and explore the effects of including external climate forcings within the reconstruction and of accounting for short-memory and…
To predict the future evolution of dynamical systems purely from observations of the past data is of great potential application. In this work, a new formulated paradigm of reservoir computing is proposed for achieving model-free…
We present Higher-Order Tensor RNN (HOT-RNN), a novel family of neural sequence architectures for multivariate forecasting in environments with nonlinear dynamics. Long-term forecasting in such systems is highly challenging, since there…
This paper presents $\mathbf{OLinear}$, a $\mathbf{linear}$-based multivariate time series forecasting model that operates in an $\mathbf{o}$rthogonally transformed domain. Recent forecasting models typically adopt the temporal forecast…
Modern computer microprocessors are composed of hundreds of millions of transistors that interact through intricate protocols. Their performance during program execution may be highly variable and present aperiodic oscillations. In this…
For nonlinear discrete time systems satisfying a controllability condition, we present a stability condition for model predictive control without stabilizing terminal constraints or costs. The condition is given in terms of an analytical…
Environmental processes resolved at a sufficiently small scale in space and time will inevitably display non-stationary behavior. Such processes are both challenging to model and computationally expensive when the data size is large.…
This work presents an alternative view on the numerical simulation of diffusion processes applied to the heat and moisture transfer through porous building materials. Traditionally, by using the finite-difference approach, the…
Reservoir computing is a powerful tool for forecasting turbulence because its simple architecture has the computational efficiency to handle large systems. Its implementation, however, often requires full state-vector measurements and…
Extreme precipitation shows non-stationary behavior over time, but also with respect to other large-scale variables. While this effect is often neglected, we propose a model including the influence of North Atlantic Oscillation, time,…
In a previous work, we presented a class of initial data to the three dimensional, periodic, incompressible Navier-Stokes equations, generating a global smooth solution although the norm of the initial data may be chosen arbitrarily large.…
The relative degree limitation for adaptive observer-based synchronization schemes is overcome. The scheme is extended to nonpassifiable systems. Two synchronization methods are described and justified based on augmented error adaptive…
Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data. Here we show that learning from noise-free observations in such systems can be achieved up…
We present a set of uniform polynomial equations that provides multidimensional on-lattice higher-order models of the lattice Boltzmann theory, while keeping compact the number of discrete velocities. As examples, we explicitly derive two-…