相关论文: Learning ergodic averages in chaotic systems

In this study, we propose a novel approach, namely the combined Convolutional Deep Autoencoder Echo State Network (CDAE ESN) model, for the analysis and forecasting of dynamics and low order statistics in coupled turbulent channel porous…

Machine Learning (ML) inspired algorithms provide a flexible set of tools for analyzing and forecasting chaotic dynamical systems. We here analyze the performance of one algorithm for the prediction of extreme events in the two-dimensional…

Effective control and prediction of dynamical systems often require appropriate handling of continuous-time and discrete, event-triggered processes. Stochastic hybrid systems (SHSs), common across engineering domains, provide a formalism…

In many practical applications, regression models are employed to uncover relationships between predictors and a response variable, yet the common assumption of constant error variance is frequently violated. This issue is further…

Forecasting the dynamics of chaotic systems from the analysis of their output signals is a challenging problem with applications in most fields of modern science. In this work, we use a laser model to compare the performance of several…

Multivariate geo-sensory time series prediction is challenging because of the complex spatial and temporal correlation. In urban water distribution systems (WDS), numerous spatial-correlated sensors have been deployed to continuously…

This work studies networked agents cooperating to track a dynamical state of nature under partial information. The proposed algorithm is a distributed Bayesian filtering algorithm for finite-state hidden Markov models (HMMs). It can be used…

A common problem in time series analysis is to predict dynamics with only scalar or partial observations of the underlying dynamical system. For data on a smooth compact manifold, Takens theorem proves a time delayed embedding of the…

A framework for probabilistic forecasting of vessel motion is developed and validated for a semisubmersible operating in long period swell. Bayesian statistical methods are applied to predictions of the heave response from a physics model…

We explore the use of Physics Informed Neural Networks to analyse nonlinear Hamiltonian Dynamical Systems with a first integral of motion. In this work, we propose an architecture which combines existing Hamiltonian Neural Network…

In this computational paper, we perform sensitivity analysis of long-time (or ensemble) averages in the chaotic regime using the shadowing algorithm. We introduce automatic differentiation to eliminate the tangent/adjoint equation solvers…

We explore the influence of precision of the data and the algorithm for the simulation of chaotic dynamics by neural networks techniques. For this purpose, we simulate the Lorenz system with different precisions using three different neural…

We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is in the form of noisy partial measurements of the past and present state of the dynamical system. Recently there have been several…

The spatiotemporal dynamics of turbulent flows is chaotic and difficult to predict. This makes the design of accurate and stable reduced-order models challenging. The overarching objective of this paper is to propose a nonlinear…

In high energy density physics (HEDP) and inertial confinement fusion (ICF), predictive modeling is complicated by uncertainty in parameters that characterize various aspects of the modeled system, such as those characterizing material…

Virtually every organism gathers information about its noisy environment and builds models from that data, mostly using neural networks. Here, we use stochastic thermodynamics to analyse the learning of a classification rule by a neural…

In the light of regularized dynamic time warping kernels, this paper re-considers the concept of time elastic centroid for a setof time series. We derive a new algorithm based on a probabilistic interpretation of kernel alignment matrices.…

In some Internet of Things (IoT) applications, multi-path propagation is a main constraint of communication channel. Recently, the chaotic baseband wireless communication system (CBWCS) is promising to eliminate the inter-symbol…

Echo state networks (ESNs) are a powerful form of reservoir computing that only require training of linear output weights whilst the internal reservoir is formed of fixed randomly connected neurons. With a correctly scaled connectivity…

Model combination is a powerful approach for achieving superior performance compared to selecting a single model. We study both theoretically and empirically the effectiveness of ensembles of Multi-Frequency Echo State Networks (MFESNs),…