26,646 research outputs found
A partially linearized sigma point filter for latent state estimation in nonlinear time series models
A new technique for the latent state estimation of a wide class of nonlinear time
series models is proposed. In particular, we develop a partially linearized sigma point filter in which random samples of possible state values are generated at the prediction step using an exact moment matching algorithm and then a linear programming-based procedure is used in the update step of the state estimation. The effectiveness of the new ¯ltering procedure is assessed via a simulation example that deals with a highly nonlinear, multivariate time series representing an interest rate process
Impact of noise on a dynamical system: prediction and uncertainties from a swarm-optimized neural network
In this study, an artificial neural network (ANN) based on particle swarm
optimization (PSO) was developed for the time series prediction. The hybrid
ANN+PSO algorithm was applied on Mackey--Glass chaotic time series in the
short-term . The performance prediction was evaluated and compared with
another studies available in the literature. Also, we presented properties of
the dynamical system via the study of chaotic behaviour obtained from the
predicted time series. Next, the hybrid ANN+PSO algorithm was complemented with
a Gaussian stochastic procedure (called {\it stochastic} hybrid ANN+PSO) in
order to obtain a new estimator of the predictions, which also allowed us to
compute uncertainties of predictions for noisy Mackey--Glass chaotic time
series. Thus, we studied the impact of noise for several cases with a white
noise level () from 0.01 to 0.1.Comment: 11 pages, 8 figure
Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks
We introduce a data-driven forecasting method for high-dimensional chaotic
systems using long short-term memory (LSTM) recurrent neural networks. The
proposed LSTM neural networks perform inference of high-dimensional dynamical
systems in their reduced order space and are shown to be an effective set of
nonlinear approximators of their attractor. We demonstrate the forecasting
performance of the LSTM and compare it with Gaussian processes (GPs) in time
series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation
and a prototype climate model. The LSTM networks outperform the GPs in
short-term forecasting accuracy in all applications considered. A hybrid
architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is
proposed to ensure convergence to the invariant measure. This novel hybrid
method is fully data-driven and extends the forecasting capabilities of LSTM
networks.Comment: 31 page
Training Echo State Networks with Regularization through Dimensionality Reduction
In this paper we introduce a new framework to train an Echo State Network to
predict real valued time-series. The method consists in projecting the output
of the internal layer of the network on a space with lower dimensionality,
before training the output layer to learn the target task. Notably, we enforce
a regularization constraint that leads to better generalization capabilities.
We evaluate the performances of our approach on several benchmark tests, using
different techniques to train the readout of the network, achieving superior
predictive performance when using the proposed framework. Finally, we provide
an insight on the effectiveness of the implemented mechanics through a
visualization of the trajectory in the phase space and relying on the
methodologies of nonlinear time-series analysis. By applying our method on well
known chaotic systems, we provide evidence that the lower dimensional embedding
retains the dynamical properties of the underlying system better than the
full-dimensional internal states of the network
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