5,401 research outputs found
Modelling and control of chaotic processes through their Bifurcation Diagrams generated with the help of Recurrent Neural Network models: Part 1âsimulation studies
Many real-world processes tend to be chaotic and also do not lead to satisfactory analytical modelling. It has been shown here that for such chaotic processes represented through short chaotic noisy time-series, a multi-input and multi-output recurrent neural networks model can be built which is capable of capturing the process trends and predicting the future values from any given starting condition. It is further shown that this capability can be achieved by the Recurrent Neural Network model when it is trained to very low value of mean squared error. Such a model can then be used for constructing the Bifurcation Diagram of the process leading to determination of desirable operating conditions. Further, this multi-input and multi-output model makes the process accessible for control using open-loop/closed-loop approaches or bifurcation control etc. All these studies have been carried out using a low dimensional discrete chaotic system of HĂ©non Map as a representative of some real-world processes
Emulating dynamic non-linear simulators using Gaussian processes
The dynamic emulation of non-linear deterministic computer codes where the
output is a time series, possibly multivariate, is examined. Such computer
models simulate the evolution of some real-world phenomenon over time, for
example models of the climate or the functioning of the human brain. The models
we are interested in are highly non-linear and exhibit tipping points,
bifurcations and chaotic behaviour. However, each simulation run could be too
time-consuming to perform analyses that require many runs, including
quantifying the variation in model output with respect to changes in the
inputs. Therefore, Gaussian process emulators are used to approximate the
output of the code. To do this, the flow map of the system under study is
emulated over a short time period. Then, it is used in an iterative way to
predict the whole time series. A number of ways are proposed to take into
account the uncertainty of inputs to the emulators, after fixed initial
conditions, and the correlation between them through the time series. The
methodology is illustrated with two examples: the highly non-linear dynamical
systems described by the Lorenz and Van der Pol equations. In both cases, the
predictive performance is relatively high and the measure of uncertainty
provided by the method reflects the extent of predictability in each system
Modeling Financial Time Series with Artificial Neural Networks
Financial time series convey the decisions and actions of a population of human actors over time. Econometric and regressive models have been developed in the past decades for analyzing these time series. More recently, biologically inspired artificial neural network models have been shown to overcome some of the main challenges of traditional techniques by better exploiting the non-linear, non-stationary, and oscillatory nature of noisy, chaotic human interactions. This review paper explores the options, benefits, and weaknesses of the various forms of artificial neural networks as compared with regression techniques in the field of financial time series analysis.CELEST, a National Science Foundation Science of Learning Center (SBE-0354378); SyNAPSE program of the Defense Advanced Research Project Agency (HR001109-03-0001
Identification of Evolving Rule-based Models.
An approach to identification of evolving fuzzy rule-based (eR) models is proposed. eR models implement a method for the noniterative update of both the rule-base structure and parameters by incremental unsupervised learning. The rule-base evolves by adding more informative rules than those that previously formed the model. In addition, existing rules can be replaced with new rules based on ranking using the informative potential of the data. In this way, the rule-base structure is inherited and updated when new informative data become available, rather than being completely retrained. The adaptive nature of these evolving rule-based models, in combination with the highly transparent and compact form of fuzzy rules, makes them a promising candidate for modeling and control of complex processes, competitive to neural networks. The approach has been tested on a benchmark problem and on an air-conditioning component modeling application using data from an installation serving a real building. The results illustrate the viability and efficiency of the approach. (c) IEEE Transactions on Fuzzy System
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
Optoelectronic Reservoir Computing
Reservoir computing is a recently introduced, highly efficient bio-inspired
approach for processing time dependent data. The basic scheme of reservoir
computing consists of a non linear recurrent dynamical system coupled to a
single input layer and a single output layer. Within these constraints many
implementations are possible. Here we report an opto-electronic implementation
of reservoir computing based on a recently proposed architecture consisting of
a single non linear node and a delay line. Our implementation is sufficiently
fast for real time information processing. We illustrate its performance on
tasks of practical importance such as nonlinear channel equalization and speech
recognition, and obtain results comparable to state of the art digital
implementations.Comment: Contains main paper and two Supplementary Material
Practical implementation of nonlinear time series methods: The TISEAN package
Nonlinear time series analysis is becoming a more and more reliable tool for
the study of complicated dynamics from measurements. The concept of
low-dimensional chaos has proven to be fruitful in the understanding of many
complex phenomena despite the fact that very few natural systems have actually
been found to be low dimensional deterministic in the sense of the theory. In
order to evaluate the long term usefulness of the nonlinear time series
approach as inspired by chaos theory, it will be important that the
corresponding methods become more widely accessible. This paper, while not a
proper review on nonlinear time series analysis, tries to make a contribution
to this process by describing the actual implementation of the algorithms, and
their proper usage. Most of the methods require the choice of certain
parameters for each specific time series application. We will try to give
guidance in this respect. The scope and selection of topics in this article, as
well as the implementational choices that have been made, correspond to the
contents of the software package TISEAN which is publicly available from
http://www.mpipks-dresden.mpg.de/~tisean . In fact, this paper can be seen as
an extended manual for the TISEAN programs. It fills the gap between the
technical documentation and the existing literature, providing the necessary
entry points for a more thorough study of the theoretical background.Comment: 27 pages, 21 figures, downloadable software at
http://www.mpipks-dresden.mpg.de/~tisea
Evolino for recurrent support vector machines
Traditional Support Vector Machines (SVMs) need pre-wired finite time windows
to predict and classify time series. They do not have an internal state
necessary to deal with sequences involving arbitrary long-term dependencies.
Here we introduce a new class of recurrent, truly sequential SVM-like devices
with internal adaptive states, trained by a novel method called EVOlution of
systems with KErnel-based outputs (Evoke), an instance of the recent Evolino
class of methods. Evoke evolves recurrent neural networks to detect and
represent temporal dependencies while using quadratic programming/support
vector regression to produce precise outputs. Evoke is the first SVM-based
mechanism learning to classify a context-sensitive language. It also
outperforms recent state-of-the-art gradient-based recurrent neural networks
(RNNs) on various time series prediction tasks.Comment: 10 pages, 2 figure
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