7,996 research outputs found
Data based identification and prediction of nonlinear and complex dynamical systems
We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin
Herding as a Learning System with Edge-of-Chaos Dynamics
Herding defines a deterministic dynamical system at the edge of chaos. It
generates a sequence of model states and parameters by alternating parameter
perturbations with state maximizations, where the sequence of states can be
interpreted as "samples" from an associated MRF model. Herding differs from
maximum likelihood estimation in that the sequence of parameters does not
converge to a fixed point and differs from an MCMC posterior sampling approach
in that the sequence of states is generated deterministically. Herding may be
interpreted as a"perturb and map" method where the parameter perturbations are
generated using a deterministic nonlinear dynamical system rather than randomly
from a Gumbel distribution. This chapter studies the distinct statistical
characteristics of the herding algorithm and shows that the fast convergence
rate of the controlled moments may be attributed to edge of chaos dynamics. The
herding algorithm can also be generalized to models with latent variables and
to a discriminative learning setting. The perceptron cycling theorem ensures
that the fast moment matching property is preserved in the more general
framework
Predicting Spatio-Temporal Time Series Using Dimension Reduced Local States
We present a method for both cross estimation and iterated time series
prediction of spatio temporal dynamics based on reconstructed local states, PCA
dimension reduction, and local modelling using nearest neighbour methods. The
effectiveness of this approach is shown for (noisy) data from a (cubic) Barkley
model, the Bueno-Orovio-Cherry-Fenton model, and the Kuramoto-Sivashinsky
model
Identification of parameters in amplitude equations describing coupled wakes
We study the flow behind an array of equally spaced parallel cylinders. A
system of Stuart-Landau equations with complex parameters is used to model the
oscillating wakes. Our purpose is to identify the 6 scalar parameters which
most accurately reproduce the experimental data of Chauve and Le Gal [{Physica
D {\bf 58}}, pp 407--413, (1992)]. To do so, we perform a computational search
for the minimum of a distance \calj. We define \calj as the sum-square
difference of the data and amplitudes reconstructed using coupled equations.
The search algorithm is made more efficient through the use of a partially
analytical expression for the gradient . Indeed
can be obtained by the integration of a dynamical system propagating backwards
in time (a backpropagation equation for the Lagrange multipliers). Using the
parameters computed via the backpropagation method, the coupled Stuart-Landau
equations accurately predicted the experimental data from Chauve and Le Gal
over a correlation time of the system. Our method turns out to be quite robust
as evidenced by using noisy synthetic data obtained from integrations of the
coupled Stuart-Landau equations. However, a difficulty remains with
experimental data: in that case the several sets of identified parameters are
shown to yield equivalent predictions. This is due to a strong discretization
or ``round-off" error arising from the digitalization of the video images in
the experiment. This ambiguity in parameter identification has been reproduced
with synthetic data subjected to the same kind of discretization.Comment: 25 pages uuencoded compressed PostScript file (58K) with 13 figures
(155K in separated file) Submitted to Physica
Non-Markov stochastic dynamics of real epidemic process of respiratory infections
The study of social networks and especially of the stochastic dynamics of the
diseases spread in human population has recently attracted considerable
attention in statistical physics. In this work we present a new statistical
method of analyzing the spread of epidemic processes of grippe and acute
respiratory track infections (ARTI) by means of the theory of discrete
non-Markov stochastic processes. We use the results of our last theory (Phys.
Rev. E 65, 046107 (2002)) to study statistical memory effects, long - range
correlation and discreteness in real data series, describing the epidemic
dynamics of human ARTI infections and grippe. We have carried out the
comparative analysis of the data of the two infections (grippe and ARTI) in one
of the industrial districts of Kazan, one of the largest cities of Russia. The
experimental data are analyzed by the power spectra of the initial time
correlation function and the memory functions of junior orders, the phase
portraits of the four first dynamic variables, the three first points of the
statistical non-Markov parameter and the locally averaged kinetic and
relaxation parameters. The received results give an opportunity to provide
strict quantitative description of the regular and stochastic components in
epidemic dynamics of social networks taking into account their time
discreteness and effects of statistical memory. They also allow to reveal the
degree of randomness and predictability of the real epidemic process in the
specific social network.Comment: 18 pages, 8figs, 1 table
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
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