1,503 research outputs found
Complex Neuro-Cognitive Systems
Cognitive functions such as a perception, thinking and acting are based on the working of the brain, one of the most complex systems we know. The traditional scientific methodology, however, has proved to be not sufficient to understand the relation between brain and cognition. The aim of this paper is to review an alternative methodology â nonlinear dynamical analysis â and to demonstrate its benefit\ud
for cognitive neuroscience in cases when the usual reductionist method fails
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
Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators
In this set of lectures, we review briefly some of the recent developments in
the study of the chaotic dynamics of nonlinear oscillators, particularly of
damped and driven type. By taking a representative set of examples such as the
Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain
the various bifurcations and chaos phenomena associated with these systems. We
use numerical and analytical as well as analogue simulation methods to study
these systems. Then we point out how controlling of chaotic motions can be
effected by algorithmic procedures requiring minimal perturbations. Finally we
briefly discuss how synchronization of identically evolving chaotic systems can
be achieved and how they can be used in secure communications.Comment: 31 pages (24 figures) LaTeX. To appear Springer Lecture Notes in
Physics Please Lakshmanan for figures (e-mail: [email protected]
Real-time support for high performance aircraft operation
The feasibility of real-time processing schemes using artificial neural networks (ANNs) is investigated. A rationale for digital neural nets is presented and a general processor architecture for control applications is illustrated. Research results on ANN structures for real-time applications are given. Research results on ANN algorithms for real-time control are also shown
Data-driven discovery of coordinates and governing equations
The discovery of governing equations from scientific data has the potential
to transform data-rich fields that lack well-characterized quantitative
descriptions. Advances in sparse regression are currently enabling the
tractable identification of both the structure and parameters of a nonlinear
dynamical system from data. The resulting models have the fewest terms
necessary to describe the dynamics, balancing model complexity with descriptive
ability, and thus promoting interpretability and generalizability. This
provides an algorithmic approach to Occam's razor for model discovery. However,
this approach fundamentally relies on an effective coordinate system in which
the dynamics have a simple representation. In this work, we design a custom
autoencoder to discover a coordinate transformation into a reduced space where
the dynamics may be sparsely represented. Thus, we simultaneously learn the
governing equations and the associated coordinate system. We demonstrate this
approach on several example high-dimensional dynamical systems with
low-dimensional behavior. The resulting modeling framework combines the
strengths of deep neural networks for flexible representation and sparse
identification of nonlinear dynamics (SINDy) for parsimonious models. It is the
first method of its kind to place the discovery of coordinates and models on an
equal footing.Comment: 25 pages, 6 figures; added acknowledgment
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