7,949 research outputs found
A bibliography on parallel and vector numerical algorithms
This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also
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
Integration of continuous-time dynamics in a spiking neural network simulator
Contemporary modeling approaches to the dynamics of neural networks consider
two main classes of models: biologically grounded spiking neurons and
functionally inspired rate-based units. The unified simulation framework
presented here supports the combination of the two for multi-scale modeling
approaches, the quantitative validation of mean-field approaches by spiking
network simulations, and an increase in reliability by usage of the same
simulation code and the same network model specifications for both model
classes. While most efficient spiking simulations rely on the communication of
discrete events, rate models require time-continuous interactions between
neurons. Exploiting the conceptual similarity to the inclusion of gap junctions
in spiking network simulations, we arrive at a reference implementation of
instantaneous and delayed interactions between rate-based models in a spiking
network simulator. The separation of rate dynamics from the general connection
and communication infrastructure ensures flexibility of the framework. We
further demonstrate the broad applicability of the framework by considering
various examples from the literature ranging from random networks to neural
field models. The study provides the prerequisite for interactions between
rate-based and spiking models in a joint simulation
Synchronization Transition of Identical Phase Oscillators in a Directed Small-World Network
We numerically study a directed small-world network consisting of
attractively coupled, identical phase oscillators. While complete
synchronization is always stable, it is not always reachable from random
initial conditions. Depending on the shortcut density and on the asymmetry of
the phase coupling function, there exists a regime of persistent chaotic
dynamics. By increasing the density of shortcuts or decreasing the asymmetry of
the phase coupling function, we observe a discontinuous transition in the
ability of the system to synchronize. Using a control technique, we identify
the bifurcation scenario of the order parameter. We also discuss the relation
between dynamics and topology and remark on the similarity of the
synchronization transition to directed percolation.Comment: This article has been accepted in AIP, Chaos. After it is published,
it will be found at http://chaos.aip.org/, 12 pages, 9 figures, 1 tabl
Data Assimilation by Artificial Neural Networks for an Atmospheric General Circulation Model: Conventional Observation
This paper presents an approach for employing artificial neural networks (NN)
to emulate an ensemble Kalman filter (EnKF) as a method of data assimilation.
The assimilation methods are tested in the Simplified Parameterizations
PrimitivE-Equation Dynamics (SPEEDY) model, an atmospheric general circulation
model (AGCM), using synthetic observational data simulating localization of
balloon soundings. For the data assimilation scheme, the supervised NN, the
multilayer perceptrons (MLP-NN), is applied. The MLP-NN are able to emulate the
analysis from the local ensemble transform Kalman filter (LETKF). After the
training process, the method using the MLP-NN is seen as a function of data
assimilation. The NN were trained with data from first three months of 1982,
1983, and 1984. A hind-casting experiment for the 1985 data assimilation cycle
using MLP-NN were performed with synthetic observations for January 1985. The
numerical results demonstrate the effectiveness of the NN technique for
atmospheric data assimilation. The results of the NN analyses are very close to
the results from the LETKF analyses, the differences of the monthly average of
absolute temperature analyses is of order 0.02. The simulations show that the
major advantage of using the MLP-NN is better computational performance, since
the analyses have similar quality. The CPU-time cycle assimilation with MLP-NN
is 90 times faster than cycle assimilation with LETKF for the numerical
experiment.Comment: 17 pages, 16 figures, monthly weather revie
Comparative evaluation of approaches in T.4.1-4.3 and working definition of adaptive module
The goal of this deliverable is two-fold: (1) to present and compare different approaches towards learning and encoding movements us- ing dynamical systems that have been developed by the AMARSi partners (in the past during the first 6 months of the project), and (2) to analyze their suitability to be used as adaptive modules, i.e. as building blocks for the complete architecture that will be devel- oped in the project. The document presents a total of eight approaches, in two groups: modules for discrete movements (i.e. with a clear goal where the movement stops) and for rhythmic movements (i.e. which exhibit periodicity). The basic formulation of each approach is presented together with some illustrative simulation results. Key character- istics such as the type of dynamical behavior, learning algorithm, generalization properties, stability analysis are then discussed for each approach. We then make a comparative analysis of the different approaches by comparing these characteristics and discussing their suitability for the AMARSi project
Solution of partial differential equations on vector and parallel computers
The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed
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