1,535,925 research outputs found
Model reconstruction from temporal data for coupled oscillator networks
In a complex system, the interactions between individual agents often lead to
emergent collective behavior like spontaneous synchronization, swarming, and
pattern formation. The topology of the network of interactions can have a
dramatic influence over those dynamics. In many studies, researchers start with
a specific model for both the intrinsic dynamics of each agent and the
interaction network, and attempt to learn about the dynamics that can be
observed in the model. Here we consider the inverse problem: given the dynamics
of a system, can one learn about the underlying network? We investigate
arbitrary networks of coupled phase-oscillators whose dynamics are
characterized by synchronization. We demonstrate that, given sufficient
observational data on the transient evolution of each oscillator, one can use
machine learning methods to reconstruct the interaction network and
simultaneously identify the parameters of a model for the intrinsic dynamics of
the oscillators and their coupling.Comment: 27 pages, 7 figures, 16 table
Modeling and Estimation for Self-Exciting Spatio-Temporal Models of Terrorist Activity
Spatio-temporal hierarchical modeling is an extremely attractive way to model
the spread of crime or terrorism data over a given region, especially when the
observations are counts and must be modeled discretely. The spatio-temporal
diffusion is placed, as a matter of convenience, in the process model allowing
for straightforward estimation of the diffusion parameters through Bayesian
techniques. However, this method of modeling does not allow for the existence
of self-excitation, or a temporal data model dependency, that has been shown to
exist in criminal and terrorism data. In this manuscript we will use existing
theories on how violence spreads to create models that allow for both
spatio-temporal diffusion in the process model as well as temporal diffusion,
or self-excitation, in the data model. We will further demonstrate how Laplace
approximations similar to their use in Integrated Nested Laplace Approximation
can be used to quickly and accurately conduct inference of self-exciting
spatio-temporal models allowing practitioners a new way of fitting and
comparing multiple process models. We will illustrate this approach by fitting
a self-exciting spatio-temporal model to terrorism data in Iraq and demonstrate
how choice of process model leads to differing conclusions on the existence of
self-excitation in the data and differing conclusions on how violence is
spreading spatio-temporally
Modeling space-time correlations of velocity fluctuations in wind farms
An analytical model for the streamwise velocity space-time correlations in
turbulent flows is derived and applied to the special case of velocity
fluctuations in large wind farms. The model is based on the Kraichnan-Tennekes
random sweeping hypothesis, capturing the decorrelation in time while including
a mean wind velocity in the streamwise direction. In the resulting model, the
streamwise velocity space-time correlation is expressed as a convolution of the
pure space correlation with an analytical temporal decorrelation kernel. Hence,
the spatio-temporal structure of velocity fluctuations in wind farms can be
derived from the spatial correlations only. We then explore the applicability
of the model to predict spatio-temporal correlations in turbulent flows in wind
farms. Comparisons of the model with data from a large eddy simulation of flow
in a large, spatially periodic wind farm are performed, where needed model
parameters such as spatial and temporal integral scales and spatial
correlations are determined from the large eddy simulation. Good agreement is
obtained between the model and large eddy simulation data showing that spatial
data may be used to model the full temporal structure of fluctuations in wind
farms.Comment: Submitted to Wind Energ
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