Collocation

DataDrivenDiffEq.InterpolationMethodType

A wrapper for the interpolation methods of DataInterpolations.jl.

Wraps the methods in such a way that they are callable as f(u,t) to create and return an interpolation of u over t. The first argument of the constructor always defines the interpolation method, all following arguments will be used in the interpolation.

Example

# Create the wrapper struct
itp_method = InterpolationMethod(QuadraticSpline)
# Create a callable interpolation
itp = itp_method(u,t)
# Return u[2]
itp(t[2])
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DataDrivenDiffEq.collocate_dataFunction
collocate_data(data, tpoints)
collocate_data(data, tpoints, kernel)

Unified interface for collocation techniques. The input can either be a CollocationKernel (see list below) or a wrapped InterpolationMethod from DataInterpolations.jl.

Computes a non-parametrically smoothed estimate of u' and u given the data, where each column is a snapshot of the timeseries at tpoints[i].

Examples

u′,u = collocate_data(data,tpoints,kernel=SigmoidKernel())
u′,u = collocate_data(data,tpoints,tpoints_sample,interp,args...)
u′,u = collocate_data(data,tpoints,interp)

Collocation Kernels

See this paper for more information.

  • EpanechnikovKernel
  • UniformKernel
  • TriangularKernel
  • QuarticKernel
  • TriweightKernel
  • TricubeKernel
  • GaussianKernel
  • CosineKernel
  • LogisticKernel
  • SigmoidKernel
  • SilvermanKernel

Interpolation Methods

See DataInterpolations.jl for more information.

  • ConstantInterpolation
  • LinearInterpolation
  • QuadraticInterpolation
  • LagrangeInterpolation
  • QuadraticSpline
  • CubicSpline
  • BSplineInterpolation
  • BSplineApprox
  • Curvefit
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Utilities

DataDrivenDiffEq.AICFunction
AIC(k, X, Y; likelihood)

Computes the Akaike Information Criterion (AIC) given the free parameters k for the data X and its estimate Y of the model. likelihood can be any function of X and Y.

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DataDrivenDiffEq.AICCFunction
AICC(k, X, Y; likelihood)

Computes the Akaike Information Criterion compensated for finite samples (AICC) given the free parameters k for the data X and its estimate Y of the model. likelihood can be any function of X and Y.

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DataDrivenDiffEq.BICFunction
BIC(k, X, Y; likelihood)

Computes Bayes Information Criterion (BIC) given the free parameters k for the data X and its estimate Y of the model. likelihood can be any function of X and Y.

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DataDrivenDiffEq.burst_samplingFunction
(
burst_sampling(x, samplesize, bursts)

)

Randomly selects n bursts of data with size samplesize from the data X.

Randomly selects n bursts of data with size samplesize from the data X and Y.

Randomly selects n bursts of data within a time window period from the data X. The time information has to be provided in t.

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DataDrivenDiffEq.subsampleFunction
subsample(x, frequency)

Returns the subsampled X with only every n-th entry.

Returns the subsampled X with a a minimum period of dt between two data points. t provides the time information.

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