# Koopman Inference

## Algorithms

DataDrivenDiffEq.DMDPINVType
mutable struct DMDPINV <: DataDrivenDiffEq.AbstractKoopmanAlgorithm

Approximates the Koopman operator K based on

K = Y / X

where Y and X are data matrices. Returns a Eigen factorization of the operator.

Fields

Signatures

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DataDrivenDiffEq.DMDSVDType
mutable struct DMDSVD{T} <: DataDrivenDiffEq.AbstractKoopmanAlgorithm

Approximates the Koopman operator K based on the singular value decomposition of X such that:

K = Y*V*Σ*U'

where Y and X = U*Σ*V' are data matrices. The singular value decomposition is truncated via the truncation parameter, which can either be an Int indiciating an index based truncation or a Real indiciating a tolerance based truncation. Returns a Eigen factorization of the operator.

Fields

• truncation

Indiciates the truncation

Signatures

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DataDrivenDiffEq.TOTALDMDType
mutable struct TOTALDMD{R, A} <: DataDrivenDiffEq.AbstractKoopmanAlgorithm

Approximates the Koopman operator K with the algorithm alg over the rank-reduced data matrices Xᵣ = X Qᵣ and Yᵣ = Y Qᵣ, where Qᵣ originates from the singular value decomposition of the joint data Z = [X; Y]. Based on this paper.

If rtol ∈ (0, 1) is given, the singular value decomposition is reduced to include only entries bigger than rtol*maximum(Σ). If rtol is an integer, the reduced SVD up to rtol is used for computation.

Fields

• truncation

• alg

Signatures

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DataDrivenDiffEq.FBDMDType
mutable struct FBDMD{R} <: DataDrivenDiffEq.AbstractKoopmanAlgorithm

Approximates the Koopman operator K via the forward-backward DMD. It is assumed that K = sqrt(K₁*inv(K₂)), where K₁ is the approximation via forward and K₂ via DMDSVD. Based on this paper.

If truncation ∈ (0, 1) is given, the singular value decomposition is reduced to include only entries bigger than truncation*maximum(Σ). If truncation is an integer, the reduced SVD up to truncation is used for computation.

Fields

• alg

Signatures

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