Ensemble Kalman Inversion

EnsembleKalmanProcesses.Inversion — Type

An ensemble Kalman Inversion process.

struct Inversion{FT<:AbstractFloat, NorV<:Union{Nothing, AbstractVector}, NorAMorUS<:Union{Nothing, LinearAlgebra.UniformScaling, AbstractMatrix}} <: EnsembleKalmanProcesses.Process

Fields

prior_mean::Union{Nothing, AbstractVector}: Mean of Gaussian parameter prior in unconstrained space
prior_cov::Union{Nothing, LinearAlgebra.UniformScaling, AbstractMatrix}: Covariance of Gaussian parameter prior in unconstrained space
impose_prior::Bool: flag to explicitly impose the prior mean and covariance during updates
default_multiplicative_inflation::AbstractFloat: if prior is imposed, inflation is often required. This sets a default multiplicative inflation with s = default_multiplicative_inflation

Constructors

Inversion(
    prior_mean,
    prior_cov,
    impose_prior,
    default_multiplicative_inflation
)

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/EnsembleKalmanInversion.jl:23.

Inversion(
    mean_prior,
    cov_prior;
    impose_prior,
    default_multiplicative_inflation
)

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/EnsembleKalmanInversion.jl:68.

Inversion(
    prior;
    impose_prior,
    default_multiplicative_inflation
)

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/EnsembleKalmanInversion.jl:79.

Inversion()

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/EnsembleKalmanInversion.jl:95.

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EnsembleKalmanProcesses.TransformInversion — Type

An ensemble transform Kalman inversion process.

struct TransformInversion{FT<:AbstractFloat, NorV<:Union{Nothing, AbstractVector}, NorAMorUS<:Union{Nothing, LinearAlgebra.UniformScaling, AbstractMatrix}} <: EnsembleKalmanProcesses.Process

Fields

prior_mean::Union{Nothing, AbstractVector}: Mean of Gaussian parameter prior in unconstrained space
prior_cov::Union{Nothing, LinearAlgebra.UniformScaling, AbstractMatrix}: Covariance of Gaussian parameter prior in unconstrained space
impose_prior::Bool: flag to explicitly impose the prior mean and covariance during updates
default_multiplicative_inflation::AbstractFloat: if prior is imposed, inflation is often required. This sets a default multiplicative inflation with s = default_multiplicative_inflation
buffer::AbstractVector: used to store matrices: buffer[1] = Y' *Γinv, buffer[2] = Y' * Γinv * Y

Constructors

TransformInversion(
    prior_mean,
    prior_cov,
    impose_prior,
    default_multiplicative_inflation,
    buffer
)

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/EnsembleTransformKalmanInversion.jl:23.

TransformInversion(
    mean_prior,
    cov_prior;
    impose_prior,
    default_multiplicative_inflation
)

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/EnsembleTransformKalmanInversion.jl:77.

TransformInversion(
    prior;
    impose_prior,
    default_multiplicative_inflation
)

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/EnsembleTransformKalmanInversion.jl:88.

TransformInversion()

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/EnsembleTransformKalmanInversion.jl:104.

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EnsembleKalmanProcesses.GaussNewtonInversion — Type

A Gauss-Newton Kalman Inversion process.

struct GaussNewtonInversion{VV<:(AbstractVector), AMorUS<:Union{LinearAlgebra.UniformScaling, AbstractMatrix}} <: EnsembleKalmanProcesses.Process

Fields

prior_mean::AbstractVector: Mean of Gaussian parameter prior in unconstrained space
prior_cov::Union{LinearAlgebra.UniformScaling, AbstractMatrix}: Covariance of Gaussian parameter prior in unconstrained space

Constructors

GaussNewtonInversion(prior_mean, prior_cov)

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/GaussNewtonKalmanInversion.jl:17.

GaussNewtonInversion(prior)

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/GaussNewtonKalmanInversion.jl:30.

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EnsembleKalmanProcesses.eki_update — Function

eki_update(
    ekp::EnsembleKalmanProcess{FT<:Real, IT, II<:Inversion},
    u::AbstractArray{FT<:Real, 2},
    g::AbstractArray{FT<:Real, 2},
    y::AbstractArray{FT<:Real, 2},
    obs_noise_cov::Union{AbstractArray{CT<:Real, 2}, LinearAlgebra.UniformScaling{CT<:Real}},
    prior_mean::Union{Nothing, AbstractVector},
    prior_cov::Union{Nothing, AbstractMatrix}
) -> Any

Return the updated parameter vectors given their current values and the corresponding forward model evaluations, using the inversion algorithm from eqns. (4) and (5) of Schillings and Stuart (2017).

Localization is implemented following the ekp.localizer.

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