Sparse Ensemble Kalman Inversion

A sparse ensemble Kalman Inversion process.

struct SparseInversion{FT<:AbstractFloat} <: EnsembleKalmanProcesses.Process

Fields

• γ::AbstractFloat: upper limit of l1-norm

• threshold_value::AbstractFloat: threshold below which the norm of parameters is pruned to zero

• uc_idx::Union{Colon, AbstractVector}: indices of parameters included in the evaluation of l1-norm constraint

• reg::AbstractFloat: a small regularization value to enhance robustness of convex optimization

Constructors

SparseInversion(; γ, threshold_value, uc_idx, reg)

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/SparseEnsembleKalmanInversion.jl:20.

SparseInversion(γ, threshold_value, uc_idx, reg)

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/SparseEnsembleKalmanInversion.jl:21.

SparseInversion(γ; threshold_value, uc_idx, reg)

defined at /home/runner/work/EnsembleKalmanProcesses.jl/EnsembleKalmanProcesses.jl/src/SparseEnsembleKalmanInversion.jl:42.

sparse_eki_update(
    ekp::EnsembleKalmanProcess{FT<:Real, IT, SparseInversion{FT<:Real}},
    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}}
) -> Any

Return the sparse updated parameter vectors given their current values and the corresponding forward model evaluations, using the inversion algorithm from eqns. (3.7) and (3.14) of Schneider et al. (2021).

Localization is applied following Tong and Morzfeld (2022).

sparse_qp(
    ekp::EnsembleKalmanProcess{FT, IT, SparseInversion{FT}},
    v_j::Array{FT, 1},
    cov_vv_inv::AbstractArray{FT, 2},
    H_u::AbstractArray{FT, 2},
    H_g::AbstractArray{FT, 2},
    y_j::Array{FT, 1};
    H_uc
) -> Any

Solve the per-ensemble-member quadratic programme with ℓ₁-norm sparsity constraint and return the updated parameter vector for ensemble member j.