romtools.workflows.inverse.run_mf_eki

romtools.workflows.inverse.run_mf_eki(model, rom_model_builder, parameter_space, observations, observations_covariance, parameter_mins=None, parameter_maxes=None, absolute_eki_directory='/home/runner/work/rom-tools-and-workflows/rom-tools-and-workflows/work/', fom_ensemble_size=10, rom_extra_ensemble_size=30, rom_tolerance=0.005, use_updated_rom_in_update_on_rebuild=True, initial_step_size=0.1, regularization_parameter=0.0001, step_size_growth_factor=1.25, step_size_decay_factor=2.0, max_step_size_decrease_trys=5, relaxation_parameter=1.05, error_norm_tolerance=1e-05, delta_params_tolerance=0.0001, max_rom_training_history=1, max_iterations=50, random_seed=1, fom_evaluation_concurrency=1, rom_evaluation_concurrency=1, restart_file=None)

Run a multi-fidelity ensemble Kalman inversion (MF-EKI) workflow.

The workflow evaluates the FOM on a smaller ensemble, augments those data with a larger ROM-only ensemble, and forms a multifidelity Kalman update. The ROM is rebuilt from accepted iteration data when its shared-sample QoI error exceeds rom_tolerance.

Parameters:

• model (QoiModel) – High-fidelity QoiModel used to define the target inverse problem.

• rom_model_builder (QoiModelBuilderWithTrainingData) – Builder that constructs surrogate QoI models from accumulated training directories and QoI data.

• parameter_space (ParameterSpace) – ParameterSpace used to draw the initial combined ensemble when restart_file is not provided.

• observations (ndarray) – Observed QoI vector \(y\).

• observations_covariance (ndarray) – Observation covariance matrix \(\Gamma_y\) used in the Kalman solve.

• parameter_mins (ndarray) – Optional lower bounds applied to sampled and updated parameters.

• parameter_maxes (ndarray) – Optional upper bounds applied to sampled and updated parameters.

• absolute_eki_directory (str) – Absolute path to the working directory. Each iteration stores FOM and ROM evaluations in iteration-specific subdirectories below this path.

• fom_ensemble_size (int) – Number of ensemble members evaluated with the high-fidelity model on each iteration.

• rom_extra_ensemble_size – Number of additional ROM-only ensemble members used to improve multifidelity covariance estimates.

• rom_tolerance (float) – Relative QoI error threshold on the shared FOM/ROM sample set used to trigger surrogate rebuilding.

• use_updated_rom_in_update_on_rebuild (bool) – When True, use the updated ROM in the update for that step. When False, use the previous ROM in the update for that step.

• initial_step_size (float) – Initial multiplier applied to the multifidelity Kalman update directions.

• regularization_parameter (float) – Tikhonov regularization added to the QoI covariance solve.

• step_size_growth_factor (float) – Factor used to increase the step size after an accepted iteration.

• step_size_decay_factor (float) – Factor used to decrease the step size after a rejected trial iteration.

• max_step_size_decrease_trys (int) – Maximum number of consecutive rejected trial steps before the routine exits.

• relaxation_parameter (float) – Acceptance threshold on the mean FOM observation-space error norm.

• error_norm_tolerance (float) – Stop when the mean FOM observation-space error norm falls below this value.

• delta_params_tolerance (float) – Stop when the norm of the proposed high-fidelity ensemble update falls below this value.

• max_rom_training_history (int) – Maximum number of accepted iterations whose training data are retained for ROM rebuilding.

• max_iterations (int) – Maximum number of EKI iterations.

• random_seed (int) – RNG seed used for the initial ensemble draw.

• fom_evaluation_concurrency (int) – Number of concurrent FOM evaluations used by each iteration.

• rom_evaluation_concurrency (int) – Number of concurrent ROM evaluations used by each iteration.

• restart_file (str) – Optional .npz restart file produced by a prior MF-EKI run. When set, the saved FOM/ROM sample sets, surrogate training history, and step size are restored.

Returns:

Tuple (fom_parameter_samples, fom_qois) for the final accepted high-fidelity sample set.