sensitivity.sensitivity_local

sensitivity.sensitivity_local

Local sensitivity analysis based on finite differences.

This module implements a local (derivative-based) sensitivity analysis using two-sided finite differences around a reference parameter set. Each model parameter is perturbed individually by a small relative amount, and the resulting change in model outputs is used to approximate local sensitivities.

The analysis is designed for deterministic simulation models and is particularly suited for: - Identifying locally influential parameters - Debugging and model inspection - Complementing global sensitivity analyses - Supporting parameter screening prior to optimization or uncertainty analysis

Sensitivities are computed for each analysis group and output variable, and can be reported both as raw sensitivities and as normalized, dimensionless sensitivities.

The implementation builds on the sbmlsim sensitivity framework and integrates with existing simulation, caching, and plotting utilities.

Notes

For each parameter p_i with reference value p_{i,0}, two perturbed simulations are generated: p_i_plus = p_{i,0} * (1 + difference) p_i_minus = p_{i,0} * (1 - difference)

Raw sensitivities are computed using a symmetric finite-difference scheme: S(q_k, p_i) = (q_k(p_i_plus) - q_k(p_i_minus)) / (p_i_plus - p_i_minus)

Normalized sensitivities represent the relative change in output per relative change in parameter: S_norm(q_k, p_i) = S(q_k, p_i) * (p_{i,0} / q_k(p_{i,0}))

Classes

Name	Description
LocalSensitivityAnalysis	Local sensitivity analysis based on symmetric finite differences.

LocalSensitivityAnalysis

sensitivity.sensitivity_local.LocalSensitivityAnalysis(
    sensitivity_simulation,
    parameters,
    groups,
    results_path,
    seed=None,
    n_cores=None,
    cache_results=False,
    difference=0.01,
)

Local sensitivity analysis based on symmetric finite differences.

This class implements a local sensitivity analysis in which each model parameter is perturbed individually by a small relative amount while all other parameters are kept at their reference values.

For each parameter, two simulations are performed (increase and decrease), in addition to a reference simulation. Sensitivities are computed for each output variable and analysis group.

Attributes

Name	Type	Description
difference	float	Relative parameter perturbation used for the finite-difference approximation (e.g., 0.01 corresponds to ±1% changes).

Methods

Name	Description
calculate_sensitivity	Compute raw and normalized local sensitivity matrices.
create_samples	Create parameter samples for the local sensitivity analysis.

calculate_sensitivity

sensitivity.sensitivity_local.LocalSensitivityAnalysis.calculate_sensitivity(
    cache_filename=None,
    cache=False,
)

Compute raw and normalized local sensitivity matrices.

This method calculates two-sided finite-difference sensitivities for each parameter–output combination and stores both raw and normalized sensitivity matrices.

Optionally, results can be read from or written to a cache file.

Parameters

Name	Type	Description	Default
cache_filename	str	Filename for caching sensitivity results.	None
cache	bool	Whether to read from and/or write to the cache.	False

create_samples

sensitivity.sensitivity_local.LocalSensitivityAnalysis.create_samples()

Create parameter samples for the local sensitivity analysis.

For each analysis group, this method constructs a sample matrix containing: - One reference parameter vector - Two perturbed parameter vectors per parameter (±difference)

The samples are stored as xarray.DataArray objects and indexed by sample and parameter identifiers.