simpeg.directives.BetaEstimate_ByEig#

class simpeg.directives.BetaEstimate_ByEig(beta0_ratio=1.0, n_pw_iter=4, seed=None, **kwargs)[source]#

Bases: BaseBetaEstimator

Estimate initial trade-off parameter (beta) by power iteration.

The initial trade-off parameter (beta) is estimated by scaling the ratio between the largest eigenvalue in the second derivative of the data misfit and the model objective function. The largest eigenvalues are estimated using the power iteration method; see simpeg.utils.eigenvalue_by_power_iteration(). The estimated trade-off parameter is used to update the beta property in the associated simpeg.inverse_problem.BaseInvProblem object prior to running the inversion. Note that a separate directive is used for updating the trade-off parameter at successive beta iterations; see BetaSchedule.

Parameters:
beta0_ratio: float

Desired ratio between data misfit and model objective function at initial beta iteration.

n_pw_iterint

Number of power iterations used to estimate largest eigenvalues.

seedNone or RandomSeed, optional

Random seed used for random sampling. It can either be an int, a predefined Numpy random number generator, or any valid input to numpy.random.default_rng.

Notes

Let \(\phi_d\) represent the data misfit, \(\phi_m\) represent the model objective function and \(\mathbf{m_0}\) represent the starting model. The first model update is obtained by minimizing the a global objective function of the form:

\[\phi (\mathbf{m_0}) = \phi_d (\mathbf{m_0}) + \beta_0 \phi_m (\mathbf{m_0})\]

where \(\beta_0\) represents the initial trade-off parameter (beta). Let \(\gamma\) define the desired ratio between the data misfit and model objective functions at the initial beta iteration (defined by the ‘beta0_ratio’ input argument). Using the power iteration approach, our initial trade-off parameter is given by:

\[\beta_0 = \gamma \frac{\lambda_d}{\lambda_m}\]

where \(\lambda_d\) as the largest eigenvalue of the Hessian of the data misfit, and \(\lambda_m\) as the largest eigenvalue of the Hessian of the model objective function. For each Hessian, the largest eigenvalue is computed using power iteration. The input parameter ‘n_pw_iter’ sets the number of power iterations used in the estimate.

For a description of the power iteration approach for estimating the larges eigenvalue, see simpeg.utils.eigenvalue_by_power_iteration().

Attributes

beta0_ratio

The estimated ratio is multiplied by this to obtain beta.

debug

verbose.debug has been deprecated.

dmisfit

Data misfit associated with the directive.

invProb

Inverse problem associated with the directive.

inversion

Inversion object associated with the directive.

n_pw_iter

Number of power iterations for estimating largest eigenvalues.

opt

Optimization algorithm associated with the directive.

reg

Regularization associated with the directive.

seed

Random seed to initialize with.

simulation

Return simulation for all data misfits.

survey

Return survey for all data misfits

verbose

Whether or not to print debugging information.

Methods

endIter()

Update inversion parameter(s) according to directive at end of iteration.

finish()

Update inversion parameter(s) according to directive at end of inversion.

initialize()

Initialize inversion parameter(s) according to directive.

validate(directive_list)

Validate directive.

Galleries and Tutorials using simpeg.directives.BetaEstimate_ByEig#

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