setup_polynomial_ensemble

pyapprox.benchmarks.setup_polynomial_ensemble(nmodels=5)

Return an ensemble of 5 univariate models of the form

$$f_{\alpha }(z)=z^{5-\alpha },\alpha =0,\dots ,4$$

where $z\sim \mathcal{U}[0,1]$

Returns:

benchmarkBenchmark

Object containing the benchmark attributes

funcallable

The function being analyzed

variableJointVariable

Class containing information about each of the nvars inputs to fun

meansnp.ndarray (nmodels)

The mean of each model fidelity

covariancenp.ndarray (nmodels)

The covariance between the outputs of each model fidelity

References

[GGEJJCP2020]

A generalized approximate control variate framework for multifidelity uncertainty quantification, Journal of Computational Physics, 408:109257, 2020.