Available Algorithms

There are currently 13 optimization algorithms implemented in MXMCPy. The algorithms are listed below along with some general information.

Multi-level Monte Carlo

Algorithm Name	Optimization	Sampling Strategy
MLMC	Analytic	Recursive Difference

Ref: Giles, M. B.: Multi-level Monte Carlo path simulation. Operations Research , vol. 56, no. 3, 2008, pp. 607–617.

Multifidelity Monte Carlo

Algorithm Name	Optimization	Sampling Strategy
MFMC	Analytic	Multifidelity

Ref: Peherstorfer, B.; Willcox, K.; and Gunzburger, M.: Optimal Model Management for Multifidelity Monte Carlo Estimation. SIAM Journal on Scientific Computing, vol. 38, 01 2016, pp. A3163–A3194

Approximate Control Variates

Algorithm Name	Optimization	Sampling Strategy
WRDIFF	Numerical	Recursive Difference
ACVIS	Numerical	Independent Samples
ACVMF	Numerical	Multifidelity
ACVKL	Numerical	Multifidelity

Ref: Gorodetsky, A.; Geraci, G.; Eldred, M.; and Jakeman, J. D.: A generalized approximate control variate framework for multifidelity uncertainty quantification. Journal of Computational Physics, 2020, p. 109257

Parametrically-defined Approximate Control Variates

Algorithm Name	Optimization	Sampling Strategy
GRDSR	Numerical	Recursive Difference
GRDMR	Numerical	Recursive Difference
GISSR	Numerical	Independent Samples
GISMR	Numerical	Independent Samples
ACVMFU	Numerical	Multifidelity
GMFSR	Numerical	Multifidelity
GMFMR	Numerical	Multifidelity

Ref: Bomarito, G. F., Leser, P. E., Warner, J. E., and Leser, W. P: On the Optimization of Approximate Control Variates with Parametrically-Defined Estimators. In Preparation.