Improving Simulation Efficiency With Quasi Control Variates

We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and an Euler discretisation, the computational cost to achieve an accuracy of O( ) is reduced from O( −3 ) to O( −2 (log ) 2 ). The analysis is supported by numerical results showing significant computational savings.

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“…This is closely related to a more generally applicable approach of quasi control variates analysed by Emsermann and Simon [5].…”

Section: Introductionmentioning

confidence: 99%

Multilevel Monte Carlo Path Simulation

Giles

2008

Operations Research

1,310

1,803

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“…That is, we make use of the relatively low computational cost of the low‐fidelity model to calculate a more accurate estimate of s B than the estimate with only n samples. Some other extensions to the control variate method generate an independent simulation with m samples to compute

{\overset{b}{true}}_{m}

. In our case, we simply require m − n additional samples of b i beyond the n samples already available.…”

Section: Multifidelity Estimatormentioning

confidence: 99%

Multifidelity approaches for optimization under uncertainty

Willcox

2014

Int. J. Numer. Meth. Engng

178

133

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SUMMARYIt is important to design robust and reliable systems by accounting for uncertainty and variability in the design process. However, performing optimization in this setting can be computationally expensive, requiring many evaluations of the numerical model to compute statistics of the system performance at every optimization iteration. This paper proposes a multifidelity approach to optimization under uncertainty that makes use of inexpensive, low-fidelity models to provide approximate information about the expensive, high-fidelity model. The multifidelity estimator is developed based on the control variate method to reduce the computational cost of achieving a specified mean square error in the statistic estimate. The method optimally allocates the computational load between the two models based on their relative evaluation cost and the strength of the correlation between them. This paper also develops an information reuse estimator that exploits the autocorrelation structure of the high-fidelity model in the design space to reduce the cost of repeatedly estimating statistics during the course of optimization. Finally, a combined estimator incorporates the features of both the multifidelity estimator and the information reuse estimator. The methods demonstrate 90% computational savings in an acoustic horn robust optimization example and practical design turnaround time in a robust wing optimization problem.

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“…Due to the construction of our model C, the theoretical value F C (t) is not available, but it can quickly be estimated [16]. For the estimation of the R(f Y ) term in (13), we use a normal-scale estimate of the density f Y of Y [6]:…”

Section: Details Of the Proposed Implementationmentioning

confidence: 99%

An efficient control variates method for yield estimation of analog circuits based on a local model

Desrumaux

Dupret

Tingleff

et al. 2012

Proceedings of the International Conference on Computer-Aided Design

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Statistical analysis of analog circuits usually relies on the standard Monte Carlo method to estimate the yield of a circuit. However, this method is limited by a slow convergence rate which leads to a prohibitive number of simulations to reach a given accuracy. In this paper, we propose to combine the kernelbased distribution estimator with the control variates method in order to obtain an accurate yield estimation with only a few hundred simulations. With respect to the auxiliary variable needed for the control variates method, we propose a quick modeling technique based on local sensitivities.

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Improving Simulation Efficiency With Quasi Control Variates

Cited by 17 publications

References 4 publications

Multilevel Monte Carlo Path Simulation

Multilevel Monte Carlo Path Simulation

Multifidelity approaches for optimization under uncertainty

An efficient control variates method for yield estimation of analog circuits based on a local model

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