Efficient quasi-Monte Carlo sampling for quantum random walks

2020 ◽  
Author(s):  
E. Atanassov ◽  
M. Durchova
Keyword(s):  
Monte Carlo ◽  
Random Walks ◽  
Monte Carlo Sampling ◽  
Quantum Random Walks ◽  
Quasi Monte Carlo

Parametric uncertainty quantification in the Rothermel model with randomised quasi-Monte Carlo methods

2015 ◽  
Vol 24 (3) ◽  
pp. 307 ◽  
Author(s):  
Yaning Liu ◽  
Edwin Jimenez ◽  
M. Yousuff Hussaini ◽  
Giray Ökten ◽  
Scott Goodrick
Keyword(s):  
Monte Carlo ◽  
Uncertainty Quantification ◽  
Monte Carlo Methods ◽  
Wildland Fire ◽  
Parametric Uncertainty ◽  
Monte Carlo Sampling ◽  
Model Parameters ◽  
Quasi Monte Carlo ◽  
Control Variate ◽  
Fuel Model

Rothermel's wildland surface fire model is a popular model used in wildland fire management. The original model has a large number of parameters, making uncertainty quantification challenging. In this paper, we use variance-based global sensitivity analysis to reduce the number of model parameters, and apply randomised quasi-Monte Carlo methods to quantify parametric uncertainties for the reduced model. The Monte Carlo estimator used in these calculations is based on a control variate approach applied to the sensitivity derivative enhanced sampling. The chaparral fuel model, selected from Rothermel's 11 original fuel models, is studied as an example. We obtain numerical results that improve the crude Monte Carlo sampling by factors as high as three orders of magnitude.

Optimization based on quasi-Monte Carlo sampling to design state estimators for non-linear systems

Optimization ◽  
2010 ◽  
Vol 59 (7) ◽  
pp. 963-984 ◽  
Author(s):  
A. Alessandri ◽  
C. Cervellera ◽  
D. Macciò ◽  
M. Sanguineti
Keyword(s):  
Monte Carlo ◽  
Linear Systems ◽  
Monte Carlo Sampling ◽  
Quasi Monte Carlo ◽  
State Estimators ◽  
Non Linear ◽  
Non Linear Systems

scholarly journals Sensitivity Study on the Influence of Cloud Microphysical Parameters on Mixed-Phase Cloud Thermodynamic Phase Partitioning in CAM5

2016 ◽  
Vol 73 (2) ◽  
pp. 709-728 ◽  
Author(s):  
Ivy Tan ◽  
Trude Storelvmo
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Time Scale ◽  
Monte Carlo Sampling ◽  
Sensitivity Study ◽  
Mixed Phase ◽  
Phase Partitioning ◽  
Quasi Monte Carlo ◽  
Microphysical Parameters ◽  
Mixed Phase Clouds

Abstract The influence of six CAM5.1 cloud microphysical parameters on the variance of phase partitioning in mixed-phase clouds is determined by application of a variance-based sensitivity analysis. The sensitivity analysis is based on a generalized linear model that assumes a polynomial relationship between the six parameters and the two-way interactions between them. The parameters, bounded such that they yield realistic cloud phase values, were selected by adopting a quasi–Monte Carlo sampling approach. The sensitivity analysis is applied globally, and to 20°-latitude-wide bands, and over the Southern Ocean at various mixed-phase cloud isotherms and reveals that the Wegener–Bergeron–Findeisen (WBF) time scale for the growth of ice crystals single-handedly accounts for the vast majority of the variance in cloud phase partitioning in mixed-phase clouds, while its interaction with the WBF time scale for the growth of snowflakes plays a secondary role. The fraction of dust aerosols active as ice nuclei in latitude bands, and the parameter related to the ice crystal fall speed and their interactions with the WBF time scale for ice are also significant. All other investigated parameters and their interactions with each other are negligible (<3%). Further analysis comparing three of the quasi–Monte Carlo–sampled simulations with spaceborne lidar observations by CALIOP suggests that the WBF process in CAM5.1 is currently parameterized such that it occurs too rapidly due to failure to account for subgrid-scale variability of liquid and ice partitioning in mixed-phase clouds.

Quasi-Monte Carlo simulation of the light environment of plants

2008 ◽  
Vol 35 (10) ◽  
pp. 837 ◽  
Author(s):  
Mikolaj Cieslak ◽  
Christiane Lemieux ◽  
Jim Hanan ◽  
Przemyslaw Prusinkiewicz
Keyword(s):  
Monte Carlo ◽  
Spectral Composition ◽  
Monte Carlo Sampling ◽  
Light Environment ◽  
Quasi Monte Carlo ◽  
Path Tracing ◽  
Environment Model ◽  
L System ◽  
Similar Program ◽  
Tracing Algorithm

The distribution of light in the canopy is a major factor regulating the growth and development of a plant. The main variables of interest are the amount of photosynthetically active radiation (PAR) reaching different elements of the plant canopy, and the quality (spectral composition) of light reaching these elements. A light environment model based on Monte Carlo (MC) path tracing of photons, capable of computing both PAR and the spectral composition of light, was developed by Měch (1997), and can be conveniently interfaced with virtual plants expressed using the open L-system formalism. To improve the efficiency of the light distribution calculations provided by Měch’s MonteCarlo program, we have implemented a similar program QuasiMC, which supports a more efficient randomised quasi-Monte Carlo sampling method (RQMC). We have validated QuasiMC by comparing it with MonteCarlo and with the radiosity-based CARIBU software (Chelle et al. 2004), and we show that these two programs produce consistent results. We also assessed the performance of the RQMC path tracing algorithm by comparing it with Monte Carlo path tracing and confirmed that RQMC offers a speed and/or accuracy improvement over MC.

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