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Monte Carlo Complexity of Parametric Integration

Stefan Heinrich, Eugène Sindambiwe
1999 Journal of Complexity  
The Monte Carlo complexity of computing integrals depending on a parameter is analyzed for smooth integrands.  ...  Moreover, because of savings due to computation on multiple grids, this rate is also higher than that of previously developed Monte Carlo algorithms for parametric integration.  ...  The following theorem settles the complexity of parametric integration and answers the question of how much better Monte Carlo methods are (as compared to deterministic schemes). Theorem 2.4.  ... 
doi:10.1006/jcom.1999.0508 fatcat:zgtyakg7gbbqjlz3drdrajfdfm

Complexity of Banach Space Valued and Parametric Integration [chapter]

Thomas Daun, Stefan Heinrich
2013 Monte Carlo and Quasi-Monte Carlo Methods 2012  
We study the complexity of Banach space valued integration. The input data are assumed to be r-smooth.  ...  For this purpose we use the Banach space results and develop a multilevel scheme which connects Banach space and parametric case.  ...  The complexity of parametric definite integration was analysed in [6] (this result is stated as part of Theorem 2 below), parametric indefinite integration has not been investigated before.  ... 
doi:10.1007/978-3-642-41095-6_12 fatcat:ueyln77eu5b7nmqtmvzef3ltci

Reweighting Lefschetz Thimbles [article]

Stefan Bluecher, Jan M. Pawlowski, Manuel Scherzer, Mike Schlosser, Ion-Olimpiu Stamatescu, Sebastian Syrkowski, Felix P.G. Ziegler
2019 arXiv   pre-print
We present a novel reweighting technique to calculate the relative weights in the Lefschetz thimble decomposition of a path integral.  ...  Monte Carlo sampling on the (main) contributing thimbles based on finding a numerical parametrization implicitly or explicitly. 2.  ...  Simulation method on Lefschetz thimbles In this section we present an algorithm for a Monte Carlo simulation on Lefschetz thimbles, assumed that we know a parametrization of all contributing thimbles.  ... 
arXiv:1901.05187v1 fatcat:3xucxwnxfbaphazetnw6hs47nm

Lattice Scalar Field Theory At Complex Coupling [article]

Scott Lawrence, Hyunwoo Oh, Yukari Yamauchi
2022 arXiv   pre-print
We demonstrate the methods of complex normalizing flows and contour deformations on scalar fields in 0+1 and 1+1 dimensions, respectively.  ...  Lattice scalar field theories encounter a sign problem when the coupling constant is complex.  ...  ACKNOWLEDGMENTS The authors are grateful to Brian Lawrence for pointing out the existence of integration contours that cannot be parametrized by the real plane, and suggesting the method of studying the  ... 
arXiv:2205.12303v2 fatcat:l562nulqzbddfddfcoadkecazm

Reweighting Lefschetz Thimbles [article]

Stefan Bluecher, Jan M. Pawlowski, Manuel Scherzer, Mike Schlosser, Ion-Olimpiu Stamatescu, Sebastian Syrkowski, Felix P.G. Ziegler
2018 arXiv   pre-print
Besides we present recipes for finding parametrizations of thimbles and anti-thimbles for a given theory.  ...  Moreover, we study some approaches to combine the Lefschetz thimble method with the Complex Langevin evolution.  ...  This work is supported by EMMI, the BMBF grant 05P12VHCTG, and is part of and supported by the DFG Collaborative Research Centre "SFB 1225 (ISOQUANT)". I.-O. Stamatescu and M.  ... 
arXiv:1803.08418v1 fatcat:ff5y665q3bhw7p74pmh3l6lj54

Multilevel Monte Carlo metamodeling

Imry Rosenbaum, Jeremy Staum
2013 2013 Winter Simulations Conference (WSC)  
Multilevel Monte Carlo (MLMC) methods have been used by the information-based complexity community in order to improve the computational efficiency of parametric integration.  ...  We extend this approach by relaxing the assumptions on differentiability of the simulation output.  ...  An effective parametric integration technique is the Multilevel Monte Carlo (MLMC) scheme suggested by Heinrich (2000) .  ... 
doi:10.1109/wsc.2013.6721446 dblp:conf/wsc/RosenbaumS13 fatcat:g6duz6shivh73khxpjihha3w2q

Monte Carlo method and sensitivity estimations

A de Lataillade, S Blanco, Y Clergent, J.L Dufresne, M El Hafi, R Fournier
2002 Journal of Quantitative Spectroscopy and Radiative Transfer  
It is shown that, starting from any existing Monte Carlo algorithm for estimation of a physical quantity A, it is possible to implement a simple additional procedure that simultaneously estimates the sensitivity  ...  of A to any problem parameter.  ...  In such contexts, the Monte Carlo method is of particular interest because of its ability to deal with complex geometries and=or complex spectral properties [10, 11] .  ... 
doi:10.1016/s0022-4073(02)00027-4 fatcat:5bnfjjc2hnchrapeujcoe2blem

Quantum Monte Carlo study of ring-shaped polariton parametric luminescence in a semiconductor microcavity

A. Verger, I. Carusotto, C. Ciuti
2007 Physical Review B  
We present a quantum Monte Carlo study of the quantum correlations in the parametric luminescence from semiconductor microcavities in the strong exciton-photon coupling regime.  ...  We compare the results of the complete multimode Monte Carlo simulations with a simplified linearized quantum Langevin analytical model.  ...  Number of Monte Carlo configurations : 50. Same cavity and integration parameters as in Fig.2.  ... 
doi:10.1103/physrevb.76.115324 fatcat:vtn7qb256vdzlfj3wby6iusa5q

Page 3766 of Mathematical Reviews Vol. , Issue 84i [page]

1984 Mathematical Reviews  
This paper describes the use of binary strings of high algorithmic complexity in order to simulate random inputs in Monte Carlo procedures.  ...  The author applies this technique to the Monte Carlo estimation of an unknown probability, deriving a threshold value for the complexity of the binary string. F.  ... 

Efficient variability analysis of photonic circuits by stochastic parametric building blocks

Abi Waqas, Daniele Melati, Bhawani Shankar Chowdhry, Andrea Melloni
2019 IEEE Journal of Selected Topics in Quantum Electronics  
building blocks with different parameters, without the need of time-consuming Monte Carlo approach.  ...  Relevant numerical examples are used to demonstrate that the proposed macro-models are truly parametric, inherently stochastic and have greater simulation efficiency compared to Monte Carlo.  ...  The results obtained by parametric BB-gPC are compared with Monte Carlo analysis on 10 4 samples. A.  ... 
doi:10.1109/jstqe.2019.2950761 fatcat:n4v4sxuahrgnvi6oc4dfsenxcq

Page 7795 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
The author gives quasi-Monte Carlo and pseudo-Monte Carlo algorithms to handle the problem. Special attention is drawn to a detailed dis- cussion of the first one.  ...  It is shown that the quasi-Monte Carlo method is most effective to treat objects with complex geometry. {For the entire collection see MR 97f:65002. } Sergei A. Nemnyugin (St.  ... 

Numerical integration over implicitly defined domains for higher order unfitted finite element methods [article]

Maxim Olshanskii, Danil Safin
2016 arXiv   pre-print
The integration methods are based on subdivision, moment--fitting, local quasi-parametrization and Monte-Carlo techniques.  ...  The paper studies the numerical complexity of the integration procedures and the performance of unfitted FEMs which employ these tools.  ...  Table 2 : 2 The number of function evaluations for the numerical integration using moment-fitting (MF), Monte-Carlo (MC), sub-triangulation (ST), and local parametrization (LP) algorithms to handle cut  ... 
arXiv:1601.06182v1 fatcat:b7el5wu72jd2tamjpzynvlmuhy

Subject Index [chapter]

2007 Advances in Chemical Physics  
CASPT2 technique, 298-299 quantum Monte Carlo (QMC) and. 2-3 semiempirical molecular orbital theory.  ...  tight-binding molecular dynamics 438-439 semiempirical molecular orbital theory: (TBMD): anharmonic effects in solids. 667-669 liquid silicon simulation. 670-674 electronic calculations, 337-345 limits of  ...  Monte Carlo (QMC) calculations. 27 tight-binding molecular dynamics (TBMD). electronic structure calculations. 684 integration. quantum Monte Carlo analysis. 51-54 Discretized path-integral representation  ... 
doi:10.1002/9780470141526.indsub fatcat:5yhbd6fqmnh75jzpezbpjz6xzu

CONTRIBUTIONS TO COMPUTATIONAL BAYESIAN STATISTICS

LEAH SOUTH
2020 Bulletin of the Australian Mathematical Society  
A common way to estimate these quantities is through Monte Carlo methods which use pseudo-random sampling to help estimate the underlying integrals.  ...  This thesis makes contributions to three areas of Monte Carlo inference: advancing methods for when the likelihood function is intractable, improving the efficiency and flexibility of sequential Monte  ...  A common way to estimate these quantities is through Monte Carlo methods which use pseudo-random sampling to help estimate the underlying integrals.  ... 
doi:10.1017/s0004972720000088 fatcat:irgqornozrbzfejrvqlve4xh5q

Page 471 of Mathematical Reviews Vol. , Issue 2001A [page]

2001 Mathematical Reviews  
. * Parametric estimates by the Monte Carlo method. VSP, Utrecht, 1999. vi+188 pp. $121.00.  ...  The Monte Carlo method employed for solution is based on first transforming the elliptic PDE into an integral equation.  ... 
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