Challenges in Developing Great Quasi-Monte Carlo Software

go back to reference SciML QuasiMonteCarlo.jl (2022). https://github.com/SciML/QuasiMonteCarlo.jl SciML QuasiMonteCarlo.jl (2022). https://​github.​com/​SciML/​QuasiMonteCarlo.​jl

go back to reference Adams, B.M., Bohnhoff, W.J., Dalbey, K.R., Ebeida, M.S., Eddy, J.P., Eldred, M.S., Hooper, R.W., Hough, P.D., Hu, K.T., Jakeman, J.D., Khalil, M., Maupin, K.A., Monschke, J.A., Ridgway, E.M., Rushdi, A.A., Seidl, D.T., Stephens, J.A., Swiler, L.P., Tran, A., Winokur, J.G.: Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.16 User’s Manual. Sandia National Laboratories (2022) Adams, B.M., Bohnhoff, W.J., Dalbey, K.R., Ebeida, M.S., Eddy, J.P., Eldred, M.S., Hooper, R.W., Hough, P.D., Hu, K.T., Jakeman, J.D., Khalil, M., Maupin, K.A., Monschke, J.A., Ridgway, E.M., Rushdi, A.A., Seidl, D.T., Stephens, J.A., Swiler, L.P., Tran, A., Winokur, J.G.: Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.16 User’s Manual. Sandia National Laboratories (2022)

go back to reference Bernholdt, D.E., Cary, J., Heroux, M., McInnes, L.C.: The science of scientific-software development and use (2022) Bernholdt, D.E., Cary, J., Heroux, M., McInnes, L.C.: The science of scientific-software development and use (2022)

go back to reference Bratley, P., Fox, B.L.: Algorithm 659: implementing Sobol’s quasirandom sequence generator. ACM Trans. Math. Softw. 14, 88–100 (1988)CrossRef Bratley, P., Fox, B.L.: Algorithm 659: implementing Sobol’s quasirandom sequence generator. ACM Trans. Math. Softw. 14, 88–100 (1988)CrossRef

go back to reference Bratley, P., Fox, B.L., Niederreiter, H.: Implementation and tests of low-discrepancy sequences. ACM Trans. Model. Comput. Simul. 2, 195–213 (1992)CrossRef Bratley, P., Fox, B.L., Niederreiter, H.: Implementation and tests of low-discrepancy sequences. ACM Trans. Model. Comput. Simul. 2, 195–213 (1992)CrossRef

go back to reference Choi, S.C.T., Ding, Y., Hickernell, F.J., Jagadeeswaran, R., Sorokin, A.G.: MCQMC 2022 figures. https://github.com/QMCSoftware/QMCSoftware/tree/develop/demos/talk_paper_demos/MCQMC2022_Article_Figures Choi, S.C.T., Ding, Y., Hickernell, F.J., Jagadeeswaran, R., Sorokin, A.G.: MCQMC 2022 figures. https://​github.​com/​QMCSoftware/​QMCSoftware/​tree/​develop/​demos/​talk_​paper_​demos/​MCQMC2022_​Article_​Figures

go back to reference Choi, S.C.T., Hickernell, F.J., Jagadeeswaran, R., McCourt, M., Sorokin, A.: QMCPy: a quasi-Monte Carlo Python library (versions 1–1.4) (2023). https://doi.org/10.5281/zenodo.3964489. https://qmcsoftware.github.io/QMCSoftware/ Choi, S.C.T., Hickernell, F.J., Jagadeeswaran, R., McCourt, M., Sorokin, A.: QMCPy: a quasi-Monte Carlo Python library (versions 1–1.4) (2023). https://​doi.​org/​10.​5281/​zenodo.​3964489. https://​qmcsoftware.​github.​io/​QMCSoftware/​

go back to reference Choi, S.C.T., Hickernell, F.J., Jagadeeswaran, R., McCourt, M.J., Sorokin, A.G.: Quasi-Monte Carlo software. In: A. Keller (ed.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Oxford, England, August 2020, Springer Proceedings in Mathematics and Statistics, pp. 23–50. Springer, Cham (2022). https://arxiv.org/abs/2102.07833 Choi, S.C.T., Hickernell, F.J., Jagadeeswaran, R., McCourt, M.J., Sorokin, A.G.: Quasi-Monte Carlo software. In: A. Keller (ed.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Oxford, England, August 2020, Springer Proceedings in Mathematics and Statistics, pp. 23–50. Springer, Cham (2022). https://​arxiv.​org/​abs/​2102.​07833

go back to reference Dick, J., Kritzer, P., Pillichshammer, F.: Lattice Rules: Numerical Integration, Approximation, and Discrepancy. Springer Series in Computational Mathematics. Springer Cham (2022). https://doi.org/10.1007/978-3-031-09951-9 Dick, J., Kritzer, P., Pillichshammer, F.: Lattice Rules: Numerical Integration, Approximation, and Discrepancy. Springer Series in Computational Mathematics. Springer Cham (2022). https://​doi.​org/​10.​1007/​978-3-031-09951-9

go back to reference Dick, J., Kuo, F., Sloan, I.H.: High dimensional integration – the Quasi-Monte Carlo way. Acta Numer. 22, 133–288 (2013). https://doi.org/10.1017/S0962492913000044MathSciNetCrossRef Dick, J., Kuo, F., Sloan, I.H.: High dimensional integration – the Quasi-Monte Carlo way. Acta Numer. 22, 133–288 (2013). https://​doi.​org/​10.​1017/​S096249291300004​4MathSciNetCrossRef

go back to reference Finley, K.: Non-code contributions are the secret to open source success. The ReadME Project, GitHub (2023). https://github.com/readme/featured/open-source-non-code-contributions Finley, K.: Non-code contributions are the secret to open source success. The ReadME Project, GitHub (2023). https://​github.​com/​readme/​featured/​open-source-non-code-contributions

go back to reference Friedel, I., Keller, A.: libseq – low discrepancy sequence library (2001). http://www.multires.caltech.edu/software/libseq/ Friedel, I., Keller, A.: libseq – low discrepancy sequence library (2001). http://​www.​multires.​caltech.​edu/​software/​libseq/​

go back to reference Friedel, I., Keller, A.: Fast generation of randomized low-discrepancy point sets. In: Fang, K.T., Hickernell, F.J., Niederreiter, H. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2000, pp. 257–273. Springer, Berlin (2002)CrossRef Friedel, I., Keller, A.: Fast generation of randomized low-discrepancy point sets. In: Fang, K.T., Hickernell, F.J., Niederreiter, H. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2000, pp. 257–273. Springer, Berlin (2002)CrossRef

go back to reference Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., Rubin, D.B.: Bayesian Data Analysis. CRC Texts in Statistical Science. Chapman & Hall (2013) Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., Rubin, D.B.: Bayesian Data Analysis. CRC Texts in Statistical Science. Chapman & Hall (2013)

go back to reference Glasserman, P.: Monte Carlo Methods in Financial Engineering, Applications of Mathematics, vol. 53. Springer, New York (2004) Glasserman, P.: Monte Carlo Methods in Financial Engineering, Applications of Mathematics, vol. 53. Springer, New York (2004)

go back to reference Grünschloß, L.: Leonhard grünschloß’s webpage. https://gruenschloss.org Grünschloß, L.: Leonhard grünschloß’s webpage. https://​gruenschloss.​org

go back to reference Hickernell, F.J., Choi, S.C.T., Jiang, L., Jiménez Rugama, Ll.A.: Monte Carlo simulation, automatic stopping criteria for. In: Davidian, M., Everitt, B., Kenett, R.S., Molenberghs, G., Piegorsch, W., Ruggeri, F. (eds.) Wiley StatsRef-Statistics Reference Online. John Wiley & Sons Ltd. (2018). https://doi.org/10.1002/9781118445112.stat08035 Hickernell, F.J., Choi, S.C.T., Jiang, L., Jiménez Rugama, Ll.A.: Monte Carlo simulation, automatic stopping criteria for. In: Davidian, M., Everitt, B., Kenett, R.S., Molenberghs, G., Piegorsch, W., Ruggeri, F. (eds.) Wiley StatsRef-Statistics Reference Online. John Wiley & Sons Ltd. (2018). https://​doi.​org/​10.​1002/​9781118445112.​stat08035

go back to reference Hickernell, F.J., Jiang, L., Liu, Y., Owen, A.B.: Guaranteed conservative fixed width confidence intervals via Monte Carlo sampling. In: Dick, J., Kuo, F.Y., Peters, G.W., Sloan, I.H. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2012, Springer Proceedings in Mathematics and Statistics, vol. 65, pp. 105–128. Springer, Berlin (2013). https://doi.org/10.1007/978-3-642-41095-6 Hickernell, F.J., Jiang, L., Liu, Y., Owen, A.B.: Guaranteed conservative fixed width confidence intervals via Monte Carlo sampling. In: Dick, J., Kuo, F.Y., Peters, G.W., Sloan, I.H. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2012, Springer Proceedings in Mathematics and Statistics, vol. 65, pp. 105–128. Springer, Berlin (2013). https://​doi.​org/​10.​1007/​978-3-642-41095-6

go back to reference Hickernell, F.J., Jiménez Rugama, Ll.A.: Reliable adaptive cubature using digital sequences. In: Cools, R., Nuyens, D. (eds.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014, Springer Proceedings in Mathematics and Statistics, vol. 163, pp. 367–383. Springer, Berlin (2016). ArXiv:1410.8615 [math.NA] Hickernell, F.J., Jiménez Rugama, Ll.A.: Reliable adaptive cubature using digital sequences. In: Cools, R., Nuyens, D. (eds.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014, Springer Proceedings in Mathematics and Statistics, vol. 163, pp. 367–383. Springer, Berlin (2016). ArXiv:​1410.​8615 [math.NA]

go back to reference Hickernell, F.J., Jiménez Rugama, Ll.A., Li, D.: Adaptive quasi-Monte Carlo methods for cubature. In: Dick, J., Kuo, F.Y., Woźniakowski, H. (eds.) Contemporary Computational Mathematics—A Celebration of the 80th Birthday of Ian Sloan, pp. 597–619. Springer (2018). https://doi.org/10.1007/978-3-319-72456-0 Hickernell, F.J., Jiménez Rugama, Ll.A., Li, D.: Adaptive quasi-Monte Carlo methods for cubature. In: Dick, J., Kuo, F.Y., Woźniakowski, H. (eds.) Contemporary Computational Mathematics—A Celebration of the 80th Birthday of Ian Sloan, pp. 597–619. Springer (2018). https://​doi.​org/​10.​1007/​978-3-319-72456-0

go back to reference Hofert, M., Lemieux, C.: qrng R package (2017). https://cran.r-project.org/web/packages/qrng/qrng.pdf Hofert, M., Lemieux, C.: qrng R package (2017). https://​cran.​r-project.​org/​web/​packages/​qrng/​qrng.​pdf

go back to reference Hong, H.S., Hickernell, F.J.: Algorithm 823: implementing scrambled digital nets. ACM Trans. Math. Softw. 29, 95–109 (2003). https://doi.org/10.1145/779359.779360CrossRef Hong, H.S., Hickernell, F.J.: Algorithm 823: implementing scrambled digital nets. ACM Trans. Math. Softw. 29, 95–109 (2003). https://​doi.​org/​10.​1145/​779359.​779360CrossRef

go back to reference Jagadeeswaran, R., Hickernell, F.J.: Fast automatic Bayesian cubature using lattice sampling. Stat. Comput. 29, 1215–1229 (2019). https://doi.org/10.1007/s11222-019-09895-9MathSciNetCrossRef Jagadeeswaran, R., Hickernell, F.J.: Fast automatic Bayesian cubature using lattice sampling. Stat. Comput. 29, 1215–1229 (2019). https://​doi.​org/​10.​1007/​s11222-019-09895-9MathSciNetCrossRef

go back to reference Jagadeeswaran, R., Hickernell, F.J.: Fast automatic Bayesian cubature using Sobol’ sampling. In: Botev, Z., Keller, A., Lemieux, C., Tuffin, B. (eds.) Advances in Modeling and Simulation: Festschrift in Honour of Pierre L’Ecuyer, pp. 301–318. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-10193-9_15 Jagadeeswaran, R., Hickernell, F.J.: Fast automatic Bayesian cubature using Sobol’ sampling. In: Botev, Z., Keller, A., Lemieux, C., Tuffin, B. (eds.) Advances in Modeling and Simulation: Festschrift in Honour of Pierre L’Ecuyer, pp. 301–318. Springer, Cham (2022). https://​doi.​org/​10.​1007/​978-3-031-10193-9_​15

go back to reference Jiang, L.: Guaranteed adaptive Monte Carlo methods for estimating means of random variables. Ph.D. thesis, Illinois Institute of Technology (2016) Jiang, L.: Guaranteed adaptive Monte Carlo methods for estimating means of random variables. Ph.D. thesis, Illinois Institute of Technology (2016)

go back to reference Jiménez Rugama, Ll.A., Gilquin, L.: Reliable error estimation for Sobol’ indices. Stat. Comput. 28, 725–738 (2018). https://doi.org/10.1007/s11222-017-9759-1 Jiménez Rugama, Ll.A., Gilquin, L.: Reliable error estimation for Sobol’ indices. Stat. Comput. 28, 725–738 (2018). https://​doi.​org/​10.​1007/​s11222-017-9759-1

go back to reference Jiménez Rugama, Ll.A., Hickernell, F.J.: Adaptive multidimensional integration based on rank-1 lattices. In: Cools, R., Nuyens, D. (eds.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014, Springer Proceedings in Mathematics and Statistics, vol. 163, pp. 407–422. Springer, Berlin (2016). ArXiv:1411.1966 Jiménez Rugama, Ll.A., Hickernell, F.J.: Adaptive multidimensional integration based on rank-1 lattices. In: Cools, R., Nuyens, D. (eds.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014, Springer Proceedings in Mathematics and Statistics, vol. 163, pp. 407–422. Springer, Berlin (2016). ArXiv:​1411.​1966

go back to reference Joe, S., Kuo, F.Y.: Sobol sequence generator. https://web.maths.unsw.edu.au/~fkuo/sobol/ Joe, S., Kuo, F.Y.: Sobol sequence generator. https://​web.​maths.​unsw.​edu.​au/​~fkuo/​sobol/​

go back to reference Joe, S., Kuo, F.Y.: Remark on algorithm 659: implementing Sobol’s quasirandom sequence generator. ACM Trans. Math. Softw. 29, 49–57 (2003)MathSciNetCrossRef Joe, S., Kuo, F.Y.: Remark on algorithm 659: implementing Sobol’s quasirandom sequence generator. ACM Trans. Math. Softw. 29, 49–57 (2003)MathSciNetCrossRef

go back to reference Joe, S., Kuo, F.Y.: Constructing Sobol sequences with better two-dimensional projections. SIAM J. Sci. Comput. 30, 2635–2654 (2008)MathSciNetCrossRef Joe, S., Kuo, F.Y.: Constructing Sobol sequences with better two-dimensional projections. SIAM J. Sci. Comput. 30, 2635–2654 (2008)MathSciNetCrossRef

go back to reference Kämmerer, L., Potts, D., Volkmer, T.: Approximation of multivariate periodic functions by trigonometric polynomials based on rank-1 lattice sampling. J. Complex. 31(4), 543–576 (2015) Kämmerer, L., Potts, D., Volkmer, T.: Approximation of multivariate periodic functions by trigonometric polynomials based on rank-1 lattice sampling. J. Complex. 31(4), 543–576 (2015)

go back to reference Kollig, T., Keller, A.: Samplepack (2002). https://www.uni-kl.de/AG-Heinrich/SamplePack.html Kollig, T., Keller, A.: Samplepack (2002). https://​www.​uni-kl.​de/​AG-Heinrich/​SamplePack.​html

go back to reference Kucherenko, S.: BRODA (2022). https://www.broda.co.uk/index.html Kucherenko, S.: BRODA (2022). https://​www.​broda.​co.​uk/​index.​html

go back to reference Kuo, F.Y., Nuyens, D.: Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients – a survey of analysis and implementation. Found. Comput. Math. 16, 1631–1696 (2016). https://people.cs.kuleuven.be/~dirk.nuyens/qmc4pde/ Kuo, F.Y., Nuyens, D.: Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients – a survey of analysis and implementation. Found. Comput. Math. 16, 1631–1696 (2016). https://​people.​cs.​kuleuven.​be/​~dirk.​nuyens/​qmc4pde/​

go back to reference L’Ecuyer, P., Marion, P., Godin, M., Puchhammer, F.: A tool for custom construction of QMC and RQMC point sets. In: Keller, A. (ed.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Oxford, 2020, Springer Proceedings in Mathematics and Statistics. Springer, Cham (2022) L’Ecuyer, P., Marion, P., Godin, M., Puchhammer, F.: A tool for custom construction of QMC and RQMC point sets. In: Keller, A. (ed.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Oxford, 2020, Springer Proceedings in Mathematics and Statistics. Springer, Cham (2022)

go back to reference L’Ecuyer, P., Meliani, L., Vaucher, J.: Ssj: a framework for stochastic simulation in Java. In: Proceedings of the Winter Simulation Conference, vol. 1, pp. 234–242. IEEE (2002) L’Ecuyer, P., Meliani, L., Vaucher, J.: Ssj: a framework for stochastic simulation in Java. In: Proceedings of the Winter Simulation Conference, vol. 1, pp. 234–242. IEEE (2002)

go back to reference L’Ecuyer, P., Munger, D., Lécot, C., Tuffin, B.: Sorting methods and convergence rates for Array-RQMC: some empirical comparisons. Math. Comput. Simul. 143, 191–201 (2018)MathSciNetCrossRef L’Ecuyer, P., Munger, D., Lécot, C., Tuffin, B.: Sorting methods and convergence rates for Array-RQMC: some empirical comparisons. Math. Comput. Simul. 143, 191–201 (2018)MathSciNetCrossRef

go back to reference L’Ecuyer, P., Puchhammer, F., Ben Abdellah, A.: Monte carlo and quasi–monte carlo density estimation via conditioning. INFORMS J. Comput. 34(3), 1729–1748 (2022) L’Ecuyer, P., Puchhammer, F., Ben Abdellah, A.: Monte carlo and quasi–monte carlo density estimation via conditioning. INFORMS J. Comput. 34(3), 1729–1748 (2022)

go back to reference Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods. CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, Philadelphia (1992) Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods. CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, Philadelphia (1992)

go back to reference Novak, E., Woźniakowski, H.: Tractability of Multivariate Problems Volume II: Standard Information for Functionals. No. 12 in EMS Tracts in Mathematics. European Mathematical Society, Zürich (2010) Novak, E., Woźniakowski, H.: Tractability of Multivariate Problems Volume II: Standard Information for Functionals. No. 12 in EMS Tracts in Mathematics. European Mathematical Society, Zürich (2010)

go back to reference Nuyens, D.: Dirk’s homepage. https://people.cs.kuleuven.be/~dirk.nuyens/ Nuyens, D.: Dirk’s homepage. https://​people.​cs.​kuleuven.​be/​~dirk.​nuyens/​

go back to reference Owen, A.B.: On dropping the first Sobol’ point. In: Keller, A. (ed.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Oxford, England, August 2020, Springer Proceedings in Mathematics and Statistics, pp. 71–86. Springer, Cham (2022). https://arxiv.org/pdf/2008.08051.pdf Owen, A.B.: On dropping the first Sobol’ point. In: Keller, A. (ed.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Oxford, England, August 2020, Springer Proceedings in Mathematics and Statistics, pp. 71–86. Springer, Cham (2022). https://​arxiv.​org/​pdf/​2008.​08051.​pdf

go back to reference Papageorgiou, A.: Finder. http://www.cs.columbia.edu/~ap/html/finder.html Papageorgiou, A.: Finder. http://​www.​cs.​columbia.​edu/​~ap/​html/​finder.​html

go back to reference Parno, M., Davis, A., Seelinger, L.: MUQ: The MIT Uncertainty Quantification library. J. Open Sour. Softw. 6(68), 3076 (2021). https://doi.org/10.21105/joss.03076 Parno, M., Davis, A., Seelinger, L.: MUQ: The MIT Uncertainty Quantification library. J. Open Sour. Softw. 6(68), 3076 (2021). https://​doi.​org/​10.​21105/​joss.​03076

go back to reference Parno, M., Seelinger, L.: Uncertainty propagation of material properties of a cantilevered beam (2022). https://um-bridge-benchmarks.readthedocs.io/en/docs/forward-benchmarks/muq-beam-propagation.html Parno, M., Seelinger, L.: Uncertainty propagation of material properties of a cantilevered beam (2022). https://​um-bridge-benchmarks.​readthedocs.​io/​en/​docs/​forward-benchmarks/​muq-beam-propagation.​html

go back to reference Paskov, S., Traub, J.: Faster valuation of financial derivatives. J. Portfolio Manag. 22, 113–120 (1995)CrossRef Paskov, S., Traub, J.: Faster valuation of financial derivatives. J. Portfolio Manag. 22, 113–120 (1995)CrossRef

go back to reference Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Köpf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: an imperative style, high-performance deep learning library. Adv. Neural Inf. Process. Syst. 32, 8026–8037 (2019) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Köpf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: an imperative style, high-performance deep learning library. Adv. Neural Inf. Process. Syst. 32, 8026–8037 (2019)

go back to reference Paulin, L., Bonneel, N., Coeurjolly, D., Iehl, J.C., Keller, A., Ostromoukhov, V.: Matbuilder: mastering sampling uniformity over projections. ACM Trans. Graph. (Proceedings of SIGGRAPH) 41(4) (2022). https://doi.org/10.1145/3528223.3530063 Paulin, L., Bonneel, N., Coeurjolly, D., Iehl, J.C., Keller, A., Ostromoukhov, V.: Matbuilder: mastering sampling uniformity over projections. ACM Trans. Graph. (Proceedings of SIGGRAPH) 41(4) (2022). https://​doi.​org/​10.​1145/​3528223.​3530063

go back to reference Potts, D., Schmischke, M.: Approximation of high-dimensional periodic functions with fourier-based methods. SIAM J. Numer. Anal. 59(5), 2393–2429 (2021) Potts, D., Schmischke, M.: Approximation of high-dimensional periodic functions with fourier-based methods. SIAM J. Numer. Anal. 59(5), 2393–2429 (2021)

go back to reference Puchhammer, F., Ben Abdellah, A., L’Ecuyer, P.: Variance reduction with Array-RQMC for tau-leaping simulation of stochastic biological and chemical reaction networks. Bull. Math. Biol. 83(8), 91 (2021)MathSciNetCrossRef Puchhammer, F., Ben Abdellah, A., L’Ecuyer, P.: Variance reduction with Array-RQMC for tau-leaping simulation of stochastic biological and chemical reaction networks. Bull. Math. Biol. 83(8), 91 (2021)MathSciNetCrossRef

go back to reference PyTorch Developers: Sobol point implementation (2020). https://github.com/pytorch/pytorch/issues/32047 PyTorch Developers: Sobol point implementation (2020). https://​github.​com/​pytorch/​pytorch/​issues/​32047

go back to reference SAS Institute: Sas documentation for the model procedure (2023). https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.4/etsug/etsug_model_sect197.htm SAS Institute: Sas documentation for the model procedure (2023). https://​documentation.​sas.​com/​doc/​en/​pgmsascdc/​9.​4_​3.​4/​etsug/​etsug_​model_​sect197.​htm

go back to reference SciPy Developers: SciPy discussion of Sobol’ sequence implementation (2020). https://github.com/scipy/scipy/pull/10844 SciPy Developers: SciPy discussion of Sobol’ sequence implementation (2020). https://​github.​com/​scipy/​scipy/​pull/​10844

go back to reference Seelinger, L., Cheng-Seelinger, V., Davis, A., Parno, M., Reinarz, A.: UM-Bridge: Uncertainty quantification and modeling bridge. J. Open Source Softw. 8(83), 4748 (2023). https://doi.org/10.21105/joss.04748 Seelinger, L., Cheng-Seelinger, V., Davis, A., Parno, M., Reinarz, A.: UM-Bridge: Uncertainty quantification and modeling bridge. J. Open Source Softw. 8(83), 4748 (2023). https://​doi.​org/​10.​21105/​joss.​04748

go back to reference Seelinger, L., Reinarz, A., Benezech, J., Lykkegaard, M.B., Tamellini, L., Scheichl, R.: Lowering the entry bar to HPC-scale uncertainty quantification (2023) Seelinger, L., Reinarz, A., Benezech, J., Lykkegaard, M.B., Tamellini, L., Scheichl, R.: Lowering the entry bar to HPC-scale uncertainty quantification (2023)

go back to reference Sloan, I.H., Joe, S.: Lattice Methods for Multiple Integration. Oxford University Press, Oxford (1994)CrossRef Sloan, I.H., Joe, S.: Lattice Methods for Multiple Integration. Oxford University Press, Oxford (1994)CrossRef

go back to reference Smith, A.M., Katz, D.S., Niemeyer, K.E.: Software citation principles. PeerJ Comput. Sci. 2, e86 (2016)CrossRef Smith, A.M., Katz, D.S., Niemeyer, K.E.: Software citation principles. PeerJ Comput. Sci. 2, e86 (2016)CrossRef

go back to reference Sorokin, A.G., Jagadeeswaran, R.: Monte Carlo for vector functions of integrals. In: Hinrichs, A., Kritzer, P., Pillichshammer, F. (eds.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Linz, Austria, July 2022, Springer Proceedings in Mathematics and Statistics. Springer, Cham (2023+). Submitted for publication Sorokin, A.G., Jagadeeswaran, R.: Monte Carlo for vector functions of integrals. In: Hinrichs, A., Kritzer, P., Pillichshammer, F. (eds.) Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Linz, Austria, July 2022, Springer Proceedings in Mathematics and Statistics. Springer, Cham (2023+). Submitted for publication

go back to reference TF Quant Finance Contributors: Quasi Monte-Carlo methods (2021). https://github.com/google/tf-quant-finance/math/qmc TF Quant Finance Contributors: Quasi Monte-Carlo methods (2021). https://​github.​com/​google/​tf-quant-finance/​math/​qmc

go back to reference The MathWorks Inc: MATLAB R2022b. Natick, MA (2022) The MathWorks Inc: MATLAB R2022b. Natick, MA (2022)

go back to reference The Numerical Algorithms Group: The NAG Library, 27th edn. Oxford, Mark (2021) The Numerical Algorithms Group: The NAG Library, 27th edn. Oxford, Mark (2021)

go back to reference Tong, X., Choi, S.C.T., Ding, Y., Hickernell, F.J., Jiang, L., Jiménez Rugama, Ll.A., Jagadeeswaran, R., Zhang, K., Zhang, Y., Zhou, X.: Guaranteed automatic integration library (GAIL): an open-source MATLAB library for function approximation, minimization, and integration. J. Open Res. Softw. 10, 7 (2022). https://doi.org/10.5334/jors.381 Tong, X., Choi, S.C.T., Ding, Y., Hickernell, F.J., Jiang, L., Jiménez Rugama, Ll.A., Jagadeeswaran, R., Zhang, K., Zhang, Y., Zhou, X.: Guaranteed automatic integration library (GAIL): an open-source MATLAB library for function approximation, minimization, and integration. J. Open Res. Softw. 10, 7 (2022). https://​doi.​org/​10.​5334/​jors.​381

go back to reference U.S. Department of Energy, Office of Advanced Scientific Computing Research: Workshop on the science of scientific-software development and use (2021). https://web.cvent.com/event/1b7d7c3a-e9b4-409d-ae2b-284779cfe72f/summary U.S. Department of Energy, Office of Advanced Scientific Computing Research: Workshop on the science of scientific-software development and use (2021). https://​web.​cvent.​com/​event/​1b7d7c3a-e9b4-409d-ae2b-284779cfe72f/​summary

go back to reference Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, I., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., Vijaykumar, A., Bardelli, A.P., Rothberg, A., Hilboll, A., Kloeckner, A., Scopatz, A., Lee, A., Rokem, A., Woods, C.N., Fulton, C., Masson, C., Häggström, C., Fitzgerald, C., Nicholson, D.A., Hagen, D.R., Pasechnik, D.V., Olivetti, E., Martin, E., Wieser, E., Silva, F., Lenders, F., Wilhelm, F., Young, G., Price, G.A., Ingold, G.L., Allen, G.E., Lee, G.R., Audren, H., Probst, I., Dietrich, J.P., Silterra, J., Webber, J.T., Slavič, J., Nothman, J., Buchner, J., Kulick, J., Schönberger, J.L., de Miranda Cardoso, J., Reimer, J., Harrington, J., Rodríguez, J.L.C., Nunez-Iglesias, J., Kuczynski, J., Tritz, K., Thoma, M., Newville, M., Kümmerer, M., Bolingbroke, M., Tartre, M., Pak, M., Smith, N.J., Nowaczyk, N., Shebanov, N., Pavlyk, O., Brodtkorb, P.A., Lee, P., McGibbon, R.T., Feldbauer, R., Lewis, S., Tygier, S., Sievert, S., Vigna, S., Peterson, S., More, S., Pudlik, T., Oshima, T., Pingel, T.J., Robitaille, T.P., Spura, T., Jones, T.R., Cera, T., Leslie, T., Zito, T., Krauss, T., Upadhyay, U., Halchenko, Y.O., Vázquez-Baeza, Y., Contributors: Scipy 1.0: fundamental algorithms for scientific computing in python. Nat. Methods 17(3), 261–272 (2020) Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, I., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., Vijaykumar, A., Bardelli, A.P., Rothberg, A., Hilboll, A., Kloeckner, A., Scopatz, A., Lee, A., Rokem, A., Woods, C.N., Fulton, C., Masson, C., Häggström, C., Fitzgerald, C., Nicholson, D.A., Hagen, D.R., Pasechnik, D.V., Olivetti, E., Martin, E., Wieser, E., Silva, F., Lenders, F., Wilhelm, F., Young, G., Price, G.A., Ingold, G.L., Allen, G.E., Lee, G.R., Audren, H., Probst, I., Dietrich, J.P., Silterra, J., Webber, J.T., Slavič, J., Nothman, J., Buchner, J., Kulick, J., Schönberger, J.L., de Miranda Cardoso, J., Reimer, J., Harrington, J., Rodríguez, J.L.C., Nunez-Iglesias, J., Kuczynski, J., Tritz, K., Thoma, M., Newville, M., Kümmerer, M., Bolingbroke, M., Tartre, M., Pak, M., Smith, N.J., Nowaczyk, N., Shebanov, N., Pavlyk, O., Brodtkorb, P.A., Lee, P., McGibbon, R.T., Feldbauer, R., Lewis, S., Tygier, S., Sievert, S., Vigna, S., Peterson, S., More, S., Pudlik, T., Oshima, T., Pingel, T.J., Robitaille, T.P., Spura, T., Jones, T.R., Cera, T., Leslie, T., Zito, T., Krauss, T., Upadhyay, U., Halchenko, Y.O., Vázquez-Baeza, Y., Contributors: Scipy 1.0: fundamental algorithms for scientific computing in python. Nat. Methods 17(3), 261–272 (2020)

go back to reference Woźniakowski, H.: Efficiency of quasi-Monte Carlo algorithms for high dimensions. In: Niederreiter, H., Spanier, J. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 1998, pp. 114–136. Springer, Berlin (2000)CrossRef Woźniakowski, H.: Efficiency of quasi-Monte Carlo algorithms for high dimensions. In: Niederreiter, H., Spanier, J. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 1998, pp. 114–136. Springer, Berlin (2000)CrossRef