Professor Frances Kuo

Professor

PhD in Mathematics, University of Waikato, New Zealand, 2002
BCMS (Hons), University of Waikato, New Zealand, 1999

Science

School of Mathematics & Statistics

CURRENT POSITION

Professor in Applied Mathematics

Frances Kuo completed a BCMS(Hons) in 1999 and a PhD in 2002 at the University of Waikato in New Zealand, and subsequently joined the School of Mathematics and Statistics at the University of New South Wales in 2003. Started as a Research Fellow, Frances obtained a UNSW Vice-Chancellor's Research Fellowship in 2004-2006, an ARC QEII Fellowship in 2007-2011, and was appointed a Senior Lecturer in 2012. She is an ARC Future Fellow since 2013, Associate Professor since 2015, and Professor since 2019. Frances was the recipient of the inaugural Information-based Complexity Young Researcher Award in 2003, and the ANZIAM J.H. Michell Medal in 2011, and the Information-based Complexity Prize in 2014. She works in the theory and applications of high dimensional integration and approximation, especially quasi-Monte Carlo methods, multilevel and multivariate decomposition techniques. Her recent interests are in their application to partial differential equations with random coefficients and uncertainty quantification.

Phone

+61 2 9385 7082

E-mail

f.kuo@unsw.edu.au

Location

School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 Australia Red Center East Wing RC-3061

Books | 2018

Sloan IH, 2018, A fortunate scientific life, http://dx.doi.org/10.1007/978-3-319-72456-0

Books | 2012

Chen JX; Gao B; Cheng YM; Zhang BJ; Yang AM; Wei KX; Gui MN; Wang L; Qu XL; CZhou G; Qu JG; Zhong SB; Yang AM; Jue JN; Zhang CX; Chen JX; Zhou L; Tang RC; Yoshino HR; Yang AM; Devetsikiotis MN; Wang CJ; Chen M; Duan ZX; Ghani NX; Kabacinski WJ; Subramaniam SR; Gao MY; Yan SH; Guo YJ; Yin HB; Mark BA; Khalil AH; Pickavet MK; Zhu R; Gagnaire MJ; Xu LJ; Khan SM; Shupke DB; Qu JG; Assi CH; Zhang YZ; Gui GF; Bao HY; Hu XW; Zou YW; Li LW; Zheng SZ; Bai XY; Shami AS; Brunner MX; Forte AR; Gong DX; Guardini IR; Hossain ER; Niyato DW; Le LX; Liao MZ; Feng LC; Lin Y; Li YJ; He JW; Hui PB; Chen LJ; Jin YL; Choi B; Shi MY; Melia TR; Eddy WM; Haddadi HR; Ott JH; Hua SY; Li KJ; Gao GH; Stiemerling MJ; Kuo F; Shi LX; Danilewicz GX; Xu YZ; Xu KW; Wang HJ; Wu CX; Zhang WM; Liu DL; Tang YX; Wei WX; Zhao YL; Baiocchi AD; Feng LC; Liao MZ, 2012, Preface
Book Chapters | 2024

Gilbert AD; Kuo FY; Sloan IH; Srikumar A, 2024, 'Theory and Construction of Quasi-Monte Carlo Rules for Asian Option Pricing and Density Estimation', in , pp. 277 - 295, http://dx.doi.org/10.1007/978-3-031-59762-6_13

Book Chapters | 2024

Kaarnioja V; Kuo FY; Sloan IH, 2024, 'Lattice-Based Kernel Approximation and Serendipitous Weights for Parametric PDEs in Very High Dimensions', in , pp. 81 - 103, http://dx.doi.org/10.1007/978-3-031-59762-6_4

Book Chapters | 2024

Kuo FY; Mo W; Nuyens D; Sloan IH; Srikumar A, 2024, 'Comparison of Two Search Criteria for Lattice-Based Kernel Approximation', in , pp. 413 - 429, http://dx.doi.org/10.1007/978-3-031-59762-6_20

Book Chapters | 2022

Gilbert AD; Kuo FY; Sloan IH, 2022, 'Preintegration is Not Smoothing When Monotonicity Fails', in Advances in Modeling and Simulation Festschrift for Pierre L Ecuyer, pp. 169 - 191, http://dx.doi.org/10.1007/978-3-031-10193-9_9

Book Chapters | 2020

Cools R; Kuo FY; Sloan IH; Nuyens D, 2020, 'Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters', in Brenner SC; Shparlinski I; Shu C-W; Szyld D (ed.), 75 Years of Mathematics of Computation, American Mathematical Society, pp. 93 - 113, http://dx.doi.org/10.1090/conm/754/15150

Book Chapters | 2006

Kuo FY; Sloan IH; Woźniakowski H, 2006, 'Lattice Rules for Multivariate Approximation in the Worst Case Setting', in Monte Carlo and Quasi-Monte Carlo Methods 2004, Springer Nature, pp. 289 - 330, http://dx.doi.org/10.1007/3-540-31186-6_18
Journal articles | 2025

Gilbert AD; Kuo FY; Srikumar A, 2025, 'DENSITY ESTIMATION FOR ELLIPTIC PDE WITH RANDOM INPUT BY PREINTEGRATION AND QUASI-MONTE CARLO METHODS', SIAM Journal on Numerical Analysis, 63, pp. 1025 - 1054, http://dx.doi.org/10.1137/24M1640070

Journal articles | 2025

Kuo FY; Mo W; Nuyens D, 2025, 'Constructing Embedded Lattice-Based Algorithms for Multivariate Function Approximation with a Composite Number of Points', Constructive Approximation, 61, pp. 81 - 113, http://dx.doi.org/10.1007/s00365-024-09688-y

Journal articles | 2024

Brown B; Griebel M; Kuo FY; Sloan IANH, 2024, 'ON THE EXPECTED UNIFORM ERROR OF BROWNIAN MOTION APPROXIMATED BY THE LÉVY-CIESIELSKI CONSTRUCTION', Bulletin of the Australian Mathematical Society, 109, pp. 581 - 593, http://dx.doi.org/10.1017/S0004972723000850

Journal articles | 2024

Ganesh M; Kuo FY; Sloan IH, 2024, 'Quasi--Monte Carlo Finite Element Analysis for Wave Propagation in Heterogeneous Random Media (Vol 9, pg 106, 2021)', SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 12, pp. 212 - 212, http://dx.doi.org/10.1137/23M1624609

Journal articles | 2024

Guth PA; Kaarnioja V; Kuo FY; Schillings C; Sloan IH, 2024, 'Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration', Numerische Mathematik, 156, pp. 565 - 608, http://dx.doi.org/10.1007/s00211-024-01397-9

Journal articles | 2024

Hakula H; Harbrecht H; Kaarnioja V; Kuo FY; Sloan IH, 2024, 'Uncertainty quantification for random domains using periodic random variables', Numerische Mathematik, 156, pp. 273 - 317, http://dx.doi.org/10.1007/s00211-023-01392-6

Journal articles | 2023

Gilbert AD; Kuo FY; Sloan IH, 2023, 'ANALYSIS OF PREINTEGRATION FOLLOWED BY QUASI-MONTE CARLO INTEGRATION FOR DISTRIBUTION FUNCTIONS AND DENSITIES', SIAM Journal on Numerical Analysis, 61, pp. 135 - 166, http://dx.doi.org/10.1137/21M146658X

Journal articles | 2023

Kuo FY; Nuyens D; Wilkes L, 2023, 'Random-prime–fixed-vector randomised lattice-based algorithm for high-dimensional integration', Journal of Complexity, 79, http://dx.doi.org/10.1016/j.jco.2023.101785

Journal articles | 2022

Gilbert AD; Kuo FY; Sloan IH, 2022, 'EQUIVALENCE BETWEEN SOBOLEV SPACES OF FIRST-ORDER DOMINATING MIXED SMOOTHNESS AND UNANCHORED ANOVA SPACES ON Rd', Mathematics of Computation, 91, pp. 1837 - 1869, http://dx.doi.org/10.1090/MCOM/3718

Journal articles | 2022

Kaarnioja V; Kazashi Y; Kuo FY; Nobile F; Sloan IH, 2022, 'Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification', Numerische Mathematik, 150, pp. 33 - 77, http://dx.doi.org/10.1007/s00211-021-01242-3

Journal articles | 2021

Ganesh M; Kuo FY; Sloan IH, 2021, 'Quasi-monte carlo finite element analysis for wave propagation in heterogeneous random media', SIAM Asa Journal on Uncertainty Quantification, 9, pp. 106 - 134, http://dx.doi.org/10.1137/20M1334164

Journal articles | 2021

Gilbert AD; Kuo FY; Sloan IH, 2021, 'Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on $\mathbb{R}^d$', , http://arxiv.org/abs/2103.16075v3

Journal articles | 2021

Guth PA; Kaarnioja V; Kuo FY; Schillings C; Sloan IH, 2021, 'A quasi-monte carlo method for optimal control under uncertainty', SIAM Asa Journal on Uncertainty Quantification, 9, pp. 354 - 383, http://dx.doi.org/10.1137/19M1294952

Journal articles | 2021

Hartung T; Jansen K; Kuo FY; Leövey H; Nuyens D; Sloan IH, 2021, 'Lattice meets lattice: Application of lattice cubature to models in lattice gauge theory', Journal of Computational Physics, 443, http://dx.doi.org/10.1016/j.jcp.2021.110527

Journal articles | 2021

Kuo FY; Migliorati G; Nobile F; Nuyens D, 2021, 'FUNCTION INTEGRATION, RECONSTRUCTION AND APPROXIMATION USING RANK-1 LATTICES', Mathematics of Computation, 90, pp. 1861 - 1897, http://dx.doi.org/10.1090/mcom/3595

Journal articles | 2020

Bilyk D; Hinrichs A; Kuo FY; Ritter K, 2020, 'Guest editors’ preface', Journal of Complexity, 61, http://dx.doi.org/10.1016/j.jco.2020.101511

Journal articles | 2020

Cools R; Kuo FY; Nuyens D; Sloan IH, 2020, 'Fast Component-by-Component Construction of Lattice Algorithms for Multivariate Approximation with Pod and Spod Weights', Mathematics of Computation, 90, pp. 787 - 812, http://dx.doi.org/10.1090/MCOM/3586

Journal articles | 2020

Kaarnioja V; Kazashi Y; Kuo FY; Nobile F; Sloan IH, 2020, 'Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification', Numerische Mathematik, 150, pp. 33 - 77, http://dx.doi.org/10.1007/s00211-021-01242-3

Journal articles | 2020

Kaarnioja V; Kuo FY; Sloan IH, 2020, 'Uncertainty quantification using periodic random variables', SIAM Journal on Numerical Analysis, 58, pp. 1068 - 1091, http://dx.doi.org/10.1137/19M1262796

Journal articles | 2020

Kuo FY; Wasilkowski GW; Woźniakowski H, 2020, 'Correction to: Lattice Algorithms for Multivariate L∞ Approximation in the Worst-Case Setting (Constructive Approximation, (2009), 30, 3, (475-493), 10.1007/s00365-009-9075-x)', Constructive Approximation, 52, pp. 177 - 179, http://dx.doi.org/10.1007/s00365-020-09498-y

Journal articles | 2019

Feischl M; Kuo FY; Sloan IH, 2019, 'Correction to: Fast random field generation with H-matrices (Math. (2018) 140:639–676, (10.1007/s00211-018-0974-2))', Numerische Mathematik, 142, pp. 787, http://dx.doi.org/10.1007/s00211-019-01033-x

Journal articles | 2019

Gilbert AD; Graham IG; Kuo FY; Scheichl R; Sloan IH, 2019, 'Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients', Numerische Mathematik, 142, pp. 863 - 915, http://dx.doi.org/10.1007/s00211-019-01046-6

Journal articles | 2019

Kritzer P; Kuo FY; Nuyens D; Ullrich M, 2019, 'Lattice rules with random n achieve nearly the optimal O(n ^{−α−1∕2} ) error independently of the dimension', Journal of Approximation Theory, 240, pp. 96 - 113, http://dx.doi.org/10.1016/j.jat.2018.09.011

Journal articles | 2018

Feischl M; Kuo FY; Sloan IH, 2018, 'Fast random field generation with H-matrices', Numerische Mathematik, 140, pp. 639 - 676, http://dx.doi.org/10.1007/s00211-018-0974-2

Journal articles | 2018

Gilbert AD; Kuo FY; Nuyens D; Wasilkowski GW, 2018, 'Efficient implementations of the multivariate decomposition method for approximating infinite-variate integrals', SIAM Journal on Scientific Computing, 40, pp. A3240 - A3266, http://dx.doi.org/10.1137/17M1161890

Journal articles | 2018

Gilbert AD; Kuo FY; Sloan IH, 2018, 'Hiding the weights—CBC black box algorithms with a guaranteed error bound', Mathematics and Computers in Simulation, 143, pp. 202 - 214, http://dx.doi.org/10.1016/j.matcom.2016.06.005

Journal articles | 2018

Graham IG; Kuo FY; Nuyens D; Scheichl R; Sloan IH, 2018, 'Analysis of circulant embedding methods for sampling stationary random fields', SIAM Journal on Numerical Analysis, 56, pp. 1871 - 1895, http://dx.doi.org/10.1137/17M1149730

Journal articles | 2018

Graham IG; Kuo FY; Nuyens D; Scheichl R; Sloan IH, 2018, 'Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients', Numerische Mathematik, 140, pp. 479 - 511, http://dx.doi.org/10.1007/s00211-018-0968-0

Journal articles | 2018

Griewank A; Kuo FY; Leövey H; Sloan IH, 2018, 'High dimensional integration of kinks and jumps—Smoothing by preintegration', Journal of Computational and Applied Mathematics, 344, pp. 259 - 274, http://dx.doi.org/10.1016/j.cam.2018.04.009

Journal articles | 2017

Griebel M; Kuo FY; Sloan IH, 2017, 'Note on "The smoothing effect of integration in Rd and the ANOVA decomposition"', Mathematics of Computation, 86, pp. 1847 - 1854, http://dx.doi.org/10.1090/mcom/3172

Journal articles | 2017

Griebel M; Kuo FY; Sloan IH, 2017, 'The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth', Mathematics of Computation, 86, pp. 1855 - 1876, http://dx.doi.org/10.1090/mcom/3171

Journal articles | 2017

Kuo FY; Nuyens D; Plaskota L; Sloan IH; Wasilkowski GW, 2017, 'Infinite-dimensional integration and the multivariate decomposition method', Journal of Computational and Applied Mathematics, 326, pp. 217 - 234, http://dx.doi.org/10.1016/j.cam.2017.05.031

Journal articles | 2017

Kuo FY; Scheichl R; Schwab C; Sloan IH; Ullmann E, 2017, 'Multilevel Quasi-Monte Carlo methods for lognormal diffusion problems', Mathematics of Computation, 86, pp. 2827 - 2860, http://dx.doi.org/10.1090/mcom/3207

Journal articles | 2017

Kuo FY; Sloan IH; Woźniakowski H, 2017, 'Multivariate integration for analytic functions with Gaussian Kernels', Mathematics of Computation, 86, pp. 829 - 853, http://dx.doi.org/10.1090/mcom/3144

Journal articles | 2016

Cools R; Kuo FY; Nuyens D; Suryanarayana G, 2016, 'Tent-transformed lattice rules for integration and approximation of multivariate non-periodic functions', Journal of Complexity, 36, pp. 166 - 181, http://dx.doi.org/10.1016/j.jco.2016.05.004

Journal articles | 2016

Dick J; Kuo FY; Le Gia QT; Schwab C, 2016, 'Multilevel higher order QMC Petrov-Galerkin discretization for affine parametric operator equations', SIAM Journal on Numerical Analysis, 54, pp. 2541 - 2568, http://dx.doi.org/10.1137/16M1078690

Journal articles | 2016

Kuo FY; Nuyens D, 2016, 'Application of Quasi-Monte Carlo Methods to Elliptic PDEs with Random Diffusion Coefficients: A Survey of Analysis and Implementation', Foundations of Computational Mathematics, 16, pp. 1631 - 1696, http://dx.doi.org/10.1007/s10208-016-9329-5

Journal articles | 2016

Kuo FY; Plaskota L; Wasilkowski GW, 2016, 'Optimal algorithms for doubly weighted approximation of univariate functions', Journal of Approximation Theory, 201, pp. 30 - 47, http://dx.doi.org/10.1016/j.jat.2015.08.007

Journal articles | 2015

Dick J; Kuo FY; Gia QTL; Schwab C; Le Gia Q, 2015, 'Fast QMC matrix-vector multiplication', SIAM Journal on Scientific Computing, 37, pp. A1436 - A1450, http://dx.doi.org/10.1137/151005518

Journal articles | 2015

Gnewuch M; Kuo FY; Niederreiter H; Woźniakowski H, 2015, 'Guest editors' preface', Journal of Complexity, 31, pp. vi, http://dx.doi.org/10.1016/S0885-064X(15)00032-1

Journal articles | 2015

Graham IG; Kuo FY; Nichols JA; Scheichl R; Schwab C; Sloan IH, 2015, 'Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients', Numerische Mathematik, 131, pp. 329 - 368, http://dx.doi.org/10.1007/s00211-014-0689-y

Journal articles | 2015

Kuo FY; Schwab C; Sloan IH, 2015, 'Multi-level Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic PDEs with Random Coefficients', Foundations of Computational Mathematics, 15, pp. 411 - 449, http://dx.doi.org/10.1007/s10208-014-9237-5

Journal articles | 2014

Dick J; Kuo FY; Le Gia QT; Nuyens D; Schwab C, 2014, 'Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs', SIAM Journal on Numerical Analysis, 52, pp. 2676 - 2702, http://dx.doi.org/10.1137/130943984

Journal articles | 2014

Gnewuch M; Kuo FY; Niederreiter H; Woźniakowski H, 2014, 'Uniform Distribution Theory and Applications', Oberwolfach Reports, 10, pp. 2837 - 2917, http://dx.doi.org/10.4171/owr/2013/49

Journal articles | 2014

Nichols JA; Kuo FY, 2014, 'Fast CBC construction of randomly shifted lattice rules achieving O (n -1 + δ) convergence for unbounded integrands over ℝs in weighted spaces with POD weights', Journal of Complexity, 30, pp. 444 - 468, http://dx.doi.org/10.1016/j.jco.2014.02.004

Journal articles | 2013

Dick J; Kuo FY; Sloan IH, 2013, 'High dimensional numerical integration - the Quasi-Monte Carlo way', Acta Numerica, 22, pp. 133 - 288, http://dx.doi.org/10.1017/S0962492913000044

Journal articles | 2013

Griebel M; Kuo FY; Sloan IH, 2013, 'The smoothing effect of integration in $R^d$ and the ANOVA decomposition', Mathematics of Computation, 82, pp. 383 - 400

Journal articles | 2013

Kuo FY; Sloan IH; Schwab C, 2013, 'Erratum: Quasi-Monte Carlo methods for high-dimensional integration: The standard (weighted hilbert space) setting and beyond (ANZIAM Journal (2011) 53 (1-37))', ANZIAM Journal, 54, pp. 216 - 219, http://dx.doi.org/10.1017/S144618111300014X

Journal articles | 2013

Sinescu V; Kuo FY; Sloan IH, 2013, 'On the Choice of Weights in a Function Space for Quasi-Monte Carlo Methods for a Class of Generalised Response Models in Statistics', Springer Proceedings in Mathematics and Statistics, 65, pp. 631 - 647, http://dx.doi.org/10.1007/978-3-642-41095-6_33

Journal articles | 2012

Kuo FY; Schwab C; Sloan IH, 2012, 'Erratum: Quasi-monte carlo methods for high-dimensional integration: The standard (weighted hilbert space) setting and beyond (ANZIAM Journal (2011) 53 (1-37) DOI: 10.1017/S1446181112000077)', Anziam Journal, 53, pp. 251, http://dx.doi.org/10.1017/S1446181112000144

Journal articles | 2012

Kuo FY; Schwab CH; Sloan IH, 2012, 'Quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients', SIAM Journal on Numerical Analysis, 50, pp. 3351 - 3374, http://dx.doi.org/10.1137/110845537

Journal articles | 2012

Kuo FY; Schwab CH; Sloan IH, 2012, 'Quasi-monte carlo methods for high-dimensional integration: The standard (weighted hilbert space) setting and beyond', ANZIAM Journal, 53, pp. 1 - 37, http://dx.doi.org/10.1017/S1446181112000077

Journal articles | 2012

Kuo FY; Wozniakowski H, 2012, 'Gauss-Hermite quadratures for functions from Hilbert spaces with Gaussian reproducing kernels', BIT Numerical Mathematics, 52, pp. 425 - 436, http://dx.doi.org/10.1007/s10543-011-0358-9

Journal articles | 2011

Graham IG; Kuo FY; Nuyens D; Scheichl R; Sloan IH, 2011, 'Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications', Journal of Computational Physics, 230, pp. 3668 - 3694, http://dx.doi.org/10.1016/j.jcp.2011.01.023

Journal articles | 2011

Hickernell FJ; Kritzer P; Kuo FY; Nuyens D, 2011, 'Weighted compound integration rules with higher order convergence for all N', Numerical Algorithms, 59, pp. 161 - 183, http://dx.doi.org/10.1007/s11075-011-9482-5

Journal articles | 2010

Cools R; Kuo FY; Nuyens D, 2010, 'Constructing lattice rules based on weighted degree of exactness and worst case error', Computing, 87, pp. 63 - 89, http://dx.doi.org/10.1007/s00607-009-0076-1

Journal articles | 2010

Griebel M; Kuo FY; Sloan IH, 2010, 'The smoothing effect of the ANOVA decomposition', Journal of Complexity, 26, pp. 523 - 551

Journal articles | 2010

Kuo FY; Sloan IH; Wasilkowski GW; Waterhouse BJ, 2010, 'Randomly shifted lattice rules with the optimal rate of convergence for unbounded integrands', Journal of Complexity, 26, pp. 135 - 160, http://dx.doi.org/10.1016/j.jco.2009.07.005

Journal articles | 2010

Kuo FY; Sloan IH; Wasilkowski GW; Wozniakowski H, 2010, 'Liberating the dimension', Journal of Complexity, 26, pp. 422 - 454

Journal articles | 2010

Kuo FY; Sloan IH; Wasilkowski GW; Wozniakowski H, 2010, 'On decompositions of multivariate functions', Mathematics of Computation, 79, pp. 953 - 966

Journal articles | 2009

Kuo FY; Wasilkowski GW; Wozniakowski H, 2009, 'Lattice algorithms for multivariate L-infinity approximation in the worst-case setting', Constructive Approximation, 30, pp. 475 - 493

Journal articles | 2009

Kuo FY; Wasilkowski GW; Wozniakowski H, 2009, 'On the power of standard information for L-infinity approximation in the randomized setting', BIT Numerical Mathematics, 49, pp. 543 - 564

Journal articles | 2009

Kuo FY; Wasilkowski GW; Wozniakowski H, 2009, 'On the power of standard information for multivariate approximation in the worst case setting', Journal of Approximation Theory, 158, pp. 97 - 125

Journal articles | 2008

Joe S; Kuo FY, 2008, 'Constructing Sobol` sequences with better two-dimensional projections', SIAM journal of scientific computation, 30, pp. 2635 - 2654

Journal articles | 2008

Kuo FY; Dunsmuir WT; Sloan IH; Wand MP; Womersley RS, 2008, 'Quasi-Monte Carlo for highly structured generalised response models', Methodology and Computing in Applied Probability, 10, pp. 239 - 275

Journal articles | 2008

Kuo FY; Giles M; Sloan IH; Waterhouse BJ, 2008, 'Quasi-Monte Carlo for finance applications', The ANZIAM Journal, 50, pp. C308 - C323

Journal articles | 2008

Kuo FY; Sloan IH; Wozniakowski H, 2008, 'Lattice rule algorithms for multivariate approximation in the average case setting', Journal of Complexity, 24, pp. 283 - 323

Journal articles | 2008

Kuo FY; Wasilkowski GW; Wozniakowski H, 2008, 'Multivariate L-infinity approximation in the worst case setting over reproducing kernel Hilbert spaces', Journal of Approximation Theory, 152, pp. 135 - 160

Journal articles | 2007

Dick J; Kritzer P; Kuo FY; Sloan IH, 2007, 'Lattice-Nystrom method for Fredholm integral equations of the second kind with convolution type kernels', Journal of Complexity, 23, pp. 752 - 772

Journal articles | 2007

Hesse K; Kuo FY; Sloan IH, 2007, 'A component-by-component approach to efficient numerical integration over products of spheres', Journal of Complexity, 23, pp. 25 - 51, http://dx.doi.org/10.1016/j.jco.2006.08.001

Journal articles | 2007

Kuo FY; Sloan IH; Wozniakowski H, 2007, 'Periodization strategy may fail in high dimensions', Numerical Algorithms, 46, pp. 369 - 391

Journal articles | 2006

Cools R; Kuo FY; Nuyens D, 2006, 'Constructing embedded lattice rules for multivariate integration', SIAM journal of scientific computation, 28, pp. 2162 - 2188

Journal articles | 2006

Kuo FY; Wasilkowski GW; Waterhouse BJ, 2006, 'Randomly shifted lattice rules for unbounded integrands', Journal of Complexity, 22, pp. 630 - 651

Journal articles | 2006

Waterhouse BJ; Kuo FY; Sloan IH, 2006, 'Randomly shifted lattice rules on the unit cube for unbounded integrands in high dimensions', Journal of Complexity, 22, pp. 71 - 101, http://dx.doi.org/10.1016/j.jco.2005.06.004

Journal articles | 2005

Dick J; Kuo FY; Pillichshammer F; Sloan IH, 2005, 'Construction algorithms for polynomial lattice rules for multivariate integration', Mathematics of Computation, 74, pp. 1895 - 1921

Journal articles | 2005

Kuo FY; Sloan IH, 2005, 'Lifting the curse of dimensionality', Notices of the American Mathematical Society, 52, pp. 1320 - 1328

Journal articles | 2005

Kuo FY; Sloan IH, 2005, 'Quasi-Monte Carlo methods can be efficient for integration over products of spheres', Journal of Complexity, 21, pp. 196 - 210

Journal articles | 2004

Dick J; Kuo FY, 2004, 'Reducing the construction cost of the component-by-component construction of good lattice rules', Mathematics of Computation, 73, pp. 1967 - 1988

Journal articles | 2003

Joe S; Kuo FY, 2003, 'Remark on algorithm 659: Implementing Sobol`s quasirandom sequence generator', ACM Transactions on Mathematical Software, 29, pp. 49 - 57

Journal articles | 2003

Kuo FY; Joe S, 2003, 'Component-by-component construction of good intermediate-rank lattice rules', SIAM Journal on Numerical Analysis, 41, pp. 1465 - 1486

Journal articles | 2003

Kuo FY, 2003, 'Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces', Journal of Complexity, 19, pp. 301 - 320

Journal articles | 2002

Kuo FY; Joe S, 2002, 'Component-by-component construction of good lattice rules with a composite number of points', Journal of Complexity, 18, pp. 943 - 976, http://dx.doi.org/10.1006/jcom.2002.0650
Working Papers | 2019

Cools R; Kuo FY; Nuyens D; Sloan IH, 2019, Fast component-by-component construction of lattice algorithms for multivariate approximation with POD and SPOD weights, http://dx.doi.org, http://arxiv.org/abs/1910.06606v1

Working Papers | 2019

Cools R; Kuo FY; Nuyens D; Sloan IH, 2019, Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters, http://dx.doi.org, http://arxiv.org/abs/1910.06604v1

Working Papers | 2019

Kazashi Y; Kuo FY; Sloan IH, 2019, Derandomised lattice rules for high dimensional integration, http://dx.doi.org, http://arxiv.org/abs/1903.05145v1

Working Papers | 2017

Brown B; Griebel M; Kuo FY; Sloan IH, 2017, On the expected uniform error of Brownian motion approximated by the Lévy-Ciesielski construction, http://dx.doi.org, http://arxiv.org/abs/1706.00915v3

Working Papers | 2012

Kuo FY; Schwab C; Sloan IH, 2012, Multi-level quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients, http://dx.doi.org, http://arxiv.org/abs/1208.6349v2
Preprints | 2025

Bartel F; Gilbert AD; Kuo FY; Sloan IH, 2025, Minimal Subsampled Rank-1 Lattices for Multivariate Approximation with Optimal Convergence Rate, http://dx.doi.org/10.48550/arxiv.2506.07729

Preprints | 2025

Gilbert AD; Giles MB; Kuo FY; Sloan IH; Srikumar A, 2025, Multilevel lattice-based kernel approximation for elliptic PDEs with random coefficients, http://arxiv.org/abs/2504.15810v1

Preprints | 2025

Gilbert AD; Kuo FY; Nuyens D; Pash G; Sloan IH; Willcox KE, 2025, Quasi-Monte Carlo methods for uncertainty quantification of tumor growth modeled by a parametric semi-linear parabolic reaction-diffusion equation, http://dx.doi.org/10.48550/arxiv.2509.25753

Preprints | 2025

Graham IG; Kuo FY; Nuyens D; Sloan IH; Spence EA, 2025, Quasi-Monte Carlo methods for uncertainty quantification of wave propagation and scattering problems modelled by the Helmholtz equation, http://arxiv.org/abs/2502.12451v1

Preprints | 2025

Keller A; Kuo FY; Nuyens D; Sloan IH, 2025, Regularity and Tailored Regularization of Deep Neural Networks, with application to parametric PDEs in uncertainty quantification, http://arxiv.org/abs/2502.12496v1

Preprints | 2024

Gilbert AD; Kuo FY; Srikumar A, 2024, Density estimation for elliptic PDE with random input by preintegration and quasi-Monte Carlo methods, http://arxiv.org/abs/2402.11807v2

Preprints | 2023

Kaarnioja V; Kuo FY; Sloan IH, 2023, Lattice-based kernel approximation and serendipitous weights for parametric PDEs in very high dimensions, http://arxiv.org/abs/2303.17755v2

Preprints | 2023

Kuo FY; Mo W; Nuyens D; Sloan IH; Srikumar A, 2023, Comparison of Two Search Criteria for Lattice-based Kernel Approximation, http://arxiv.org/abs/2304.01685v1

Preprints | 2023

Kuo FY; Nuyens D; Wilkes L, 2023, Random-prime--fixed-vector randomised lattice-based algorithm for high-dimensional integration, http://arxiv.org/abs/2304.10413v1

Preprints | 2022

Gilbert AD; Kuo FY; Sloan IH; Srikumar A, 2022, Theory and construction of Quasi-Monte Carlo rules for option pricing and density estimation, http://arxiv.org/abs/2212.11493v2

Preprints | 2022

Guth PA; Kaarnioja V; Kuo FY; Schillings C; Sloan IH, 2022, Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration, http://dx.doi.org/10.1007/s00211-024-01397-9

Preprints | 2022

Hakula H; Harbrecht H; Kaarnioja V; Kuo FY; Sloan IH, 2022, Uncertainty quantification for random domains using periodic random variables, http://arxiv.org/abs/2210.17329v2

Conference Papers | 2022

Hartung T; Jansen K; Kuo FY; Leövey H; Nuyens D; Sloan IH, 2022, 'Lattice field computations via recursive numerical integration', in Proceedings of Science

Preprints | 2022

Kuo FY; Mo W; Nuyens D, 2022, Constructing Embedded Lattice-based Algorithms for Multivariate Function Approximation with a Composite Number of Points, http://arxiv.org/abs/2209.01002v1

Preprints | 2021

Gilbert AD; Kuo FY; Sloan IH, 2021, Analysis of preintegration followed by quasi-Monte Carlo integration for distribution functions and densities, http://arxiv.org/abs/2112.10308v5

Preprints | 2021

Gilbert AD; Kuo FY; Sloan IH, 2021, Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on $\mathbb{R}^d$, http://arxiv.org/abs/2103.16075v3

Preprints | 2021

Gilbert AD; Kuo FY; Sloan IH, 2021, Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on $\mathbb{R}^d$, http://dx.doi.org/10.48550/arxiv.2103.16075

Preprints | 2021

Gilbert AD; Kuo FY; Sloan IH, 2021, Preintegration is not smoothing when monotonicity fails, http://arxiv.org/abs/2112.11621v1

Preprints | 2021

Hartung T; Jansen K; Kuo FY; Leövey H; Nuyens D; Sloan IH, 2021, Lattice field computations via recursive numerical integration, http://arxiv.org/abs/2112.05069v1

Preprints | 2020

Ganesh M; Kuo FY; Sloan IH, 2020, Quasi-Monte Carlo finite element analysis for wave propagation in heterogeneous random media, http://arxiv.org/abs/2004.12268v3

Preprints | 2020

Hartung T; Jansen K; Kuo FY; Leövey H; Nuyens D; Sloan IH, 2020, Lattice meets lattice: Application of lattice cubature to models in lattice gauge theory, http://dx.doi.org/10.1016/j.jcp.2021.110527

Preprints | 2020

Kaarnioja V; Kazashi Y; Kuo FY; Nobile F; Sloan IH, 2020, Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification, http://dx.doi.org/10.1007/s00211-021-01242-3

Preprints | 2020

Kaarnioja V; Kazashi Y; Kuo FY; Nobile F; Sloan IH, 2020, Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification, http://dx.doi.org/10.48550/arxiv.2007.06367

Preprints | 2019

Cools R; Kuo FY; Nuyens D; Sloan IH, 2019, Fast component-by-component construction of lattice algorithms for multivariate approximation with POD and SPOD weights, http://dx.doi.org/10.48550/arxiv.1910.06606

Preprints | 2019

Cools R; Kuo FY; Nuyens D; Sloan IH, 2019, Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters, http://dx.doi.org/10.48550/arxiv.1910.06604

Preprints | 2019

Guth PA; Kaarnioja V; Kuo FY; Schillings C; Sloan IH, 2019, A quasi-Monte Carlo Method for an Optimal Control Problem Under Uncertainty, http://arxiv.org/abs/1910.10022v1

Preprints | 2019

Kaarnioja V; Kuo FY; Sloan IH, 2019, Uncertainty quantification using periodic random variables, http://arxiv.org/abs/1905.07693v4

Conference Papers | 2019

Kazashi Y; Kuo FY; Sloan IH, 2019, 'Derandomised lattice rules for high dimensional integration', in CTAC 2018 Computational Techniques and Applications Conference, Australian Mathematical Society, Newcastle, Australia, pp. C247 - C260, presented at CTAC 2018 Computational Techniques and Applications Conference, Newcastle, Australia, 27 November 2019 - 30 November 2019, http://dx.doi.org/10.21914/anziamj.v60i0.14110

Preprints | 2019

Kazashi Y; Kuo FY; Sloan IH, 2019, Derandomised lattice rules for high dimensional integration, http://dx.doi.org/10.48550/arxiv.1903.05145

Preprints | 2019

Kuo FY; Migliorati G; Nobile F; Nuyens D, 2019, Function integration, reconstruction and approximation using rank-1 lattices, http://arxiv.org/abs/1908.01178v4

Preprints | 2018

Gilbert AD; Graham IG; Kuo FY; Scheichl R; Sloan IH, 2018, Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients, http://arxiv.org/abs/1808.02639v3

Preprints | 2018

Gilbert AD; Kuo FY; Sloan IH, 2018, Hiding the weights -- CBC black box algorithms with a guaranteed error bound, http://arxiv.org/abs/1810.03394v1

Preprints | 2018

Kazashi Y; Kuo FY; Sloan IH, 2018, Worst-case error for unshifted lattice rules without randomisation, http://arxiv.org/abs/1811.05676v1

Preprints | 2017

Brown B; Griebel M; Kuo FY; Sloan IH, 2017, On the expected uniform error of Brownian motion approximated by the Lévy-Ciesielski construction, http://dx.doi.org/10.48550/arxiv.1706.00915

Preprints | 2017

Feischl M; Kuo F; Sloan IH, 2017, Fast random field generation with $H$-matrices, http://arxiv.org/abs/1702.08637v4

Preprints | 2017

Gilbert AD; Kuo FY; Nuyens D; Wasilkowski GW, 2017, Efficient implementations of the Multivariate Decomposition Method for approximating infinite-variate integrals, http://arxiv.org/abs/1712.06782v3

Preprints | 2017

Giles MB; Kuo FY; Sloan IH, 2017, Combining sparse grids, multilevel MC and QMC for elliptic PDEs with random coefficients, http://arxiv.org/abs/1711.02437v1

Preprints | 2017

Graham IG; Kuo FY; Nuyens D; Scheichl R; Sloan IH, 2017, Analysis of circulant embedding methods for sampling stationary random fields, http://arxiv.org/abs/1710.00751v2

Preprints | 2017

Graham IG; Kuo FY; Nuyens D; Scheichl R; Sloan IH, 2017, Circulant embedding with QMC -- analysis for elliptic PDE with lognormal coefficients, http://arxiv.org/abs/1710.09254v2

Preprints | 2017

Griewank A; Kuo FY; Leövey H; Sloan IH, 2017, High dimensional integration of kinks and jumps -- smoothing by preintegration, http://arxiv.org/abs/1712.00920v1

Preprints | 2017

Kritzer P; Kuo FY; Nuyens D; Ullrich M, 2017, Lattice rules with random $n$ achieve nearly the optimal $\mathcal{O}(n^{-α-1/2})$ error independently of the dimension, http://dx.doi.org/10.1016/j.jat.2018.09.011

Preprints | 2017

Kuo FY; Nuyens D, 2017, Application of quasi-Monte Carlo methods to PDEs with random coefficients -- an overview and tutorial, http://arxiv.org/abs/1710.10984v1

Preprints | 2017

Kuo FY; Nuyens D, 2017, Hot new directions for quasi-Monte Carlo research in step with applications, http://arxiv.org/abs/1710.09905v1

Preprints | 2016

Cools R; Kuo FY; Nuyens D; Suryanarayana G, 2016, Tent-transformed lattice rules for integration and approximation of multivariate non-periodic functions, http://dx.doi.org/10.48550/arxiv.1606.00648

Conference Papers | 2016

Giles MB; Kuo FY; Sloan IH, 2016, 'Combining sparse grids, multilevel MC and QMC for elliptic PDEs with random coefficients', in Springer Proceedings in Mathematics and Statistics, Stanford, USA, pp. 265 - 281, presented at Monte Carlo and Quasi-Monte Carlo Methods 2016, Stanford, USA, 14 August 2016 - 19 August 2016, http://dx.doi.org/10.1007/978-3-319-91436-7_14

Conference Papers | 2016

Kuo FY; Nuyens D, 2016, 'Application of quasi-monte carlo methods to PDEs with random coefficients – An overview and tutorial', in Springer Proceedings in Mathematics and Statistics, Stanford, USA, pp. 53 - 71, presented at Monte Carlo and Quasi-Monte Carlo Methods 2016, Stanford, USA, 14 August 2016 - 19 August 2016, http://dx.doi.org/10.1007/978-3-319-91436-7_3

Conference Papers | 2016

Kuo FY; Nuyens D, 2016, 'Hot new directions for Quasi-Monte Carlo research in step with applications', in Springer Proceedings in Mathematics and Statistics, Standford, USA, pp. 123 - 144, presented at Monte Carlo and Quasi-Monte Carlo Methods 2016, Standford, USA, 14 August 2016 - 19 August 2016, http://dx.doi.org/10.1007/978-3-319-91436-7_6

Preprints | 2016

Kuo FY; Nuyens D, 2016, Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients - a survey of analysis and implementation, http://arxiv.org/abs/1606.06613v1

Preprints | 2015

Dick J; Kuo FY; Gia QTL; Schwab C, 2015, Fast QMC matrix-vector multiplication, http://arxiv.org/abs/1501.06286v1

Preprints | 2015

Kuo FY; Nuyens D; Plaskota L; Sloan IH; Wasilkowski GW, 2015, Infinite-dimensional integration and the multivariate decomposition method, http://arxiv.org/abs/1501.05445v3

Preprints | 2015

Kuo FY; Scheichl R; Schwab C; Sloan IH; Ullmann E, 2015, Multilevel Quasi-Monte Carlo Methods for Lognormal Diffusion Problems, http://arxiv.org/abs/1507.01090v2

Preprints | 2014

Dick J; Kuo F; Gia QTL; Schwab C, 2014, Multi-level higher order QMC Galerkin discretization for affine parametric operator equations, http://arxiv.org/abs/1406.4432v2

Preprints | 2013

Dick J; Kuo FY; Gia QTL; Nuyens D; Schwab C, 2013, Higher order QMC Galerkin discretization for parametric operator equations, http://dx.doi.org/10.1137/130943984

Conference Papers | 2013

Dick J; Kuo FY; Peters GW; Sloan IH, 2013, 'Preface', in Springer Proceedings in Mathematics and Statistics, pp. v - viii

Conference Proceedings (Editor of) | 2013

Dick J; Kuo FY; Peters GW; Sloan IH; Dick J; Kuo FY; Peters GW; Sloan IH, (eds.), 2013, 'Monte Carlo and quasi-Monte Carlo methods 2012', Springer Berlin Heidelberg, Vol. 65, http://dx.doi.org/10.1007/978-3-642-41095-6

Preprints | 2012

Kuo FY; Schwab C; Sloan IH, 2012, Multi-level quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients, http://dx.doi.org/10.48550/arxiv.1208.6349

Conference Papers | 2006

Dick J; Kritzer P; Kuo FY, 2006, 'Approximation of functions using digital nets', in 7th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, Ulm, Germany, presented at 7th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, Ulm, Germany, 14 August 2006 - 18 August 2006

Conference Papers | 2004

Kuo FY; Sloan IH; Wozniakowski H, 2004, 'Lattice rules for multivariate approximation in the worst case setting', in Monte Carlo and Quasi-Monte Carlo Methods 2004, France, presented at Monte Carlo and Quasi-Monte Carlo Methods 2004, France, 07 June 2004 - 10 June 2004

Conference Papers | 2002

Dick J; Kuo FY, 2002, 'Constructing good lattice rules with millions of points', in 5th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2002), National University of Singapore, presented at 5th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2002), National University of Singapore, 25 November 2002 - 28 November 2002

ARC Discovery Project (together with Ian Sloan) "High dimensional approximation, learning, and uncertainty" (2024 - 2026)
FWO Senior Research Project (together with Dirk Nuyens and Ronald Cools at KU Leuven, Belgium) "Analysis and Construction of Optimal Lattice Based Cubature: Theoretical developments for new algorithms, and randomization techniques, for non-periodic integrands" (2020 - 2023)
ARC Discovery Project (together with Ian Sloan) "High dimensional computation and uncertainty" (2021 - 2023)
ARC Discovery Project (together with Ian Sloan) "Towards a science of high dimensional computation" (2018 - 2020)
ARC Discovery Project (together with A/Professor Josef Dick and Professor Ian Sloan) "Quantifying uncertainty: innovations in high dimensional computation" (2015 - 2017)
ARC Future Fellowship "Liberating the dimension - frontier technologies for very high dimensional problems" (2013 - 2017)
ARC Discovery Project (together with Professor Ian Sloan) "Very high dimensional computation - a new frontier in numerical analysis" (2011 - 2013)
ARC Queen Elizabeth II Fellowship, Discovery Project "Innovative methods for very high dimensional problems" (2007 - 2011)
UNSW Vice-Chancellors' Postdoctoral Fellowship (2004 - 2006)

2014 Information-Based Complexity Prize
2011 ANZIAM JH Michell Medal
2003 Inaugural Information-Based Complexity Young Researcher Award

RESEARCH INTERESTS

Quasi-Monte Carlo methods for high-dimensional numerical integration and approximation; partial differential equations with random coefficients and uncertainty quantification.

EXTERNAL

Associate Editor of Mathematics of Computation (2016 - current)
Associate Editor of SIAM Journal on Scientific Computing (2019 - 2024)
Associate Editor of SIAM Journal on Numerical Analysis (2016 - 2024)
Associate Editor of SMAI Journal of Computational Mathematics (2018 - 2022)
Associate Editor of Foundations of Computational Mathematics (2020 - 2021)
Associate Editor of International Journal for Uncertainty Quantification (2019 - 2021)
Associate Editor of Journal of Complexity (2008 - 2019)
Member of MCM Steering Committee (2023 - current)
Member of MATRIX Scientific Committee (2019 - 2021)
Member of FoCM Board of Directors (2014 - 2020)
Member of AMSI Scientific Advisory Committee (2014 - 2016)
Member of HDA Steering Committee (2015 - current)
Member of MCQMC Steering Committee (2006 - 2016)

TEACHING DUTIES

MATH1081 Discrete Mathematics (2008, 2012, 2013, 2018, 2019)
MATH1131 Mathematics 1A (2006, 2007, 2019, 2020, 2021)
MATH2089 Numerical Methods and Statistics (2013, 2020, 2021, 2022, 2023, 2024)
MATH3101 Computing Methods for Differential Equations (2004, 2005)
MATH5175 Quasi-Monte Carlo and Finite Element Methods (2012, 2013)
MATH5295 Finite Element and Quasi-Monte Carlo and Methods (2015)

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CURRENT POSITION

RESEARCH INTERESTS

EXTERNAL

TEACHING DUTIES