By Professor Frances Kuo

Preprints

Gilbert AD; Giles MB; Kuo FY; Sloan IH; Srikumar A, 2026, Multilevel lattice-based kernel approximation for elliptic PDEs with random coefficients, http://dx.doi.org/10.48550/arxiv.2504.15810

Gilbert AD; Kuo FY; Nuyens D; Pash G; Sloan IH; Willcox KE, 2026, 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

Keller A; Kuo FY; Nuyens D; Sloan IH, 2026, Lattice-based Deep Neural Networks: Regularity and Tailored Regularization, http://dx.doi.org/10.48550/arxiv.2603.02809

Keller A; Kuo FY; Nuyens D; Sloan IH, 2026, Regularity and tailored regularization of Deep Neural Networks, with application to parametric PDEs in uncertainty quantification, http://dx.doi.org/10.48550/arxiv.2502.12496

Bartel F; Gilbert AD; Kuo FY; Sloan IH, 2026, Minimal Subsampled Rank-1 Lattices for Multivariate Approximation with Optimal Convergence Rate, http://dx.doi.org/10.48550/arxiv.2506.07729

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://dx.doi.org/10.48550/arxiv.2502.12451

Gilbert AD; Kuo FY; Srikumar A, 2024, Density estimation for elliptic PDE with random input by preintegration and quasi-Monte Carlo methods, http://dx.doi.org/10.48550/arxiv.2402.11807

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, http://dx.doi.org/10.48550/arxiv.2208.02767

Gilbert AD; Kuo FY; Sloan IH; Srikumar A, 2023, Theory and construction of Quasi-Monte Carlo rules for option pricing and density estimation, http://dx.doi.org/10.48550/arxiv.2212.11493

Hakula H; Harbrecht H; Kaarnioja V; Kuo FY; Sloan IH, 2023, Uncertainty quantification for random domains using periodic random variables, http://dx.doi.org/10.48550/arxiv.2210.17329

Kaarnioja V; Kuo FY; Sloan IH, 2023, Lattice-based kernel approximation and serendipitous weights for parametric PDEs in very high dimensions, http://dx.doi.org/10.48550/arxiv.2303.17755

Brown B; Griebel M; Kuo FY; Sloan IH, 2023, On the expected uniform error of Brownian motion approximated by the Lévy-Ciesielski construction, http://dx.doi.org/10.48550/arxiv.1706.00915

Kuo FY; Nuyens D; Wilkes L, 2023, Random-prime--fixed-vector randomised lattice-based algorithm for high-dimensional integration, http://dx.doi.org/10.48550/arxiv.2304.10413

Kuo FY; Mo W; Nuyens D; Sloan IH; Srikumar A, 2023, Comparison of Two Search Criteria for Lattice-based Kernel Approximation, http://dx.doi.org/10.48550/arxiv.2304.01685

Gilbert AD; Kuo FY; Sloan IH, 2022, Analysis of preintegration followed by quasi-Monte Carlo integration for distribution functions and densities, http://dx.doi.org/10.48550/arxiv.2112.10308

Kuo FY; Mo W; Nuyens D, 2022, Constructing Embedded Lattice-based Algorithms for Multivariate Function Approximation with a Composite Number of Points, http://dx.doi.org/10.48550/arxiv.2209.01002

Gilbert AD; Kuo FY; Sloan IH, 2021, Preintegration is not smoothing when monotonicity fails, http://dx.doi.org/10.48550/arxiv.2112.11621

Hartung T; Jansen K; Kuo FY; Leövey H; Nuyens D; Sloan IH, 2021, Lattice field computations via recursive numerical integration, http://dx.doi.org/10.48550/arxiv.2112.05069

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

Kaarnioja V; Kazashi Y; Kuo FY; Nobile F; Sloan IH, 2021, Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification, http://dx.doi.org/10.48550/arxiv.2007.06367

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, http://dx.doi.org/10.48550/arxiv.2011.05451

Ganesh M; Kuo FY; Sloan IH, 2021, Quasi-Monte Carlo finite element analysis for wave propagation in heterogeneous random media, http://dx.doi.org/10.48550/arxiv.2004.12268

Kuo FY; Migliorati G; Nobile F; Nuyens D, 2020, Function integration, reconstruction and approximation using rank-1 lattices, http://dx.doi.org/10.48550/arxiv.1908.01178

Kaarnioja V; Kuo FY; Sloan IH, 2020, Uncertainty quantification using periodic random variables, http://dx.doi.org/10.48550/arxiv.1905.07693

Guth PA; Kaarnioja V; Kuo FY; Schillings C; Sloan IH, 2019, A quasi-Monte Carlo Method for an Optimal Control Problem Under Uncertainty, http://dx.doi.org/10.48550/arxiv.1910.10022

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

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

Gilbert AD; Graham IG; Kuo FY; Scheichl R; Sloan IH, 2019, Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients, http://dx.doi.org/10.48550/arxiv.1808.02639

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

Kazashi Y; Kuo FY; Sloan IH, 2018, Worst-case error for unshifted lattice rules without randomisation, http://dx.doi.org/10.48550/arxiv.1811.05676

Gilbert AD; Kuo FY; Sloan IH, 2018, Hiding the weights -- CBC black box algorithms with a guaranteed error bound, http://dx.doi.org/10.48550/arxiv.1810.03394

Gilbert AD; Kuo FY; Nuyens D; Wasilkowski GW, 2018, Efficient implementations of the Multivariate Decomposition Method for approximating infinite-variate integrals, http://dx.doi.org/10.48550/arxiv.1712.06782

Kritzer P; Kuo FY; Nuyens D; Ullrich M, 2018, Lattice rules with random $n$ achieve nearly the optimal $\mathcal{O}(n^{-α-1/2})$ error independently of the dimension, http://dx.doi.org/10.48550/arxiv.1706.04502

Graham IG; Kuo FY; Nuyens D; Scheichl R; Sloan IH, 2018, Circulant embedding with QMC -- analysis for elliptic PDE with lognormal coefficients, http://dx.doi.org/10.48550/arxiv.1710.09254

Graham IG; Kuo FY; Nuyens D; Scheichl R; Sloan IH, 2018, Analysis of circulant embedding methods for sampling stationary random fields, http://dx.doi.org/10.48550/arxiv.1710.00751

Feischl M; Kuo F; Sloan IH, 2018, Fast random field generation with $H$-matrices, http://dx.doi.org/10.48550/arxiv.1702.08637

Griewank A; Kuo FY; Leövey H; Sloan IH, 2017, High dimensional integration of kinks and jumps -- smoothing by preintegration, http://dx.doi.org/10.48550/arxiv.1712.00920

Giles MB; Kuo FY; Sloan IH, 2017, Combining sparse grids, multilevel MC and QMC for elliptic PDEs with random coefficients, http://dx.doi.org/10.48550/arxiv.1711.02437

Kuo FY; Nuyens D, 2017, Application of quasi-Monte Carlo methods to PDEs with random coefficients -- an overview and tutorial, http://dx.doi.org/10.48550/arxiv.1710.10984

Kuo FY; Nuyens D, 2017, Hot new directions for quasi-Monte Carlo research in step with applications, http://dx.doi.org/10.48550/arxiv.1710.09905

Kuo FY; Nuyens D; Plaskota L; Sloan IH; Wasilkowski GW, 2016, Infinite-dimensional integration and the multivariate decomposition method, http://dx.doi.org/10.48550/arxiv.1501.05445

Kuo FY; Scheichl R; Schwab C; Sloan IH; Ullmann E, 2016, Multilevel Quasi-Monte Carlo Methods for Lognormal Diffusion Problems, http://dx.doi.org/10.48550/arxiv.1507.01090

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://dx.doi.org/10.48550/arxiv.1606.06613

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

Dick J; Kuo F; Gia QTL; Schwab C, 2015, Multi-level higher order QMC Galerkin discretization for affine parametric operator equations, http://dx.doi.org/10.48550/arxiv.1406.4432

Dick J; Kuo FY; Gia QTL; Nuyens D; Schwab C, 2015, Higher order QMC Galerkin discretization for parametric operator equations, http://dx.doi.org/10.48550/arxiv.1309.4624

Dick J; Kuo FY; Gia QTL; Schwab C, 2015, Fast QMC matrix-vector multiplication, http://dx.doi.org/10.48550/arxiv.1501.06286

Kuo FY; Schwab C; Sloan IH, 2014, 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

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