By Emeritus Professor Ian Hugh Sloan

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

Gia QTL; Sloan IH; Wendland H, 2025, Vector-Valued Gaussian Processes for Approximating Divergence- or Rotation-free Vector Fields, http://dx.doi.org/10.48550/arxiv.2511.12535

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

Sloan IH; Kaarnioja V, 2024, Doubling the rate -- improved error bounds for orthogonal projection with application to interpolation, http://dx.doi.org/10.48550/arxiv.2308.06052

Hamann J; Gia QTL; Sloan IH; Womersley RS, 2024, Removing the mask -- reconstructing a scalar field on the sphere from a masked field, http://dx.doi.org/10.48550/arxiv.2309.14815

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

Alodat T; Gia QTL; Sloan IH, 2024, On approximation for time-fractional stochastic diffusion equations on the unit sphere, http://dx.doi.org/10.48550/arxiv.2212.05690

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

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; 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

Brauchart JS; Grabner PJ; Sloan IH; Womersley RS, 2022, Needlets Liberated, http://dx.doi.org/10.48550/arxiv.2207.12838

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

Hamann J; Gia QTL; Sloan IH; Wang YG; Womersley RS, 2020, A New Probe of Gaussianity and Isotropy applied to the CMB Maps, http://dx.doi.org/10.48550/arxiv.1911.11442

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

Gilbert AD; Graham IG; Scheichl R; Sloan IH, 2019, Bounding the spectral gap for an elliptic eigenvalue problem with uniformly bounded stochastic coefficients, http://dx.doi.org/10.48550/arxiv.1901.10470

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

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

Gia QTL; Sloan IH; Womersley RS; Wang YG, 2018, Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere, http://dx.doi.org/10.48550/arxiv.1801.03212

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

Brauchart JS; Dick J; Saff EB; Sloan IH; Wang YG; Womersley RS, 2017, Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces, http://dx.doi.org/10.48550/arxiv.1407.8311

Gia QTL; Sloan IH; Wang YG; Womerlsey RS, 2016, Needlet approximation for isotropic random fields on the sphere, http://dx.doi.org/10.48550/arxiv.1512.07790

Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2016, Random Point Sets on the Sphere—Hole Radii, Covering, and Separation, http://dx.doi.org/10.1080/10586458.2016.1226209

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

Wang YG; Sloan IH; Womersley RS, 2016, Riemann localisation on the sphere, http://dx.doi.org/10.48550/arxiv.1510.06834

Wang YG; Gia QTL; Sloan IH; Womersley RS, 2016, Fully discrete needlet approximation on the sphere, http://dx.doi.org/10.48550/arxiv.1502.05806

Wang H; Sloan IH, 2015, On filtered polynomial approximation on the sphere, http://dx.doi.org/10.48550/arxiv.1509.03792

Pereverzyev SV; Sloan IH; Tkachenko P, 2015, Parameter choice strategies for least-squares approximation of noisy smooth functions on the sphere, http://dx.doi.org/10.48550/arxiv.1501.02090

Cao H; Pereverzyev SV; Sloan IH; Tkachenko P, 2015, Two-parameter regularization of ill-posed spherical pseudo-differential equations in the space of continuous functions, http://dx.doi.org/10.48550/arxiv.1501.00362

Gia QTL; Sloan IH; Wendland H, 2014, Zooming from Global to Local: A Multiscale RBF Approach, http://dx.doi.org/10.48550/arxiv.1406.1333

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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