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Mathematics Institute

Dr Tim Sullivan | Publications

This is a list of all publications, ordered reverse-chronologically; preprints that are later published after peer review are re-sorted according to their final publication date. See also for a categorised version of this list.

  1. I. Klebanov and T. J. Sullivan. 鈥淭ransporting higher-order quadrature rules: Quasi-Monte Carlo points and sparse grids for mixture distributions.鈥 Stat. Comput. 36(1):no. 46, 19pp., 2026.
  2. O. Ernst, F. Nobile, C. Schillings, and T. J. Sullivan (ed.). Uncertainty Quantification, 20–25 April 2025, Oberwolfach Reports, 2025.
  3. J. Bunker, M. Girolami, H. Lambley, A. M. Stuart, and T. J. Sullivan. 鈥淎utoencoders in function space.鈥 J. Mach. Learn. Res. 26(165):1–54, 2025.
  4. I. Klebanov, H. Lambley, and T. J. Sullivan. 鈥淐lassification of small-ball modes and maximum a posteriori estimators.鈥 arXiv Preprint, 2025.
  5. T. J. Sullivan. 鈥淗ille's theorem for Bochner integrals of functions with values in locally convex spaces.鈥 Real Anal. Exchange 49(2):377–388, 2024.
  6. I. R. Best, T. J. Sullivan, and J. R. Kermode. 鈥淯ncertainty quantification in atomistic simulations of silicon using interatomic potentials.鈥 J. Chem. Phys. 161(6):064112, 14pp., 2024.
  7. T. Matsumoto and T. J. Sullivan. 鈥淚mages of Gaussian and other stochastic processes under closed, densely-defined, unbounded linear operators.鈥 Anal. Appl. 22(3):619–633, 2024.
  8. H. Lambley and T. J. Sullivan. 鈥淎n order-theoretic perspective on modes and maximum a posteriori estimation in Bayesian inverse problems.鈥 SIAM/ASA J. Uncertain. Quantif. 11(4):1195–1224, 2023.
  9. K. Pentland, M. Tamborrino, and T. J. Sullivan. 鈥淓rror bound analysis of the stochastic parareal algorithm.鈥 SIAM J. Sci. Comput. 45(5):A2657–A2678, 2023.
  10. H. C. Lie, D. Rudolf, B. Sprungk, and T. J. Sullivan. 鈥淒imension-independent Markov chain Monte Carlo on the sphere.鈥 Scand. J. Statist. 41pp., 2023.
  11. K. Pentland, M. Tamborrino, T. J. Sullivan, J. Buchanan, and L. C. Appel. 鈥淕Parareal: A time-parallel ODE solver using Gaussian process emulation.鈥 Stat. Comput. 33(1):no. 20, 23pp., 2023.
  12. M. Mollenhauer, N. M眉cke, and T. J. Sullivan. 鈥淟earning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem.鈥 arXiv Preprint, 2022.
  13. J. Cockayne, M. M. Graham, C. J. Oates, T. J. Sullivan, and O. Teymur. 鈥淭esting whether a learning procedure is calibrated.鈥 J. Mach. Learn. Res. 23(203):1–36, 2022.
  14. P. Hennig, I. C. F. Ipsen, M. Mahsereci, and T. J. Sullivan (ed.). Probabilistic Numerical Methods — From Theory to Implementation, Dagstuhl Reports 11(9):102–119, 2022.
  15. H. C. Lie, M. Stahn, and T. J. Sullivan. 鈥淩andomised one-step time integration methods for deterministic operator differential equations.鈥 Calcolo 59(1):13, 33pp., 2022.
  16. B. Ayanbayev, I. Klebanov, H. C. Lie, and T. J. Sullivan. 鈥溛-convergence of Onsager–Machlup functionals: II. Infinite product measures on Banach spaces.鈥 Inverse Probl. 38(2):025006, 35pp., 2022.
  17. B. Ayanbayev, I. Klebanov, H. C. Lie, and T. J. Sullivan. 鈥溛-convergence of Onsager–Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems.鈥 Inverse Probl. 38(2):025005, 32pp., 2022.
  18. I. Klebanov, B. Sprungk, and T. J. Sullivan. 鈥淭he linear conditional expectation in Hilbert space.鈥 Bernoulli 27(4):2267–2299, 2021.
  19. J. Wang, J. Cockayne, O. Chkrebtii, T. J. Sullivan, and C. J. Oates. 鈥淏ayesian numerical methods for nonlinear partial differential equations.鈥 Stat. Comput. 31(5), 2021.
  20. H. C. Lie, T. J. Sullivan, and A. L. Teckentrup. 鈥淓rror bounds for some approximate posterior measures in Bayesian inference鈥 in Numerical Mathematics and Advanced Applications ENUMATH 2019, ed. F. J. Vermolen and C. Vuik. Lecture Notes in Computational Science and Engineering 139:275–283, 2021.
  21. F. Sch盲fer, T. J. Sullivan, and H. Owhadi. 鈥淐ompression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexity.鈥 Multiscale Model. Simul. 19(2):688–730, 2021.
  22. H. Kersting, T. J. Sullivan, and P. Hennig. 鈥淐onvergence rates of Gaussian ODE filters.鈥 Stat. Comput. 30(6):1791–1816, 2020.
  23. L. Bonnet, J.-L. Akian, 脡. Savin, and T. J. Sullivan. 鈥淎daptive reconstruction of imperfectly-observed monotone functions, with applications to uncertainty quantification.鈥 Algorithms 13(8):196, 2020.
  24. I. Klebanov, I. Schuster, and T. J. Sullivan. 鈥淎 rigorous theory of conditional mean embeddings.鈥 SIAM J. Math. Data Sci. 2(3):583–606, 2020.
  25. M. McKerns, F. J. Alexander, K. S. Hickman, T. J. Sullivan, and D. E. Vaughan. 鈥淥ptimal bounds on nonlinear partial differential equations in model certification, validation, and experimental design鈥 in Handbook on Big Data and Machine Learning in the Physical Sciences, Volume 2: Advanced Analysis Solutions for Leading Experimental Techniques, ed. K. K. van Dam, K. G. Yager, S. I. Campbell, R. Farnsworth, and M. van Dam. World Scientific Series on Emerging Technologies 271–306, 2020.
  26. C. J. Oates, J. Cockayne, D. Prangle, T. J. Sullivan, and M. Girolami. 鈥淥ptimality criteria for probabilistic numerical methods鈥 in Multivariate Algorithms and Information-Based Complexity, ed. F. J. Hickernell and P. Kritzer. Radon Series on Computational and Applied Mathematics 27:65–88, 2020.
  27. E. Nava-Yazdani, H.-C. Hege, T. J. Sullivan, and C. von Tycowicz. 鈥淕eodesic analysis in Kendall's shape space with epidemiological applications.鈥 J. Math. Imaging Vis. 62(4):549–559, 2020.
  28. O. Ernst, F. Nobile, C. Schillings, and T. J. Sullivan (eds.). Uncertainty Quantification, 11–15 March 2019, Oberwolfach Reports 16(1):695–772, 2019.
  29. J. Cockayne, C. J. Oates, T. J. Sullivan, and M. Girolami. 鈥淏ayesian probabilistic numerical methods.鈥 SIAM Rev. 61(4):756–789, 2019.
  30. M. Girolami, I. C. F. Ipsen, C. J. Oates, A. B. Owen, and T. J. Sullivan. 鈥淓ditorial: Special Edition on Probabilistic Numerics.鈥 Stat. Comput. 29(6):1181–1183, 2019.
  31. C. J. Oates and T. J. Sullivan. 鈥淎 modern retrospective on probabilistic numerics.鈥 Stat. Comput. 29(6):1335–1351, 2019.
  32. H. C. Lie, A. M. Stuart, and T. J. Sullivan. 鈥淪trong convergence rates of probabilistic integrators for ordinary differential equations.鈥 Stat. Comput. 29(6):1265–1283, 2019.
  33. T. J. Sullivan. 鈥淐ontributed discussion on the article 鈥楢 Bayesian conjugate gradient method鈥.鈥 Bayesian Anal. 14(3):985–989, 2019.
  34. O. Teymur, H. C. Lie, T. J. Sullivan, and B. Calderhead. 鈥淚mplicit probabilistic integrators for ODEs鈥 in Advances in Neural Information Processing Systems 31 (NIPS 2018), ed. S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett. 7244–7253, 2018.
  35. H. C. Lie, T. J. Sullivan, and A. L. Teckentrup. 鈥淩andom forward models and log-likelihoods in Bayesian inverse problems.鈥 SIAM/ASA J. Uncertain. Quantif. 6(4):1600–1629, 2018.
  36. H. C. Lie and T. J. Sullivan. 鈥淓rratum: Equivalence of weak and strong modes of measures on topological vector spaces (2018 Inverse Problems 34 115013).鈥 Inverse Probl. 34(12):129601, 2018.
  37. H. C. Lie and T. J. Sullivan. 鈥淓quivalence of weak and strong modes of measures on topological vector spaces.鈥 Inverse Probl. 34(11):115013, 2018.
  38. H. C. Lie and T. J. Sullivan. 鈥淨uasi-invariance of countable products of Cauchy measures under non-unitary dilations.鈥 Electron. Commun. Prob. 23(8):1–6, 2018.
  39. I. Schuster, P. G. Constantine, and T. J. Sullivan. 鈥淓xact active subspace Metropolis–Hastings, with applications to the Lorenz-96 system.鈥 arXiv Preprint, 2017.
  40. T. J. Sullivan. 鈥淲ell-posedness of Bayesian inverse problems in quasi-Banach spaces with stable priors鈥 in 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Weimar 2017, ed. C. K枚nke and C. Trunk. Proceedings in Applied Mathematics and Mechanics 17(1):871–874, 2017.
  41. T. J. Sullivan. 鈥淲ell-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors.鈥 Inverse Probl. Imaging 11(5):857–874, 2017.
  42. J. Cockayne, C. J. Oates, T. J. Sullivan, and M. Girolami. 鈥淧robabilistic numerical methods for PDE-constrained Bayesian inverse problems鈥 in Proceedings of the 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, ed. G. Verdoolaege. AIP Conference Proceedings 1853:060001-1–060001-8, 2017.
  43. J. Cockayne, C. J. Oates, T. J. Sullivan, and M. Girolami. 鈥淧robabilistic meshless methods for partial differential equations and Bayesian inverse problems.鈥 arXiv Preprint, 2016.
  44. T. J. Sullivan. Introduction to Uncertainty Quantification, volume 63 of Texts in Applied Mathematics. Springer, 2015. ISBN 978-3-319-23394-9 (hardcover), 978-3-319-23395-6 (e-book).
  45. H. Owhadi, C. Scovel, and T. J. Sullivan. 鈥淥n the brittleness of Bayesian inference.鈥 SIAM Rev. 57(4):566–582, 2015.
  46. H. Owhadi, C. Scovel, and T. J. Sullivan. 鈥淏rittleness of Bayesian inference under finite information in a continuous world.鈥 Electron. J. Stat. 9(1):1–79, 2015.
  47. P.-H. T. Kamga, B. Li, M. McKerns, L. H. Nguyen, M. Ortiz, H. Owhadi, and T. J. Sullivan. 鈥淥ptimal uncertainty quantification with model uncertainty and legacy data.鈥 J. Mech. Phys. Solids 72:1–19, 2014.
  48. T. J. Sullivan. 鈥淥ptimal Uncertainty Quantification for Hypervelocity Impact鈥 in Uncertainty Quantification in Computational Fluid Dynamics, 15–19 September 2014, von Karman Institute for Fluid Dynamics, Belgium, and 2–3 June 2014, Stanford University, United States. STO-AVT-VKI Lecture Series, AVT-235, , 2014.
  49. T. J. Sullivan, M. McKerns, M. Ortiz, H. Owhadi, and C. Scovel. 鈥淥ptimal uncertainty quantification: Distributional robustness versus Bayesian brittleness.鈥 ASME J. Med. Dev. 7(4):040920, 2013.
  50. T. J. Sullivan, M. McKerns, D. Meyer, F. Theil, H. Owhadi, and M. Ortiz. 鈥淥ptimal uncertainty quantification for legacy data observations of Lipschitz functions.鈥 ESAIM Math. Model. Numer. Anal. 47(6):1657–1689, 2013.
  51. H. Owhadi, C. Scovel, T. J. Sullivan, M. McKerns, and M. Ortiz. 鈥淥ptimal Uncertainty Quantification.鈥 SIAM Rev. 55(2):271–345, 2013.
  52. T. J. Sullivan, M. Koslowski, F. Theil, and M. Ortiz. 鈥淭hermalization of rate-independent processes by entropic regularization.鈥 Discrete Contin. Dyn. Syst. Ser. S 6(1):215–233, 2013.
  53. L. Rast, T. J. Sullivan, and V. K. Tewary. 鈥淪tratified graphene/noble metal systems for low-loss plasmonics applications.鈥 Phys. Rev. B 87(4):045428, 2013.
  54. M. Ortiz, M. McKerns, H. Owhadi, T. J. Sullivan, and C. Scovel. 鈥淥ptimal Uncertainty Quantification鈥 in Advanced Computational Engineering, 12–18 February 2012, ed. O. Allix, C. Carstensen, J. Schr枚der, and P. Wriggers. Oberwolfach Reports 9(1):537–540, 2012.
  55. T. J. Sullivan, M. Koslowski, F. Theil, and M. Ortiz. 鈥淭hermalization of rate-independent processes by entropic regularization鈥 in Interplay of Analysis and Probability in Physics, 22–28 January 2012, ed. W. K枚nig, P. M枚rters, M. Peletier, and J. Zimmer. Oberwolfach Reports 9(1):322–325, 2012.
  56. M. Adams, A. Lashgari, B. Li, M. McKerns, J. Mihaly, M. Ortiz, H. Owhadi, A. J. Rosakis, M. Stalzer, and T. J. Sullivan. 鈥淩igorous model-based uncertainty quantification with application to terminal ballistics. Part II: Systems with uncontrollable inputs and large scatter.鈥 J. Mech. Phys. Solids 60(5):1002–1019, 2012.
  57. A. A. Kidane, A. Lashgari, B. Li, M. McKerns, M. Ortiz, G. Ravichandran, M. Stalzer, and T. J. Sullivan. 鈥淩igorous model-based uncertainty quantification with application to terminal ballistics. Part I: Systems with controllable inputs and small scatter.鈥 J. Mech. Phys. Solids 60(5):983–1001, 2012.
  58. T. J. Sullivan and H. Owhadi. 鈥淒istances and diameters in concentration inequalities: from geometry to optimal assignment of sampling resources.鈥 Int. J. Uncertain. Quantif. 2(1):21–38, 2012.
  59. C. Scovel, H. Owhadi, T. J. Sullivan, M. McKerns, and M. Ortiz. 鈥淲hat is UQ?鈥 in ADTSC Science Highlights 2012. Los Alamos National Laboratory, LA-UR 12-20429:26–27, 2012.
  60. M. M. McKerns, L. Strand, T. J. Sullivan, A. Fang, and M. A. G. Aivazis. 鈥淏uilding a Framework for Predictive Science鈥 in Proceedings of the 10th Python in Science Conference (SciPy 2011), June 2011, ed. S. van der Walt and J. Millman. 67–78, 2011.
  61. T. J. Sullivan, U. Topcu, M. McKerns, and H. Owhadi. 鈥淯ncertainty quantification via codimension-one partitioning.鈥 Internat. J. Numer. Methods Engrg. 85(12):1499–1521, 2011.
  62. T. J. Sullivan and F. Theil. 鈥淥n gradient descents in random wiggly energies鈥 in Microstructures in Solids: From Quantum Models to Continua, 14–20 March 2010, ed. A. Mielke and M. Ortiz. Oberwolfach Reports 7(1):739–741, 2010.
  63. M. McKerns, H. Owhadi, C. Scovel, T. J. Sullivan, and M. Ortiz. 鈥淭he optimal uncertainty algorithm in the mystic framework.鈥 Caltech CACR Technical Report No. 523, August 2010.
  64. T. J. Sullivan, M. McKerns, U. Topcu, and H. Owhadi. 鈥淯ncertainty quantification via codimension-one domain partitioning and a new concentration inequality.鈥 Proc. Soc. Behav. Sci. 2(6):7751–7752, 2010.
  65. F. Theil, T. J. Sullivan, M. Koslowski, and M. Ortiz. 鈥淒issipative systems in contact with a heat bath: Application to Andrade creep鈥 in Proceedings of the IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, Bochum, Germany, September 22–26, 2008, ed. K. Hackl. IUTAM Bookseries 21:261–272, 2010.
  66. T. J. Sullivan, M. Koslowski, F. Theil, and M. Ortiz. 鈥淥n the behavior of dissipative systems in contact with a heat bath: Application to Andrade creep.鈥 J. Mech. Phys. Solids 57(7):1058–1077, 2009.
  67. T. J. Sullivan and F. Theil. 鈥淒eterministic stick-slip dynamics in a one-dimensional random potential鈥 in Analysis and Numerics for Rate-Independent Processes, 25 February–3 March 2007, ed. G. Dal Maso, G. Francfort, A. Mielke, and T. Roub铆膷ek. Oberwolfach Reports 4(1):652–655, 2007.

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