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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 this pageLink opens in a new window for a categorised version of this list.

  1. T. Matsumoto and T. J. Sullivan. “Images of Gaussian and other stochastic processes under closed, densely-defined, unbounded linear operators.” Anal. Appl., 2024. Accepted for publication. arXiv:2305.03594Link opens in a new window
  2. T. J. Sullivan. “Hille’s theorem for Bochner integrals of functions with values in locally convex spaces.” arXiv Preprint, 2024. arXiv:2401.01845Link opens in a new window
  3. H. Lambley and T. J. Sullivan. “An order-theoretic perspective on modes and maximum a posteriori estimation in Bayesian inverse problems.” SIAM/ASA J. Uncertain. Quantif. 11(4):1195–1224, 2023. doi:10.1137/22M154243XLink opens in a new window arXiv:2209.11517Link opens in a new window
  4. K. Pentland, M. Tamborrino, and T. J. Sullivan. “Error bound analysis of the stochastic parareal algorithm.” SIAM J. Sci. Comput. 45(5):A2657–A2678, 2023. doi:10.1137/22M1533062Link opens in a new window arXiv:2211.05496Link opens in a new window
  5. I. Klebanov and T. J. Sullivan. “Transporting higher-order quadrature rules: Quasi-Monte Carlo points and sparse grids for mixture distributions.” arXiv Preprint, 2023. arXiv:2308.10081Link opens in a new window
  6. I. Klebanov and T. J. Sullivan. “A ‘periodic table’ of modes and maximum a posteriori estimators.” arXiv Preprint, 2023. arXiv:2306.16278Link opens in a new window
  7. H. C. Lie, D. Rudolf, B. Sprungk, and T. J. Sullivan. “Dimension-independent Markov chain Monte Carlo on the sphere.” Scand. J. Statist. 41pp., 2023. doi:10.1111/sjos.12653Link opens in a new window arXiv:2112.12185Link opens in a new window
  8. K. Pentland, M. Tamborrino, T. J. Sullivan, J. Buchanan, and L. C. Appel. “GParareal: A time-parallel ODE solver using Gaussian process emulation.” Stat. Comput. 33(1):no. 20, 23pp., 2023. doi:10.1007/s11222-022-10195-yLink opens in a new window arXiv:2201.13418Link opens in a new window
  9. M. Mollenhauer, N. Mücke, and T. J. Sullivan. “Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem.” arXiv Preprint, 2022. arXiv:2211.08875Link opens in a new window
  10. J. Cockayne, M. M. Graham, C. J. Oates, T. J. Sullivan, and O. Teymur. “Testing whether a learning procedure is calibrated.” J. Mach. Learn. Res. 23(203):1–36, 2022. https://jmlr.org/papers/volume23/21-1065/21-1065.pdfLink opens in a new window arXiv:2012.12670Link opens in a new window
  11. 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. doi:10.4230/DagRep.11.9.102Link opens in a new window
  12. H. C. Lie, M. Stahn, and T. J. Sullivan. “Randomised one-step time integration methods for deterministic operator differential equations.” Calcolo 59(1):13, 33pp., 2022. doi:10.1007/s10092-022-00457-6Link opens in a new window arXiv:2103.16506Link opens in a new window
  13. B. Ayanbayev, I. Klebanov, H. C. Lie, and T. J. Sullivan. “Γ-convergence of Onsager–Machlup functionals: II. Infinite product measures on Banach spaces.” Inverse Probl. 38(2):025006, 35pp., 2022. doi:10.1088/1361-6420/ac3f82Link opens in a new window arXiv:2108.04598Link opens in a new window
  14. B. Ayanbayev, I. Klebanov, H. C. Lie, and T. J. Sullivan. “Γ-convergence of Onsager–Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems.” Inverse Probl. 38(2):025005, 32pp., 2022. doi:10.1088/1361-6420/ac3f81Link opens in a new window arXiv:2108.04597Link opens in a new window
  15. I. Klebanov, B. Sprungk, and T. J. Sullivan. “The linear conditional expectation in Hilbert space.” Bernoulli 27(4):2267–2299, 2021. doi:10.3150/20-BEJ1308Link opens in a new window arXiv:2008.12070Link opens in a new window
  16. J. Wang, J. Cockayne, O. Chkrebtii, T. J. Sullivan, and C. J. Oates. “Bayesian numerical methods for nonlinear partial differential equations.” Stat. Comput. 31(5), 2021. doi:10.1007/s11222-021-10030-wLink opens in a new window arXiv:2104.12587Link opens in a new window
  17. H. C. Lie, T. J. Sullivan, and A. L. Teckentrup. “Error bounds for some approximate posterior measures in Bayesian inference” 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. doi:10.1007/978-3-030-55874-1_26Link opens in a new window arXiv:1911.05669Link opens in a new window
  18. F. Schäfer, T. J. Sullivan, and H. Owhadi. “Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexity.” Multiscale Model. Simul. 19(2):688–730, 2021. doi:10.1137/19M129526XLink opens in a new window arXiv:1706.02205Link opens in a new window
  19. H. Kersting, T. J. Sullivan, and P. Hennig. “Convergence rates of Gaussian ODE filters.” Stat. Comput. 30(6):1791–1816, 2020. doi:10.1007/s11222-020-09972-4Link opens in a new window arXiv:1807.09737Link opens in a new window
  20. L. Bonnet, J.-L. Akian, É. Savin, and T. J. Sullivan. “Adaptive reconstruction of imperfectly-observed monotone functions, with applications to uncertainty quantification.” Algorithms 13(8):196, 2020. doi:10.3390/a13080196Link opens in a new window arXiv:2007.05236Link opens in a new window
  21. I. Klebanov, I. Schuster, and T. J. Sullivan. “A rigorous theory of conditional mean embeddings.” SIAM J. Math. Data Sci. 2(3):583–606, 2020. doi:10.1137/19M1305069Link opens in a new window arXiv:1912.00671Link opens in a new window
  22. M. McKerns, F. J. Alexander, K. S. Hickman, T. J. Sullivan, and D. E. Vaughan. “Optimal bounds on nonlinear partial differential equations in model certification, validation, and experimental design” 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. doi:10.1142/9789811204579_0014Link opens in a new window arXiv:2009.06626Link opens in a new window
  23. C. J. Oates, J. Cockayne, D. Prangle, T. J. Sullivan, and M. Girolami. “Optimality criteria for probabilistic numerical methods” 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. doi:10.1515/9783110635461-005Link opens in a new window arXiv:1901.04326Link opens in a new window
  24. E. Nava-Yazdani, H.-C. Hege, T. J. Sullivan, and C. von Tycowicz. “Geodesic analysis in Kendall's shape space with epidemiological applications.” J. Math. Imaging Vis. 62(4):549–559, 2020. doi:10.1007/s10851-020-00945-wLink opens in a new window arXiv:1906.11950Link opens in a new window
  25. O. Ernst, F. Nobile, C. Schillings, and T. J. Sullivan (ed.). Uncertainty Quantification, 11–15 March 2019, Oberwolfach Reports 16(1):695–772, 2019. doi:10.4171/OWR/2019/12Link opens in a new window
  26. J. Cockayne, C. J. Oates, T. J. Sullivan, and M. Girolami. “Bayesian probabilistic numerical methods.” SIAM Rev. 61(4):756–789, 2019. doi:10.1137/17M1139357Link opens in a new window arXiv:1702.03673Link opens in a new window
  27. M. Girolami, I. C. F. Ipsen, C. J. Oates, A. B. Owen, and T. J. Sullivan. “Editorial: Special Edition on Probabilistic Numerics.” Stat. Comput. 29(6):1181–1183, 2019. doi:10.1007/s11222-019-09892-yLink opens in a new window
  28. C. J. Oates and T. J. Sullivan. “A modern retrospective on probabilistic numerics.” Stat. Comput. 29(6):1335–1351, 2019. doi:10.1007/s11222-019-09902-zLink opens in a new window arXiv:1901.04457Link opens in a new window
  29. H. C. Lie, A. M. Stuart, and T. J. Sullivan. “Strong convergence rates of probabilistic integrators for ordinary differential equations.” Stat. Comput. 29(6):1265–1283, 2019. doi:10.1007/s11222-019-09898-6Link opens in a new window arXiv:1703.03680Link opens in a new window
  30. T. J. Sullivan. “Contributed discussion on the article ‘A Bayesian conjugate gradient method’.” Bayesian Anal. 14(3):985–989, 2019. doi:10.1214/19-BA1145Link opens in a new window arXiv:1906.10240Link opens in a new window
  31. O. Teymur, H. C. Lie, T. J. Sullivan, and B. Calderhead. “Implicit probabilistic integrators for ODEs” 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. http://papers.nips.cc/paper/7955-implicit-probabilistic-integrators-for-odesLink opens in a new window arXiv:1805.07970Link opens in a new window
  32. H. C. Lie, T. J. Sullivan, and A. L. Teckentrup. “Random forward models and log-likelihoods in Bayesian inverse problems.” SIAM/ASA J. Uncertain. Quantif. 6(4):1600–1629, 2018. doi:10.1137/18M1166523Link opens in a new window arXiv:1712.05717Link opens in a new window
  33. H. C. Lie and T. J. Sullivan. “Erratum: Equivalence of weak and strong modes of measures on topological vector spaces (2018 Inverse Problems 34 115013).” Inverse Probl. 34(12):129601, 2018. doi:10.1088/1361-6420/aae55bLink opens in a new window
  34. H. C. Lie and T. J. Sullivan. “Equivalence of weak and strong modes of measures on topological vector spaces.” Inverse Probl. 34(11):115013, 2018. doi:10.1088/1361-6420/aadef2Link opens in a new window arXiv:1708.02516Link opens in a new window
  35. H. C. Lie and T. J. Sullivan. “Quasi-invariance of countable products of Cauchy measures under non-unitary dilations.” Electron. Commun. Prob. 23(8):1–6, 2018. doi:10.1214/18-ECP113Link opens in a new window arXiv:1611.10289Link opens in a new window
  36. I. Schuster, P. G. Constantine, and T. J. Sullivan. “Exact active subspace Metropolis–Hastings, with applications to the Lorenz-96 system.” arXiv Preprint, 2017. arXiv:1712.02749Link opens in a new window
  37. T. J. Sullivan. “Well-posedness of Bayesian inverse problems in quasi-Banach spaces with stable priors” in 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Weimar 2017, ed. C. Könke and C. Trunk. Proceedings in Applied Mathematics and Mechanics 17(1):871–874, 2017. doi:10.1002/pamm.201710402Link opens in a new window arXiv:1710.05610Link opens in a new window
  38. T. J. Sullivan. “Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors.” Inverse Probl. Imaging 11(5):857–874, 2017. doi:10.3934/ipi.2017040Link opens in a new window arXiv:1605.05898Link opens in a new window
  39. J. Cockayne, C. J. Oates, T. J. Sullivan, and M. Girolami. “Probabilistic numerical methods for PDE-constrained Bayesian inverse problems” 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. doi:10.1063/1.4985359Link opens in a new window arXiv:1701.04006Link opens in a new window
  40. J. Cockayne, C. J. Oates, T. J. Sullivan, and M. Girolami. “Probabilistic meshless methods for partial differential equations and Bayesian inverse problems.” arXiv Preprint, 2016. arXiv:1605.07811Link opens in a new window
  41. 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). doi:10.1007/978-3-319-23395-6Link opens in a new window
  42. H. Owhadi, C. Scovel, and T. J. Sullivan. “On the brittleness of Bayesian inference.” SIAM Rev. 57(4):566–582, 2015. doi:10.1137/130938633Link opens in a new window arXiv:1308.6306Link opens in a new window
  43. H. Owhadi, C. Scovel, and T. J. Sullivan. “Brittleness of Bayesian inference under finite information in a continuous world.” Electron. J. Stat. 9(1):1–79, 2015. doi:10.1214/15-EJS989Link opens in a new window arXiv:1304.6772Link opens in a new window
  44. P.-H. T. Kamga, B. Li, M. McKerns, L. H. Nguyen, M. Ortiz, H. Owhadi, and T. J. Sullivan. “Optimal uncertainty quantification with model uncertainty and legacy data.” J. Mech. Phys. Solids 72:1–19, 2014. doi:10.1016/j.jmps.2014.07.007Link opens in a new window
  45. T. J. Sullivan. “Optimal Uncertainty Quantification for Hypervelocity Impact” 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.
  46. T. J. Sullivan, M. McKerns, M. Ortiz, H. Owhadi, and C. Scovel. “Optimal uncertainty quantification: Distributional robustness versus Bayesian brittleness.” ASME J. Med. Dev. 7(4):040920, 2013. doi:10.1115/1.4025786Link opens in a new window
  47. T. J. Sullivan, M. McKerns, D. Meyer, F. Theil, H. Owhadi, and M. Ortiz. “Optimal uncertainty quantification for legacy data observations of Lipschitz functions.” ESAIM Math. Model. Numer. Anal. 47(6):1657–1689, 2013. doi:10.1051/m2an/2013083Link opens in a new window arXiv:1202.1928Link opens in a new window
  48. H. Owhadi, C. Scovel, T. J. Sullivan, M. McKerns, and M. Ortiz. “Optimal Uncertainty Quantification.” SIAM Rev. 55(2):271–345, 2013. doi:10.1137/10080782XLink opens in a new window arXiv:1009.0679Link opens in a new window
  49. T. J. Sullivan, M. Koslowski, F. Theil, and M. Ortiz. “Thermalization of rate-independent processes by entropic regularization.” Discrete Contin. Dyn. Syst. Ser. S 6(1):215–233, 2013. doi:10.3934/dcdss.2013.6.215Link opens in a new window arXiv:1209.3619Link opens in a new window
  50. L. Rast, T. J. Sullivan, and V. K. Tewary. “Stratified graphene/noble metal systems for low-loss plasmonics applications.” Phys. Rev. B 87(4):045428, 2013. doi:10.1103/PhysRevB.87.045428Link opens in a new window arXiv:1301.5620Link opens in a new window
  51. M. Ortiz, M. McKerns, H. Owhadi, T. J. Sullivan, and C. Scovel. “Optimal Uncertainty Quantification” in Advanced Computational Engineering, 12–18 February 2012, ed. O. Allix, C. Carstensen, J. Schröder, and P. Wriggers. Oberwolfach Reports 9(1):537–540, 2012. doi:10.4171/OWR/2012/09Link opens in a new window
  52. T. J. Sullivan, M. Koslowski, F. Theil, and M. Ortiz. “Thermalization of rate-independent processes by entropic regularization” in Interplay of Analysis and Probability in Physics, 22–28 January 2012, ed. W. König, P. Mörters, M. Peletier, and J. Zimmer. Oberwolfach Reports 9(1):322–325, 2012. doi:10.4171/OWR/2012/06Link opens in a new window
  53. M. Adams, A. Lashgari, B. Li, M. McKerns, J. Mihaly, M. Ortiz, H. Owhadi, A. J. Rosakis, M. Stalzer, and T. J. Sullivan. “Rigorous model-based uncertainty quantification with application to terminal ballistics. Part II: Systems with uncontrollable inputs and large scatter.” J. Mech. Phys. Solids 60(5):1002–1019, 2012. doi:10.1016/j.jmps.2011.12.002Link opens in a new window
  54. A. A. Kidane, A. Lashgari, B. Li, M. McKerns, M. Ortiz, G. Ravichandran, M. Stalzer, and T. J. Sullivan. “Rigorous model-based uncertainty quantification with application to terminal ballistics. Part I: Systems with controllable inputs and small scatter.” J. Mech. Phys. Solids 60(5):983–1001, 2012. doi:10.1016/j.jmps.2011.12.001Link opens in a new window
  55. T. J. Sullivan and H. Owhadi. “Distances and diameters in concentration inequalities: from geometry to optimal assignment of sampling resources.” Int. J. Uncertain. Quantif. 2(1):21–38, 2012. doi:10.1615/Int.J.UncertaintyQuantification.v2.i1.30Link opens in a new window
  56. C. Scovel, H. Owhadi, T. J. Sullivan, M. McKerns, and M. Ortiz. “What is UQ?” in ADTSC Science Highlights 2012. Los Alamos National Laboratory, LA-UR 12-20429:26–27, 2012.
  57. M. M. McKerns, L. Strand, T. J. Sullivan, A. Fang, and M. A. G. Aivazis. “Building a Framework for Predictive Science” in Proceedings of the 10th Python in Science Conference (SciPy 2011), June 2011, ed. S. van der Walt and J. Millman. 67–78, 2011. doi:10.25080/Majora-ebaa42b7-00dLink opens in a new window arXiv:1202.1056Link opens in a new window
  58. T. J. Sullivan, U. Topcu, M. McKerns, and H. Owhadi. “Uncertainty quantification via codimension-one partitioning.” Internat. J. Numer. Methods Engrg. 85(12):1499–1521, 2011. doi:10.1002/nme.3030Link opens in a new window
  59. T. J. Sullivan and F. Theil. “On gradient descents in random wiggly energies” 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. doi:10.4171/OWR/2010/14Link opens in a new window
  60. M. McKerns, H. Owhadi, C. Scovel, T. J. Sullivan, and M. Ortiz. “The optimal uncertainty algorithm in the mystic framework.” Caltech CACR Technical Report No. 523, August 2010. arXiv:1202.1055Link opens in a new window
  61. T. J. Sullivan, M. McKerns, U. Topcu, and H. Owhadi. “Uncertainty quantification via codimension-one domain partitioning and a new concentration inequality.” Proc. Soc. Behav. Sci. 2(6):7751–7752, 2010. doi:10.1016/j.sbspro.2010.05.211Link opens in a new window
  62. F. Theil, T. J. Sullivan, M. Koslowski, and M. Ortiz. “Dissipative systems in contact with a heat bath: Application to Andrade creep” 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. doi:10.1007/978-90-481-9195-6_20Link opens in a new window
  63. T. J. Sullivan, M. Koslowski, F. Theil, and M. Ortiz. “On the behavior of dissipative systems in contact with a heat bath: Application to Andrade creep.” J. Mech. Phys. Solids 57(7):1058–1077, 2009. doi:10.1016/j.jmps.2009.03.006Link opens in a new window
  64. T. J. Sullivan and F. Theil. “Deterministic stick-slip dynamics in a one-dimensional random potential” in Analysis and Numerics for Rate-Independent Processes, 25 February–3 March 2007, ed. G. Dal Maso, G. Francfort, A. Mielke, and T. Roubíček. Oberwolfach Reports 4(1):652–655, 2007. doi:10.4171/OWR/2007/11Link opens in a new window