Tim Sullivan

Publications

Reverse-chronological list of all publications

Preprints and technical reports

  1. J. Bunker, M. Girolami, H. Lambley, A. M. Stuart, and T. J. Sullivan. “Autoencoders in function space.” arXiv Preprint, 2024. arXiv:2408.01362 BibTeX
  2. 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:2308.10081 BibTeX
  3. I. Klebanov and T. J. Sullivan. “A ‘periodic table’ of modes and maximum a posteriori estimators.” arXiv Preprint, 2023. arXiv:2306.16278 BibTeX
  4. 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:2211.08875 BibTeX
  5. 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:1712.02749 BibTeX
  6. 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:1605.07811 BibTeX
  7. 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:1202.1055 BibTeX

Journal articles

  1. T. J. Sullivan. “Hille's theorem for Bochner integrals of functions with values in locally convex spaces.” Real Anal. Exchange 49(2):377–388, 2024. doi:10.14321/realanalexch.49.2.1719547551 arXiv:2401.01845 BibTeX
  2. I. R. Best, T. J. Sullivan, and J. R. Kermode. “Uncertainty quantification in atomistic simulations of silicon using interatomic potentials.” J. Chem. Phys. 161(6):064112, 14pp., 2024. doi:10.1063/5.0214590 arXiv:2402.15419 BibTeX
  3. T. Matsumoto and T. J. Sullivan. “Images of Gaussian and other stochastic processes under closed, densely-defined, unbounded linear operators.” Anal. Appl. 22(3):619–633, 2024. doi:10.1142/S0219530524400025 arXiv:2305.03594 BibTeX
  4. 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:10.1137/22M154243X arXiv:2209.11517 BibTeX
  5. 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:10.1137/22M1533062 arXiv:2211.05496 BibTeX
  6. H. C. Lie, D. Rudolf, B. Sprungk, and T. J. Sullivan. “Dimension-independent Markov chain Monte Carlo on the sphere.” Scand. J. Statist. 50(4):1818–1858, 2023. doi:10.1111/sjos.12653 arXiv:2112.12185 BibTeX
  7. 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-y arXiv:2201.13418 BibTeX
  8. 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.pdf arXiv:2012.12670 BibTeX
  9. 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/s10092-022-00457-6 arXiv:2103.16506 BibTeX
  10. 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/ac3f82 arXiv:2108.04598 BibTeX
  11. 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/ac3f81 arXiv:2108.04597 BibTeX
  12. 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-BEJ1308 arXiv:2008.12070 BibTeX
  13. 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):no. 55, 20pp., 2021. doi:10.1007/s11222-021-10030-w arXiv:2104.12587 BibTeX
  14. 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:10.1137/19M129526X arXiv:1706.02205 BibTeX
  15. H. Kersting, T. J. Sullivan, and P. Hennig. “Convergence rates of Gaussian ODE filters.” Stat. Comput. 30(6):1791–1816, 2020. doi:10.1007/s11222-020-09972-4 arXiv:1807.09737 BibTeX
  16. 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):no. 196, 21pp., 2020. doi:10.3390/a13080196 arXiv:2007.05236 BibTeX
  17. 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:10.1137/19M1305069 arXiv:1912.00671 BibTeX
  18. 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-w arXiv:1906.11950 BibTeX
  19. J. Cockayne, C. J. Oates, T. J. Sullivan, and M. Girolami. “Bayesian probabilistic numerical methods.” SIAM Rev. 61(4):756–789, 2019. doi:10.1137/17M1139357 arXiv:1702.03673 BibTeX
  20. 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-y BibTeX
  21. 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-z arXiv:1901.04457 BibTeX
  22. 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/s11222-019-09898-6 arXiv:1703.03680 BibTeX
  23. T. J. Sullivan. “Contributed discussion on the article ‘A Bayesian conjugate gradient method’.” Bayesian Anal. 14(3):985–989, 2019. doi:10.1214/19-BA1145 arXiv:1906.10240 BibTeX
  24. 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:10.1137/18M1166523 arXiv:1712.05717 BibTeX
  25. 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/aae55b BibTeX
  26. 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/aadef2 arXiv:1708.02516 BibTeX
  27. 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-ECP113 arXiv:1611.10289 BibTeX
  28. 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.2017040 arXiv:1605.05898 BibTeX
  29. H. Owhadi, C. Scovel, and T. J. Sullivan. “On the brittleness of Bayesian inference.” SIAM Rev. 57(4):566–582, 2015. doi:10.1137/130938633 arXiv:1308.6306 BibTeX
  30. 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-EJS989 arXiv:1304.6772 BibTeX
  31. 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.2014.07.007 BibTeX
  32. 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:10.1115/1.4025786 BibTeX
  33. 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/2013083 arXiv:1202.1928 BibTeX
  34. H. Owhadi, C. Scovel, T. J. Sullivan, M. McKerns, and M. Ortiz. “Optimal Uncertainty Quantification.” SIAM Rev. 55(2):271–345, 2013. doi:10.1137/10080782X arXiv:1009.0679 BibTeX
  35. 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.2013.6.215 arXiv:1209.3619 BibTeX
  36. 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.87.045428 arXiv:1301.5620 BibTeX
  37. 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.2011.12.002 BibTeX
  38. 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.2011.12.001 BibTeX
  39. 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.i1.30 BibTeX
  40. 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.3030 BibTeX
  41. 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.2010.05.211 BibTeX
  42. 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.2009.03.006 BibTeX

Articles in proceedings and other collections

  1. 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.11.9.102 BibTeX
  2. 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_26 arXiv:1911.05669 BibTeX
  3. 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_0014 arXiv:2009.06626 BibTeX
  4. 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:10.1515/9783110635461-005 arXiv:1901.04326 BibTeX
  5. 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/2019/12 BibTeX
  6. 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-odes arXiv:1805.07970 BibTeX
  7. 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.201710402 arXiv:1710.05610 BibTeX
  8. 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:10.1063/1.4985359 arXiv:1701.04006 BibTeX
  9. 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. BibTeX
  10. 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/2012/09 BibTeX
  11. 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/2012/06 BibTeX
  12. 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. BibTeX
  13. 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-ebaa42b7-00d arXiv:1202.1056 BibTeX
  14. 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/2010/14 BibTeX
  15. 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_20 BibTeX
  16. 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/2007/11 BibTeX

Books

  1. 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:10.1007/978-3-319-23395-6 BibTeX
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