Tim Sullivan


  1. C. J. Oates & T. J. Sullivan. “A modern retrospective on probabilistic numerics.” arXiv Preprint, 2019. arXiv:1901.04457 BibTeX
  2. C. J. Oates, J. Cockayne, D. Prangle, T. J. Sullivan & M. Girolami. “Optimality criteria for probabilistic numerical methods.” arXiv Preprint, 2019. arXiv:1901.04326 BibTeX
  3. H. C. Lie, A. M. Stuart & T. J. Sullivan. “Strong convergence rates of probabilistic integrators for ordinary differential equations.” Stat. Comput., 2019. Accepted for publication. arXiv:1703.03680 BibTeX
  4. H. C. Lie & 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
  5. E. Nava-Yazdani, H.-C. Hege, C. von Tycowicz & T. J. Sullivan. “A shape trajectories approach to longitudinal statistical analysis.” ZIB Report No. 18-42, 2018. BibTeX
  6. H. Kersting, T. J. Sullivan & P. Hennig. “Convergence rates of Gaussian ODE filters.” arXiv Preprint, 2018. arXiv:1807.09737 BibTeX
  7. O. Teymur, H. C. Lie, T. J. Sullivan & 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 & R. Garnett. 2018. arXiv:1805.07970 BibTeX
  8. H. C. Lie, T. J. Sullivan & 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
  9. H. C. Lie & 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
  10. H. C. Lie & 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
  11. I. Schuster, P. G. Constantine & T. J. Sullivan. “Exact active subspace Metropolis–Hastings, with applications to the Lorenz-96 system.” arXiv Preprint, 2017. arXiv:1712.02749 BibTeX
  12. 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
  13. F. Schäfer, T. J. Sullivan & H. Owhadi. “Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexity.” arXiv Preprint, 2017. arXiv:1706.02205 BibTeX
  14. J. Cockayne, C. Oates, T. J. Sullivan & M. Girolami. “Bayesian Probabilistic Numerical Methods.” arXiv Preprint, 2017. arXiv:1702.03673 BibTeX
  15. J. Cockayne, C. Oates, T. J. Sullivan & 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
  16. 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
  17. J. Cockayne, C. J. Oates, T. J. Sullivan & M. Girolami. “Probabilistic meshless methods for partial differential equations and Bayesian inverse problems.” arXiv Preprint, 2016. arXiv:1605.07811 BibTeX
  18. 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
  19. H. Owhadi, C. Scovel & T. J. Sullivan. “On the brittleness of Bayesian inference.” SIAM Rev. 57(4):566–582, 2015. doi:10.1137/130938633 arXiv:1308.6306 BibTeX
  20. H. Owhadi, C. Scovel & 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
  21. 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
  22. P.-H. T. Kamga, B. Li, M. McKerns, L. H. Nguyen, M. Ortiz, H. Owhadi & 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
  23. T. J. Sullivan, M. McKerns, M. Ortiz, H. Owhadi & C. Scovel. “Optimal uncertainty quantification: Distributional robustness versus Bayesian brittleness.” ASME J. Med. Dev. 7(4):040920, 2013. doi:10.1115/1.4025786 BibTeX
  24. T. J. Sullivan, M. McKerns, D. Meyer, F. Theil, H. Owhadi & 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
  25. H. Owhadi, C. Scovel, T. J. Sullivan, M. McKerns & M. Ortiz. “Optimal Uncertainty Quantification.” SIAM Rev. 55(2):271–345, 2013. doi:10.1137/10080782X arXiv:1009.0679 BibTeX
  26. L. Rast, T. J. Sullivan & 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
  27. T. J. Sullivan, M. Koslowski, F. Theil & 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
  28. T. J. Sullivan & 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
  29. M. Ortiz, M. McKerns, H. Owhadi, T. J. Sullivan & C. Scovel. “Optimal Uncertainty Quantification” in Advanced Computational Engineering, 12–18 February 2012, ed. O. Allix, C. Carstensen, J. Schröder & P. Wriggers. Oberwolfach Reports 9(1)2012. doi:10.4171/OWR/2012/09 BibTeX
  30. T. J. Sullivan, M. Koslowski, F. Theil & 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 & J. Zimmer. Oberwolfach Reports 9(1)2012. doi:10.4171/OWR/2012/06 BibTeX
  31. M. Adams, A. Lashgari, B. Li, M. McKerns, J. M. Mihaly, M. Ortiz, H. Owhadi, A. J. Rosakis, M. Stalzer & 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
  32. A. A. Kidane, A. Lashgari, B. Li, M. McKerns, M. Ortiz, H. Owhadi, G. Ravichandran, M. Stalzer & 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
  33. C. Scovel, H. Owhadi, T. J. Sullivan, M. McKerns & M. Ortiz. “What is UQ?” in ADTSC Science Highlights 2012. Los Alamos National Laboratory, LA-UR 12-20429:26–27, 2012. BibTeX
  34. M. M. McKerns, L. Strand, T. J. Sullivan, A. Fang & 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 & J. Millman. 67–78, 2011. arXiv:1202.1056 BibTeX
  35. T. J. Sullivan, U. Topcu, M. McKerns & H. Owhadi. “Uncertainty quantification via codimension-one partitioning.” Internat. J. Numer. Methods Engrg. 85(12):1499–1521, 2011. doi:10.1002/nme.3030 BibTeX
  36. M. McKerns, H. Owhadi, C. Scovel, T. J. Sullivan & M. Ortiz. “The optimal uncertainty algorithm in the mystic framework.” Caltech CACR Technical Report No. 523, August 2010. arXiv:1202.1055 BibTeX
  37. T. J. Sullivan & 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 & M. Ortiz. Oberwolfach Reports 7(1):739–741, 2010. doi:10.4171/OWR/2010/14 BibTeX
  38. T. J. Sullivan, M. McKerns, U. Topcu & H. Owhadi. “Uncertainty quantification via codimension-one domain partitioning and a new concentration inequality.” 2(6):7751–7752, 2010. doi:10.1016/j.sbspro.2010.05.211 BibTeX
  39. F. Theil, T. J. Sullivan, M. Koslowski & 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
  40. T. J. Sullivan, M. Koslowski, F. Theil & 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
  41. T. J. Sullivan & 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 & T. Roubíček. Oberwolfach Reports 4(1):652–655, 2007. doi:10.4171/OWR/2007/11 BibTeX