Tim Sullivan

Junior Professor in Applied Mathematics:
Risk and Uncertainty Quantification

Publications

  1. 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), 2017. To appear. arXiv:1710.05610
  2. H. C. Lie & T. J. Sullivan. “Equivalence of weak and strong modes of measures on topological vector spaces.” arXiv Preprint, 2017. arXiv:1708.02516
  3. 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
  4. H. C. Lie, A. M. Stuart & T. J. Sullivan. “Strong convergence rates of probabilistic integrators for ordinary differential equations.” arXiv Preprint, 2017. arXiv:1703.03680
  5. J. Cockayne, C. Oates, T. J. Sullivan & M. Girolami. “Bayesian Probabilistic Numerical Methods.” arXiv Preprint, 2017. arXiv:1702.03673
  6. 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
  7. T. J. Sullivan. “Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors.” Inverse Problems and Imaging 11(5):857–874, 2017. doi:10.3934/ipi.2017040 arXiv:1605.05898
  8. H. C. Lie & T. J. Sullivan. “Quasi-invariance of countable products of Cauchy measures under translations and non-unitary dilations.” arXiv Preprint, 2016. arXiv:1611.10289
  9. 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
  10. 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
  11. H. Owhadi, C. Scovel & T. J. Sullivan. “On the brittleness of Bayesian inference.” SIAM Review 57(4):566–582, 2015. doi:10.1137/130938633 arXiv:1308.6306
  12. H. Owhadi, C. Scovel & T. J. Sullivan. “Brittleness of Bayesian inference under finite information in a continuous world.” Electronic Journal of Statistics 9(1):1–79, 2015. doi:10.1214/15-EJS989 arXiv:1304.6772
  13. 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.
  14. 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.” Journal of the Mechanics and Physics of Solids 72:1–19, 2014. doi:10.1016/j.jmps.2014.07.007
  15. T. J. Sullivan, M. McKerns M. Ortiz, H. Owhadi & C. Scovel. “Optimal uncertainty quantification: Distributional robustness versus Bayesian brittleness.” ASME Journal of Medical Devices 7(4):040920, 2013. doi:10.1115/1.4025786
  16. T. J. Sullivan, M. McKerns, D. Meyer, F. Theil, H. Owhadi & M. Ortiz. “Optimal uncertainty quantification for legacy data observations of Lipschitz functions.” ESAIM. Mathematical Modelling and Numerical Analysis 47(6):1657–1689, 2013. doi:10.1051/m2an/2013083 arXiv:1202.1928
  17. H. Owhadi, C. Scovel, T. J. Sullivan, M. McKerns & M. Ortiz. “Optimal Uncertainty Quantification.” SIAM Review 55(2):271–345, 2013. doi:10.1137/10080782X arXiv:1009.0679
  18. L. Rast, T. J. Sullivan & V. K. Tewary. “Stratified graphene/noble metal systems for low-loss plasmonics applications.” Physical Review B 87(4):045428, 2013. doi:10.1103/PhysRevB.87.045428 arXiv:1301.5620
  19. T. J. Sullivan, M. Koslowski, F. Theil & M. Ortiz. “Thermalization of rate-independent processes by entropic regularization.” Discrete and Continuous Dynamical Systems. Series S 6(1):215–233, 2013. doi:10.3934/dcdss.2013.6.215 arXiv:1209.3619
  20. T. J. Sullivan & H. Owhadi. “Distances and diameters in concentration inequalities: from geometry to optimal assignment of sampling resources.” International Journal for Uncertainty Quantification 2(1):21–38, 2012. doi:10.1615/Int.J.UncertaintyQuantification.v2.i1.30
  21. 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
  22. 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
  23. 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.” Journal of the Mechanics and Physics of Solids 60(5):1002–1019, 2012. doi:10.1016/j.jmps.2011.12.002
  24. 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.” Journal of the Mechanics and Physics of Solids 60(5):983–1001, 2012. doi:10.1016/j.jmps.2011.12.001
  25. 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.
  26. 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
  27. T. J. Sullivan, U. Topcu, M. McKerns & H. Owhadi. “Uncertainty quantification via codimension-one partitioning.” International Journal for Numerical Methods in Engineering 85(12):1499–1521, 2011. doi:10.1002/nme.3030
  28. 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
  29. 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
  30. T. J. Sullivan, M. McKerns, U. Topcu & H. Owhadi. “Uncertainty quantification via codimension-one domain partitioning and a new concentration inequality.” Procedia — Social and Behavioral Sciences 2(6):7751–7752, 2010. doi:10.1016/j.sbspro.2010.05.211
  31. 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
  32. 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.” Journal of the Mechanics and Physics of Solids 57(7):1058–1077, 2009. doi:10.1016/j.jmps.2009.03.006
  33. 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