Research and Publications

All manuscripts and publications are available on my Google Scholar page or my ResearchGate page.

The list below is infrequently maintained.

 

Preprints

  1. N. Rummel, D. A. Messenger, S. Becker, V. Dukic, and D. M. Bortz. WENDy for Nonlinear-in-Parameter ODEs. arXiv:2502.08881, Feb. 2025.
  2. S. Minor, D. A. Messenger, V. Dukic, and D. M. Bortz. Learning Weather Models from Data with WSINDy.
    arXiv:2501.00738, Jan. 2025.
  3. C. Bonneville, X. He, A. Tran, J. S. Park, W. Fries, D. A. Messenger, S. W. Cheung, Y. Shin, D. M. Bortz,
    D. Ghosh, J.-S. Chen, J. Belof, and Y. Choi. A Comprehensive Review of Latent Space Dynamics
    Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling. arXiv:2403.10748,
    Mar. 2024.

Refereed Articles & Book Chapters

  1. G. Vasey, D. A. Messenger, D. M. Bortz, A. Christlieb, and B. O’Shea. Influence of initial conditions on data-driven model identification and information entropy for ideal mhd problems. J. Comput. Phys., 524:113719, Mar. 2025. doi
  2. X. He, A. Tran, D. M. Bortz, and Y. Choi. Physics-informed active learning with simultaneous weak-form latent space dynamics identification. Int. J. Numer. Methods Eng., 126(1):e7634, Jan. 2025. doi
  3. D. A. Messenger and D. M. Bortz. Asymptotic consistency of the WSINDy algorithm in the limit of continuum data. IMA J. Numer. Anal., page drae086, Dec. 2024. doi
  4. D. A. Messenger, J. W. Burby, and D. M. Bortz. Coarse-Graining Hamiltonian Systems Using WSINDy. Sci. Rep., 14(14457):1–24, 2024. doi
  5. B. P. Russo, D. A. Messenger, D. M. Bortz, and J. A. Rosenfeld. Weighted Composition Operators for Learning Nonlinear Dynamics. IFAC-PapersOnLine, 58(17):97–102, 2024. doi
  6. D. M. Bortz, D. A. Messenger, and A. Tran. Weak form-based data-driven modeling: Computationally Efficient and Noise Robust Equation Learning and Parameter Inference. In S. Mishra and A. Townsend, editors, Numerical Analysis Meets achine Learning, volume 25 of Handbook of Numerical Analysis, pages 54–82. Elsevier, 2024. doi
  7. L. R. Baker, M. Gordon, B. P. Ziemba, V. Gershuny, J. J. Falke, and D. M. Bortz. Learning diffusion coefficients, kinetic parameters, and the number of underlying states from a multi-state diffusion process: Robustness results and application to PDK-1/PKCα dynamics. In B. Sriraman, editor, Handbookof Visual, Experimental and Computational Mathematics - Bridges through Data. Springer Nature, 2024. doi
  8. A. Tran, X. He, D. A. Messenger, Y. Choi, and D. M. Bortz. Weak-Form Latent Space Dynamics Identification. Comput. Methods Appl. Mech. Eng., 427:116998, July 2024. doi
  9. D. M. Bortz, D. A. Messenger, and V. Dukic. Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamics. Bull. Math. Biol., 85(110), 2023. doi
  10. D. A. Messenger, G. E. Wheeler, X. Liu, and D. M. Bortz. Learning Anisotropic Interaction Rules from Individual Trajectories in a Heterogeneous Cellular Population. J. R. Soc. Interface, 19(195):20220412, Oct. 2022. doi
  11. D. A. Messenger and D. M. Bortz. Learning mean-field equations from particle data using WSINDy. Physica D, 439:133406, Nov. 2022. doi
  12. D. A. Messenger, E. Dall’Anese, and D. M. Bortz. Online Weak-form Sparse Identification of Partial
    Differential Equations. In Proc. Third Math. Sci. Mach. Learn. Conf., volume 190 of Proceedings of
    Machine Learning Research, pages 241–256. PMLR, 2022. link
  13. J. M. Wentz, J. C. Cameron, and D. M. Bortz. Analytical Singular Value Decomposition for a Class of
    Stoichiometry Matrices. SIAM J. Matrix Anal. Appl., 43(3):1109–1147, Sept. 2022. doi
  14. G. E. Wheeler, A. Purkayastha, E. N. Bunker, D. M. Bortz, and X. Liu. Protocol for Analysis and Consolidation of TrackMate Outputs for Measuring Two-Dimensional Cell Motility using Nuclear Tracking. J. Vis. Exp., 178:e62885, Dec. 2021. doi
  15. D. A. Messenger and D. M. Bortz. Weak SINDy: Galerkin-Based Data-Driven Model Selection. Multiscale Model. Simul., 19(3):1474–1497, 2021. doi
  16. J. M. Wentz and D. M. Bortz. Boundedness of a class of discretized reaction-diffusion systems. SIAM J. Appl. Math., 81(5):1870–1892, 2021. doi
  17. D.A. Messenger and D.M. Bortz. Weak SINDy For Partial Differential Equations. J. Comp. Physics, 443:110525, October 15, 2021. doi
  18. A. G. Buchwald, J. Bayham, j. adams, D. M. Bortz, K. Colborn, O. Zarella, M. Buran, J. Samet, D. Ghosh, R. Herlihy, and E. J. Carlton. Estimating the impact of state-wide policies to reduce the spread of SARS-CoV-2 in Colorado in real-time. Emergning Infect. Dis., 27(9), June 2021. doi
  19. H.J. Dudley, Z.J. Ren, and D.M. Bortz. Competitive Exclusion in a DAE Model for Microbial Electrolysis Cells. Math. Biosci. Eng. 17(5):6217-6239, 2020. doi
  20. A. G. Buchwald, J. Adams, D. M. Bortz, and E. J. Carlton. Infectious Disease Transmission Models to Predict, Evaluate and Improve Understanding of SARS-COV-2 Trajectory and Interventions. Annals of the American Thoracic Society, 17(10):1204–1206, Oct. 2020. doi
  21. N. C. Hill, J. W. Tay, S. L. Altus, D. M. Bortz, and J. C. Cameron. Life cycle of a cyanobacterial carboxysome. Science Advances 6(19):eaba1269, 2020. doi
  22. K. A. Moore, S. L. Altus, J. W. Tay, J. Fox, E. B. Johnson, D. M. Bortz, and J. C. Cameron. Mechanical Regulation of Photosynthesis. Nature Microbiology 5(23 Mar):757-767, 2020. doi
  23. J. A. Stotsky and D. M. Bortz. A Posteriori Error Analysis of Fluid-Structure Interactions: Time Dependent Error. Computer Methods in Applied Mechanics and Engineering, 356(1 Nov.):1-15, 2019. doiarXiv:1807.03279
  24. J. T. Nardini and D. M. Bortz. The influence of numerical error on parameter estimation and uncertainty quantification for advective PDE models. Inverse Problems, 35(6):065003, 2019. doi arXiv:1807.09652
  25. H. J. Dudley, L. Lu, Z. J. Ren, and D. M. Bortz. Sensitivity and Bifurcation Analysis of a Differential-Algebraic Equation Model for a Microbial Electrolysis Cell. SIAM J. Appl. Dyn. Syst., 18(2):709-728, 2019. doi arXiv:1802.06326
  26. J.A. Stotsky, V. Dukic, & D.M. Bortz. A Point Process Model for Generating Biofilms with Realistic Microstructure and Rheology, Eur. J. Appl. Math., 29(6):1141-1177, Dec. 2018 doiarXiv:1707.05739
  27. E.P. Kightley, A. Pearson, J.A. Evans, & D.M. Bortz. Fragmentation of biofilm-seeded bacterial aggregates in shear flow, Eur. J. Appl. Math., 29(6):1062-1078, Dec. 2018 doiarXiv:1610.03560
  28. J.M. Wentz, A.R. Mendenhall, & D.M. Bortz. Pattern Formation in the Longevity-Related Expression of Heat Shock Protein-16.2 in Caenorhabditis elegans, Bulletin of Mathematical Biology, 80(10):2669-2697, 2018. doiarXiv:1706.03085
  29. J.T. Nardini & D.M. Bortz. Investigation of a Structured Fisher's Equation with Applications in Biochemistry, SIAM J. Appl. Math., 78(3):1712–1736, 2018 doiarXiv:1602.07033
  30. V. Dukic & D.M. Bortz, Uncertainty Quantification Using Probabilistic Numerics: Application to Models in Mathematical Epidemiology, Inverse Problems in Science and Engineering, 28(2):223-232, 2018. doi
  31. I. Mirzaev and D.M. Bortz. A numerical framework for computing steady states of structured population models and their stability. Math. Biosci. Eng., 14(4):933–952, Aug. 2017. doiarXiv
  32. D.M. Bortz, Characteristic roots for two-lag linear delay differential equations, Discrete and Continuous Dynamical System - B, 21(8): 2409-2422, 2016. doi
  33. I. Mirzaev, E.C. Byrne, & D.M. Bortz. An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations, Inverse Problems, 32(9), 095005, September 2016. doi arXiv:1510.01355
  34. D.D. Keck & D.M. Bortz. Generalized sensitivity functions for size-structured population models, Journal of Inverse and Ill-posed Problems, 24(3):309-321, June 2016. doi arXiv:1406.0212
  35. J.T. Nardini, D.A. Chapnick, X. Liu, D.M. Bortz. Modeling Keratinocyte Wound Healing Dynamics: Cell-cell Adhesion Promotes Sustained Collective Migration, Journal of Theoretical Biology, 400(July):103-117, 2016. doi arXiv:1506.07081
  36. J.A. Stotsky, J.F. Hammond, L. Pavlovsky, E.J. Stewart, J.G. Younger, M.J. Solomon, D.M. Bortz. Variable Viscosity and Density Biofilm Simulations using an Immersed Boundary Method, Part II: Experimental Validation and the Heterogeneous Rheology-IBM, Journal of Computational Physics, 317(July):204-222, 2016 doi. arXiv:1504.07326
  37. D.M. Bortz. Eigenvalues for a Two-lag linear delay differential equation, IFAC-PapersOnline, 48(12):13-16, 2015 doi
  38. I. Mirzaev & D.M. Bortz. Laplacian Dynamics with Synthesis and Degradation, Bulletin of Mathematical Biology, 77(6):1013–1045, 2015 doi arXiv:1404.6477.
  39. D.M. Bortz. Chapter 17: Modeling and simulation for nanomaterials in fluids: Nanoparticle self-assembly. In V. Tewary & Y. Zhang, editors, Modeling, characterization, and production of nanomaterials (Electronics, Photonics and Energy applications), 419-441, Woodhead/Elsevier, 2015.
  40. S. Sircar, E. Aisenbrey, S. Bryant & D.M. Bortz, Determining average osmolarity in Poly(ethylene glycol)-Chondrotin sulfate gels mimicking cartillage. Journal of Theoretical Biology, 364(Jan):394-406, 2015. doi arXiv:1308.4421
  41. S. Sircar, J. G. Younger, & D.M. Bortz. Sticky surface: sphere–sphere adhesion dynamics. Journal of Biological Dynamics, 9(sup1): 79-89, 2015 doi arXiv:1301.2504
  42. S.M. Kissler, C. Cichowitz, S. Sankaranarayanan, & D.M. Bortz. Determination of personalized diabetes treatment plans using a two-delay model. Journal of Theoretical Biology, 359(Oct), 101-111, 2014 doi arXiv:1403.0638
  43. J. F. Hammond, E. J. Stewart, M. J. Solomon, J. G. Younger, & D.M. Bortz. Variable viscosity and density biofilm simulations using an Immersed Boundary Method, Part I: numerical scheme and convergence results. Computer Modeling in Engineering & Sciences, 98(3), 295-340, 2014 doi arXiv:1302.3663 (Invited paper as a part of a special issue on Computational Mechanobiology and Soft Matter Mechanics.)
  44. G. Lambert, A. Bergman, Q. Zhang, D.M. Bortz, & R. Austin. Physics of Biofilms: The Initial Stages of Biofilm Formation and Dynamics. New J. Physics, 16(4):045005, Apr. 2014. doi
  45. S. Sircar & D.M. Bortz. Impact of flow on ligand-mediated bacterial flocculation. Mathematical Biosciences, 245(2):314-321, Oct. 2013. doi
  46. A. Satorius, J. Szafranski, A. Rivera, D. Pynes, M. Ghanesan, M. J. Solomon, D. Newton, D.M. Bortz, & J. G. Younger, Complement C5a Generation by Staphylococcus epidermidis Biofilms. SHOCK, 39(4):336-342, Apr. 2013. doi
  47. E. C. Conrad, Y.-Y. Hsu, D.M. Bortz, & J. G. Younger. Spatiotemporal Dynamics of Complement C5a Production within Bacterial Extracellular Polymeric Substance. Journal of Innate Immunity, 5(2):114-123, Jan. 2013. (cover art!). doi
  48. C. W. Curtis & D.M. Bortz, Propagation of fronts in the Fisher-Kolmogorov equation with quadratically varying diffusion. Phys. Rev. E, 86(6):066108, Dec. 2012. doi arXiv:1207.1097
  49. M. Thornton, C. Irvin, H. M. Chung, D.M. Bortz, M. J. Solomon, & J. G. Younger, Multicellularity and Antibiotic Resistance in Klebsiella pneumoniae Grown under Bloodstream-Mimicking Fluid Dynamic Conditions. Journal of Infectious Diseases, 206(4):588-595, Aug. 2012. doi
  50. J. F. Hammond & D.M. Bortz, Analytical solutions to Fisher’s equation with time-variable coefficients. Applied Mathematics and Computation, 218(6):2497-2508, 2011. doi
  51. E. C. Byrne, S. Dzul, M. J. Solomon, J. G. Younger, & D.M. Bortz, Postfragmentation density function for bacterial aggregates in laminar flow. Phys. Rev. E, 83(4):41911, 2011. doi
  52. S. P. Dzul, M. M. Thornton, D. N. Hohne, E. J. Stewart, A. A. Shah, D.M. Bortz, M. J. Solomon, and J. G. Younger.Contribution of the Klebsiella pneumoniae Capsule to Bacterial Aggregate and Biofilm Microstructures. Applied Environmental Microbiology, 77(5):1777–1782, Mar. 2011. doi
  53. C. M. Nypaver, M. M. Thornton, S. M. Yin, D. O. Bracho, P. W. Nelson, A. E. Jones, D.M. Bortz, & J. G. Younger, Dynamics of Human Complement―Mediated Killing of Klebsiella pneumoniae, American journal of respiratory cell and molecular biology, 43(5):585-590, 2010. doi
  54. H. Chung, M. M. Cartwright, D.M. Bortz, T. L. Jackson, & J. G. Younger, Dynamical System Analysis of Staphylococcus epidermidis Bloodstream Infection, SHOCK, 30(5):518-526, November 2008. doi (cover art!)
  55. D.M. Bortz, T. L. Jackson, K. A. Taylor, A. P. Thompson, & J. G. Younger, Klebsiella pneumoniae flocculation dynamics, Bulletin of Mathematical Biology, 70(3):745-768, April 2008. doi
  56. D.M. Bortz & P. W. Nelson, Model selection and mixed-effects modeling of HIV infection dynamics, Bulletin of Mathematical Biology, 68(8):2005-2025, November 2006. doi
  57. S. Ciupe, B. L. Bivort, D.M. Bortz, & P. W. Nelson, Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models, Mathematical Biosciences, 200(1):1-27, March 2006.doi
  58. I. Ben-David, S. E. Price, D.M. Bortz, S. Cohen, A. L. Bauer, T. L. Jackson, & J. G. Younger, Dynamics of intrapulmonary bacterial growth in a murine model of repeated microaspirations, Am. J. Respiratory Cell & Molecular Biology, 33(5):476-482, November 2005. doi
  59. H. T. Banks & D.M. Bortz, A parameter sensitivity methodology in the context of HIV delay equation models, Journal of Mathematical Biology, 50(6):607-625, June 2005. doi
  60. H. T. Banks & D.M. Bortz, Inverse Problems for a Class of Measure Dependent Dynamical Systems, Journal of Inverse and Ill-posed Problems, 13(2):103-121, April 2005. doi
  61. D.M. Bortz & P. W. Nelson, Sensitivity analysis of nonlinear lumped parameter models of HIV infection dynamics, Bulletin of Mathematical Biology, 66(5):1009-1026, September 2004. doi
  62. H. T. Banks, D.M. Bortz, G. A. Pinter, & L. K. Potter, Chapter 6: Modeling and imaging techniques with potential for applications in bioterrorism. In H. T. Banks and C. Castillo-Chavez, editors, Bioterrorism: Mathematical Modeling Applications in Homeland Security, volume 28 of Frontiers in Applied Mathematics, pages 129-154, SIAM, Phildelphia, PA, 2003.
  63. H. T. Banks, D.M. Bortz, & S. E. Holte, Incorporation of variability into the mathematical modeling of viral delays in HIV infection dynamics, Mathematical Biosciences, 183(1):63-91, May 2003. doi
  64. D.M. Bortz, A. D. Rubio, H. T. Banks, A. B. Cain, & R. C. Smith, Control of open bay acoustics by harmonic mass injection, International Journal of Aeroacoustics, 1(1):65-81, March 2002. doi
  65. A. B. Cain, A. D. Rubio, D.M. Bortz, H. T. Banks, & R. C. Smith, Reduced Order Modeling in Control of Open Cavity Acoustics, Proceedings of the AIAA, AIAA-2000-1928, June 2000.
  66. D.M. Bortz & C. T. Kelley, The simplex gradient and noisy optimization problems. In J. T. Borggaard, J. Burns, E. Cliff, and S. Schreck, editors, Computational Methods in Optimal Design and Control, volume 24 of Progress in Systems and Control Theory, Birkhauser, 1998, pp. 77-90.
  67. I. Ambats, D.M. Bortz, A. Connolly, A. Derlicki, M. Derrick, W. Kahle, & J. Thron, Studies of Hadron-Electron Separators for the ZEUS Barrel Calorimeter, Nuclear Instruments and Methods in Physics Research Section A, 368(2):364-377, 1996. doi

Other Publications

  1. T. Kusher, D.M. Bortz, D. Maahs, S. Sankaranarayanan, A data-driven approach to artificial pancreas verification and synthesis, ICCPS '18 Proceedings of the 9th ACM/IEEE International Conference on Cyber-Physical Systems Pages 242-252, 2018. doi
  2. S. H. Friedman, A. R. A. Anderson, D. M. Bortz, A. G. Fletcher, H. B. Frieboes, A. Ghaffarizadeh, D. R. Grimes, A. Hawkins-Daarud, S. Hoehme, E. F. Juarez, C. Kesselman, R. Merks, S. M. Mumenthaler, P. K. Newton, K.-A. Norton, R. Rawat, R. C. Rockne, D. Ruderman, J. Scott, S. S. Sindi, J. L. Sparks, K. Swanson, D. B. Agus, and P. Macklin. MultiCellDS: A community-developed standard for curating microenvironment-dependent multicellular data. bioRxiv:090456, Nov. 2016.
  3. S. H. Friedman, A. R. A. Anderson, D. M. Bortz, A. G. Fletcher, H. B. Frieboes, A. Ghaffarizadeh, D. R. Grimes, A. Hawkins-Daarud, S. Hoehme, E. F. Juarez, C. Kesselman, R. M. H. Merks, S. M. Mumenthaler, P. K. Newton, K.-A. Norton, R. Rawat, R. C. Rockne, D. Ruderman, J. Scott, S. S. Sindi, J. L. Sparks, K. Swanson, D. B. Agus, and P. Macklin. MultiCellDS: A standard and a community for sharing multicellular data. bioRxiv:090696, Sept. 2016.
  4. I. Mirzaev & D.M. Bortz. Criteria for linearized stability for a size-structured population model. arXiv:1502.02754
  5. E. C. Conrad, A. E. Satorius, P. Sharma, D.M. Bortz, & J. G. Younger. The Host Response to Line Sepsis: Experimental and Computational Analysis of Complement Activation against Coagulase-Negative Staphylococcal Biofilms. Annals of Emergency Medicine, 62(4):S153, 2013.
  6. J. G. Younger, M. M. Thornton, C. Babcock, H. M. Chung-Esaki, D.M. Bortz, & M. J. Solomon. Bloodstream-like fluid dynamic conditions promote multicellularity and antibiotic resistance in in Klebsiella pneumoniae. SHOCK, 37(1):58, 2012.
  7. D.M. Bortz & A. J. Christlieb. Scandalously Parallelizable Mesh Generation. arXiv:1103.5268
  8. M. M. Thornton, D. N. Hohne, M. J. Solomon, D.M. Bortz, & J. G. Younger. Bacterial aggregation during growth under low shear: implications for bacteremia. SHOCK, 31(7):22, 2009.
  9. D.M. Bortz & A. J. Christlieb. Random numerical discretizations. In Abstracts of the International Conference Inverse Problems: Modeling and Simulation, pages 29–30, 2008.
  10. D. Li, D. Hohne, D.M. Bortz, J. Bull, & J. G. Younger Modeling bacterial clearance from the bloodstream using computational fluid dynamics and monte carlo simulation. J. Critical Care, 22(4):344, Dec. 2007.
  11. J. G. Younger, H. Y. Chung, M. Cartwright, D.M. Bortz, & T. L. Jackson, Neutropenic S-epidermidis bacteremia modeled as a pharmacodynamic system, SHOCK, 27(Supplement 1):68-69, June 2007.
  12. D.M. Bortz. Accurate model selection computations. J. Critical Care, 21(4):359, Dec. 2006.
  13. H. Chung, T. L. Jackson, D.M. Bortz, M. Cartwright, & J. G. Younger, Multiple-compartment bacterial clearance kinetics during murine bacteremia, Journal of Critical Care, 21(4):359-360, December 2006.
  14. D.M. Bortz, T. L. Jackson, & J. G. Younger, Estimation and identification of Klebsiella pneumoniae flocculation dynamics, In Abstracts of the International Conference Inverse Problems: Modeling and Simulation, pages 15-17, 2006.
  15. J. G. Younger, K. Taylor, A. Thompson, & D.M. Bortz. Quantification and modeling of aggregate bacterial growth in suspension: Implications for bacteremia. SHOCK, pages 79–80, June 2006.
  16. I. Ben-David, S. E. Price, S. Cohen, D.M. Bortz, T. L. Jackson, & J. G. Younger, Complement C3 is necessary for early suppression of intrapulmonary bacterial growth, SHOCK, 23(Supplement 3):79-80, June 2005.
  17. A. L. Bauer, D.M. Bortz, D. Gammack, I. Ben-David, A. Stein, T. L. Jackson, & J. G. Younger, Virulence of Klebsiella pneumoniae predicted by nonlinear biodistributive mathematical model, SHOCK, 21(Supplement 2):29,2004.
  18. D.M. Bortz, Modeling, Analysis, and Estimation of an in vitro HIV Infection Using Functional Differential Equations, Ph.D. dissertation, North Carolina State University, Raleigh, NC, 2002.
  19. D.M. Bortz, R. Guy, J. Hood, K. Kirkpatrick, V. Nguyen, & V. Shimanovich, Modeling HIV infection dynamics using delay equations, In P. A. Gremaud, Z. Li, R. C. Smith, and H. T. Tran, editors, Proceedings of the 2000 Industrial Mathematics Modeling Workshop for Graduate Students, pages 48-58. Technical Report CRSC-TR00-24, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, October 2000.
  20. A. B. Cain, A. D. Rubio, D.M. Bortz, H. T. Banks, & R. C. Smith, Optimizing control of open bay acoustics, Tech. Report CRSC-TR00-09, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, May 2000.
  21. A. S. Bondarenko, D.M. Bortz, & J. J. Moré, COPS: Large-scale nonlinearly constrained optimization problems, Tech. Report ANL/MCS-TM-237, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, September 1998, revised October 1999.
  22. P. Barnes, D.M. Bortz, S. Frank, I. Loladze, E. Packard, & M. Santhanam, Power transformer clearance checking, In F. Reitich, J. S. Scroggs, and H. T. Tran, editors, Proceedings of the 1997 Industrial Mathematics Modeling Workshop for Graduate Students. Technical Report CRSC-TR98-09, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, February, 1998.