Publications in VIVO

Co-author Network

Bortz, David

Professor

Positions

Professor, Applied Mathematics
Professor, Computer Science

Research Areas

Research

research overview

Dr. Bortz's research in focused on the methodology of data-driven modeling and scientific machine learning as applied to complex systems including: cellular migration, infectious diseases, disease ecology, atmospheric fluid models, and computational plasma physics.

keywords

Data-driven modeling, Scientific Machine Learning, Applied Mathematics, Mathematical Biology

Publications

selected publications

chapter
- Bias and Coverage Properties of the WENDy-IRLS Algorithm. 1-108. 2026
- Learning Diffusion Coefficients, Kinetic Parameters, and the Number of Underlying States from a Multistate Diffusion Process: Robustness Results and Application to PDK1/PKCα Dynamics. 1-36. 2024
- Weak form-based data-driven modeling. Handbook of Numerical Analysis. 53-82. 2024
- Modeling and simulation for nanomaterials in fluids: Nanoparticle self-assembly. 419-441. 2015
- Modeling and simulation of nanomaterials in fluids. 419-441. 2015
- 6. Modeling and Imaging Techniques with Potential for Application in Bioterrorism. 129-154. 2003
- Modeling and Imaging Techniques with Potential for Application in Bioterrorism 2003
- Modeling and imaging techniques with potential for application in bioterrorism. 129-154. 2003
- The simplex gradient and noisy optimization problems. 77-90. 1998
conference proceeding
- Weighted Composition Operators for Learning Nonlinear Dynamics. IFAC-PapersOnLine. 97-102. 2024
- Online Weak-form Sparse Identification of Partial Differential Equations 2022
- A Data-Driven Approach to Artificial Pancreas Verification and Synthesis. 242-252. 2018
- A Data-Driven Approach to Artificial Pancreas Verification and Synthesis. 242-252. 2018
- PERSONALIZED DATA-DRIVEN VERIFICATION AND SYNTHESIS FOR ARTIFICIAL PANCREAS CONTROLLERS. Diabetes Technology and Therapeutics. A36-A37. 2018
- Optimizing control of open bay acoustics 2000
journal article
- Asymptotic consistency of the WSINDy algorithm in the limit of continuum data. IMA Journal of Numerical Analysis. 2025
- Learning structured population models from data with WSINDy.. PLoS Computational Biology. e1013742. 2025
- Learning Physically Interpretable Atmospheric Models From Data With WSINDy 2025
- Influence of initial conditions on data-driven model identification and information entropy for ideal mhd problems. Journal of Computational Physics. 2025
- Physics-Informed Active Learning With Simultaneous Weak-Form Latent Space Dynamics Identification. International Journal for Numerical Methods in Engineering. 2025
- Weak-form latent space dynamics identification. Computer Methods in Applied Mechanics and Engineering. 2024
- Coarse-graining Hamiltonian systems using WSINDy. Scientific Reports. 2024
- Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics. Bulletin of Mathematical Biology. 2023
- Learning mean-field equations from particle data using WSINDy. Physica D : Non-linear phenomena. 2022
- Learning anisotropic interaction rules from individual trajectories in a heterogeneous cellular population. Journal of the Royal Society Interface. 2022
- ANALYTICAL SINGULAR VALUE DECOMPOSITION FOR A CLASS OF STOICHIOMETRY MATRICES. SIAM Journal on Matrix Analysis and Applications. 1109-1147. 2022
- Protocol for Analysis and Consolidation of TrackMate Outputs for Measuring Two-Dimensional Cell Motility using Nuclear Tracking. Journal of Visualized Experiments. 2021
- Weak SINDy for partial differential equations. Journal of Computational Physics. 2021
- Estimating the Impact of Statewide Policies to Reduce Spread of Severe Acute Respiratory Syndrome Coronavirus 2 in Real Time, Colorado, USA. Emerging Infectious Diseases. 2312-2322. 2021
- BOUNDEDNESS OF A CLASS OF SPATIALLY DISCRETE REACTION-DIFFUSION SYSTEMS. SIAM Journal on Applied Mathematics. 1870-1892. 2021
- WEAK SINDy: GALERKIN-BASED DATA-DRIVEN MODEL SELECTION. Multiscale Modeling and Simulation. 1474-1497. 2021
- Infectious Disease Transmission Models to Predict, Evaluate, and Improve Understanding of COVID-19 Trajectory and Interventions. Annals of the American Thoracic Society. 1204-1206. 2020
- Life cycle of a cyanobacterial carboxysome. Science Advances. 2020
- Mechanical regulation of photosynthesis in cyanobacteria. Nature Microbiology. 757-+. 2020
- Competitive exclusion in a DAE model for microbial electrolysis cells. Mathematical Biosciences and Engineering. 6217-6239. 2020
- A posteriori error analysis of fluid-structure interactions: Time dependent error. Computer Methods in Applied Mechanics and Engineering. 1-15. 2019
- The influence of numerical error on parameter estimation and uncertainty quantification for advective PDE models. Inverse Problems. 2019
- Sensitivity and Bifurcation Analysis of a Differential-Algebraic Equation Model for a Microbial Electrolysis Cell. SIAM Journal on Applied Dynamical Systems. 709-728. 2019
- A point process model for generating biofilms with realistic microstructure and rheology. European Journal of Applied Mathematics. 1141-1177. 2018
- Fragmentation of biofilm-seeded bacterial aggregates in shear flow. European Journal of Applied Mathematics. 1062-1078. 2018
- Pattern Formation in the Longevity-Related Expression of Heat Shock Protein-16.2 in Caenorhabditis elegans. Bulletin of Mathematical Biology. 2669-2697. 2018
- INVESTIGATION OF A STRUCTURED FISHER'S EQUATION WITH APPLICATIONS IN BIOCHEMISTRY. SIAM Journal on Applied Mathematics. 1712-1736. 2018
- Uncertainty quantification using probabilistic numerics: application to models in mathematical epidemiology. Inverse Problems in Science and Engineering. 223-232. 2018
- A NUMERICAL FRAMEWORK FOR COMPUTING STEADY STATES OF STRUCTURED POPULATION MODELS AND THEIR STABILITY. Mathematical Biosciences and Engineering. 933-952. 2017
- MultiCellDS: a standard and a community for sharing multicellular data 2016
- MultiCellDS: a community-developed standard for curating microenvironment-dependent multicellular data 2016
- CHARACTERISTIC ROOTS FOR TWO-LAG LINEAR DELAY DIFFERENTIAL EQUATIONS. Discrete and Continuous Dynamical Systems - Series B. 2409-2422. 2016
- An inverse problem for a class of conditional probability measure-dependent evolution equations. Inverse Problems. 2016
- Variable viscosity and density biofilm simulations using an immersed boundary method, part II: Experimental validation and the heterogeneous rheology-IBM. Journal of Computational Physics. 204-222. 2016
- Modeling keratinocyte wound healing dynamics: Cell-cell adhesion promotes sustained collective migration. Journal of Theoretical Biology. 103-117. 2016
- Generalized sensitivity functions for size-structured population models. Journal of Inverse and Ill-Posed Problems. 309-321. 2016
- Sticky surface: sphere-sphere adhesion dynamics. Journal of Biological Dynamics. 79-89. 2015
- Laplacian Dynamics with Synthesis and Degradation. Bulletin of Mathematical Biology. 1013-1045. 2015
- Determining equilibrium osmolarity in poly(ethylene glycol)/chondrotin sulfate gels mimicking articular cartilage. Journal of Theoretical Biology. 397-406. 2015
- Eigenvalues for a Two-Lag Linear Delay Differential Equation. IFAC-PapersOnLine. 13-16. 2015
- Determination of personalized diabetes treatment plans using a two-delay model. Journal of Theoretical Biology. 101-111. 2014
- Physics of biofilms: the initial stages of biofilm formation and dynamics. New Journal of Physics. 2014
- Variable Viscosity and Density Biofilm Simulations using an Immersed Boundary Method, Part I: Numerical Scheme and Convergence Results. CMES - Computer Modeling in Engineering and Sciences. 295-340. 2014
- Impact of flow on ligand-mediated bacterial flocculation. Mathematical Biosciences. 314-321. 2013
- The Host Response to Line Sepsis: Experimental and Computational Analysis of Complement Activation against Coagulase-Negative Staphylococcal Biofilms. Annals of Emergency Medicine. S153-S153. 2013
- COMPLEMENT C5A GENERATION BY STAPHYLOCOCCAL BIOFILMS. Shock. 336-342. 2013
- Spatiotemporal Dynamics of Complement C5a Production within Bacterial Extracellular Polymeric Substance. Journal of Innate Immunity. 114-123. 2013
- Propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion. Physical Review E. 2012
- Multicellularity and Antibiotic Resistance in Klebsiella pneumoniae Grown Under Bloodstream-Mimicking Fluid Dynamic Conditions. Journal of Infectious Diseases. 588-595. 2012
- BLOODSTREAM-LIKE FLUID DYNAMIC CONDITIONS PROMOTE MULTICELLULARITY AND ANTIBIOTIC RESISTANCE IN KLEBSIELLA PNEUMONIAE. Shock. 58-58. 2012
- Analytical solutions to Fisher's equation with time-variable coefficients. Applied Mathematics and Computation. 2497-2508. 2011
- Postfragmentation density function for bacterial aggregates in laminar flow (vol 83, 041911, 2011). Physical Review E: Statistical, Nonlinear, and Soft Matter Physics. 2011
- Postfragmentation density function for bacterial aggregates in laminar flow. Physical Review E. 2011
- Postfragmentation density function for bacterial aggregates in laminar flow. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics. 2011
- Contribution of the Klebsiella pneumoniae Capsule to Bacterial Aggregate and Biofilm Microstructures. Applied and Environmental Microbiology. 1777-1782. 2011
- Dynamics of Human Complement-Mediated Killing of Klebsiella pneumoniae. American Journal of Respiratory Cell and Molecular Biology. 585-590. 2010
- A REAL-TIME ASSAY FOR IDENTIFYING COMPLEMENT-MEDIATED BACTERIAL KILLING DEFECTS IN SEPTIC PATIENTS. Shock. 85-85. 2009
- BACTERIAL AGGREGATION DURING GROWTH UNDER LOW SHEAR: IMPLICATIONS FOR BACTEREMIA. Shock. 22-22. 2009
- DYNAMICAL SYSTEM ANALYSIS OF STAPHYLOCOCCUS EPIDERMIDIS BLOODSTREAM INFECTION. Shock. 518-526. 2008
- Klebsiella pneumoniae flocculation dynamics. Bulletin of Mathematical Biology. 745-768. 2008
- Modeling bacterial clearance from the bloodstream using computational fluid dynamics and Monte Carlo simulation. Journal of Critical Care. 344-344. 2007
- Neutropenic S-epidermidis bacteremia modeled as a pharmacodynamic system. Shock. 68-69. 2007
- Neutropenic Staphylococcus epidermidis Bacteremia in a Multicompartment Pharmacokinetic System. Academic Emergency Medicine. S178-S179. 2007
- Accurate model selection computations. Journal of Critical Care. 359-359. 2006
- Multiple-compartment bacterial clearance kinetics during murine bacteremia. Journal of Critical Care. 359-360. 2006
- Model selection and mixed-effects modeling of HIV infection dynamics. Bulletin of Mathematical Biology. 2005-2025. 2006
- Quantification and modeling of aggregate bacterial growth in suspension: Implications for bacteremia.. Shock. 79-80. 2006
- Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models. Mathematical Biosciences. 1-27. 2006
- Dynamics of intrapulmonary bacterial growth in a murine model of repeated microaspiration. American Journal of Respiratory Cell and Molecular Biology. 476-482. 2005
- A parameter sensitivity methodology in the context of HIV delay equation models. Journal of Mathematical Biology. 607-625. 2005
- Complement C3 is necessary for early suppression of intrapulmonary bacterial growth.. Shock. 79-80. 2005
- Inverse problems for a class of measure dependent dynamical systems. Journal of Inverse and Ill-Posed Problems. 103-121. 2005
- Inverse problems for a class of measure dependent dynamical systems. Journal of Inverse and Ill-Posed Problems. 103-121. 2005
- Sensitivity analysis of a nonlinear lumped parameter model of HIV infection dynamics. Bulletin of Mathematical Biology. 1009-1026. 2004
- Virulence of klebsiella pneumoniae predicted by nonlinear biodistributive mathematical model. Shock. 29-29. 2004
- Incorporation of variability into the modeling of viral delays in HIV infection dynamics. Mathematical Biosciences. 63-91. 2003
- Control of Open Bay Acoustics by Harmonic Mass Injection. International Journal of Aeroacoustics. 65-81. 2002
- Studies of hadron-electron separators for the ZEUS barrel calorimeter. Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. 364-377. 1996

Background

education and training

Ph.D., North Carolina State University at Raleigh 2002
M.S., North Carolina State University at Raleigh 2000
B.A., Rice University 1997

awards and honors

Outstanding Investigator Award (R35), conferred by National Institutes of Health, 2023
Exceptional Graduate Faculty Mentor Award, conferred by Graduate School, 2019

International Activities

geographic focus

Australia Country
Canada Country
Europe Continent
France Country
India Country
Italy Country
North America Continent
South Korea Country
United Kingdom Country

Other Profiles

ORCID iD

http://orcid.org/0000-0003-1163-7317

Google Scholar

https://scholar.google.com/citations?user=7wkmJU8AAAAJ&hl=en

ResearchGate

https://www.researchgate.net/profile/David_Bortz

Github

https://github.com/MathBioCU