David M. Bortz

Generating author description...

All published works

Action	Title	Year	Authors
+ PDF Chat	Influence of initial conditions on data-driven model identification and information entropy for ideal mhd problems	2025	Gina Vasey Daniel A. Messenger David M. Bortz Andrew Christlieb Brian W. O’Shea
+ PDF Chat	Learning Weather Models from Data with WSINDy	2025	Seth Minor Daniel A. Messenger Vanja Dukić David M. Bortz
+	Asymptotic consistency of the WSINDy algorithm in the limit of continuum data	2024	Daniel A. Messenger David M. Bortz
+ PDF Chat	Physics‐Informed Active Learning With Simultaneous Weak‐Form Latent Space Dynamics Identification	2024	Xiaolong He April Tran David M. Bortz Youngsoo Choi
+ PDF Chat	The Weak Form Is Stronger Than You Think	2024	Daniel A. Messenger April Tran Vanja Dukić David M. Bortz
+ PDF Chat	WgLaSDI: Weak-Form Greedy Latent Space Dynamics Identification	2024	Xiaolong He April Tran David M. Bortz Youngsoo Choi
+	Weak-form latent space dynamics identification	2024	April Tran Xiaolong He Daniel A. Messenger Youngsoo Choi David M. Bortz
+ PDF Chat	A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling	2024	Christophe Bonneville Xiaolong He April Tran Jun Sur Park William Fries Daniel A. Messenger Siu Wun Cheung Yeonjong Shin David M. Bortz Debojyoti Ghosh
+	Weak form-based data-driven modeling	2024	David M. Bortz Daniel A. Messenger April Tran
+ PDF Chat	Coarse-Graining Hamiltonian Systems Using WSINDy	2023	Daniel A. Messenger J. W. Burby David M. Bortz
+ PDF Chat	Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics	2023	David M. Bortz Daniel A. Messenger Vanja Dukić
+	Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamics	2023	David M. Bortz Daniel A. Messenger Vanja Dukić
+	Coarse-Graining Hamiltonian Systems Using WSINDy	2023	Daniel A. Messenger J. W. Burby David M. Bortz
+	Weak-Form Latent Space Dynamics Identification	2023	April Tran Xiaolong He Daniel A. Messenger Youngsoo Choi David M. Bortz
+	Influence of initial conditions on data-driven model identification and information entropy for ideal mhd problems	2023	Gina Vasey Daniel A. Messenger David M. Bortz Andrew Christlieb Brian W. O’Shea
+	Learning anisotropic interaction rules from individual trajectories in a heterogeneous cellular population	2022	Daniel A. Messenger Graycen E. Wheeler Xuedong Liu David M. Bortz
+	Analytical Singular Value Decomposition for a Class of Stoichiometry Matrices	2022	Jacqueline Wentz Jeffrey C. Cameron David M. Bortz
+	Learning mean-field equations from particle data using WSINDy	2022	Daniel A. Messenger David M. Bortz
+	Online Weak-form Sparse Identification of Partial Differential Equations	2022	Daniel A. Messenger Emiliano Dall’Anese David M. Bortz
+	Asymptotic Analysis of a General Multi-Structured Population Model	2022	Sabina L. Altus Jeffrey C. Cameron David M. Bortz
+	Learning Anisotropic Interaction Rules from Individual Trajectories in a Heterogeneous Cellular Population	2022	Daniel A. Messenger Graycen E. Wheeler Xuedong Liu David M. Bortz
+	Learning diffusion coefficients, kinetic parameters, and the number of underlying states from a multi-state diffusion process: robustness results and application to PDK1/PKC$α$, dynamics	2022	Lewis R. Baker Moshe T. Gordon Brian P. Ziemba Victoria Gershuny Joseph J. Falke David M. Bortz
+	Asymptotic consistency of the WSINDy algorithm in the limit of continuum data	2022	Daniel A. Messenger David M. Bortz
+ PDF Chat	Estimating the Impact of Statewide Policies to Reduce Spread of Severe Acute Respiratory Syndrome Coronavirus 2 in Real Time, Colorado, USA	2021	Andrea G. Buchwald Jude Bayham jimi adams David M. Bortz Kathryn Colborn Olivia Zarella Meghan Buran Jonathan M. Samet Debashis Ghosh Rachel Herlihy
+	Weak SINDy for partial differential equations	2021	Daniel A. Messenger David M. Bortz
+ PDF Chat	Weak SINDy: Galerkin-Based Data-Driven Model Selection	2021	Daniel A. Messenger David M. Bortz
+ PDF Chat	Boundedness of a Class of Spatially Discrete Reaction-Diffusion Systems	2021	Jacqueline Wentz David M. Bortz
+	Analytical singular value decomposition for a class of stoichiometry matrices	2021	Jacqueline Wentz Jeffrey C. Cameron David M. Bortz
+	Infectious Disease Transmission Models to Predict, Evaluate, and Improve Understanding of COVID-19 Trajectory and Interventions	2020	Andrea G. Buchwald jimi adams David M. Bortz Elizabeth J. Carlton
+	Weak SINDy: Galerkin-Based Data-Driven Model Selection	2020	Daniel A. Messenger David M. Bortz
+ PDF Chat	A posteriori error analysis of fluid–structure interactions: Time dependent error	2019	Jay A. Stotsky David M. Bortz
+	Competitive Exclusion in a DAE Model for Microbial Electrolysis Cells	2019	Harry J. Dudley Zhiyong Jason Ren David M. Bortz
+	Boundedness of a class of discretized reaction-diffusion systems	2019	Jacqueline Wentz David M. Bortz
+	Competitive Exclusion in a DAE Model for Microbial Electrolysis Cells	2019	Harry J. Dudley Zhiyong Jason Ren David M. Bortz
+	Boundedness of a class of discretized reaction-diffusion systems	2019	Jacqueline Wentz David M. Bortz
+ PDF Chat	Pattern Formation in the Longevity-Related Expression of Heat Shock Protein-16.2 in Caenorhabditis elegans	2018	Jacqueline Wentz Alexander Mendenhall David M. Bortz
+ PDF Chat	A point process model for generating biofilms with realistic microstructure and rheology	2018	Jay A. Stotsky Vanja Dukić David M. Bortz
+ PDF Chat	Investigation of a Structured Fisher's Equation with Applications in Biochemistry	2018	John T. Nardini David M. Bortz
+	Sensitivity and Bifurcation Analysis of a DAE Model for a Microbial Electrolysis Cell	2018	Harry J. Dudley Lu Lu Zhiyong Jason Ren David M. Bortz
+	On the existence of non-trivial steady-state size-distributions for a class of flocculation equations	2018	Inom Mirzaev David M. Bortz
+	The Influence of Numerical Error on an Inverse Problem Methodology in PDE Models	2018	John T. Nardini David M. Bortz
+	A Point Process Model for Generating Biofilms with Realistic Microstructure and Rheology	2017	Jay A. Stotsky Vanja Dukić David M. Bortz
+	Pattern Formation in the Longevity-Related Expression of Heat Shock Protein-16.2 in Caenorhabditis elegans	2017	Jacqueline Wentz Alexander Mendenhall David M. Bortz
+	A numerical framework for computing steady states of structured population models and their stability	2017	Inom Mirzaev David M. Bortz
+	A Point Process Model for Generating Biofilms with Realistic Microstructure and Rheology	2017	Jay A. Stotsky Vanja Dukić David M. Bortz
+ PDF Chat	Characteristic roots for two-lag linear delay differential equations	2016	David M. Bortz
+ PDF Chat	An inverse problem for a class of conditional probability measure-dependent evolution equations	2016	Inom Mirzaev Erin Byrne David M. Bortz
+ PDF Chat	Modeling keratinocyte wound healing dynamics: Cell–cell adhesion promotes sustained collective migration	2016	John T. Nardini Douglas A. Chapnick Xuedong Liu David M. Bortz
+ PDF Chat	Variable viscosity and density biofilm simulations using an immersed boundary method, part II: Experimental validation and the heterogeneous rheology-IBM	2016	Jay A. Stotsky Jason F. Hammond Leonid Pavlovsky Elizabeth Stewart John G. Younger Michael J. Solomon David M. Bortz
+	A numerical framework for computing steady states of size-structured population models and their stability	2016	Inom Mirzaev David M. Bortz
+	Surface Forces on a Deforming Ellipsoid in Shear Flow	2016	E. P. Kightley A. Pearson Jane Evans David M. Bortz
+	Investigation of a Structured Fisher's Equation with Applications in Biochemistry	2016	John T. Nardini David M. Bortz
+	Stability of steady states for a class of flocculation equations with growth and removal	2015	Inom Mirzaev David M. Bortz
+	The effects of MAPK activity on cell-cell adhesion during wound healing	2015	John T. Nardini Douglas A. Chapnick Xuedong Liu David M. Bortz
+ PDF Chat	Generalized sensitivity functions for size-structured population models	2015	Dustin D. Keck David M. Bortz
+	Criteria for linearized stability for a size-structured population model	2015	Inom Mirzaev David M. Bortz
+	Eigenvalues for a Two-Lag Linear Delay Differential Equation∗∗Portions of this work were performed with support from DARPA, AFRL, and HRL, under contract FA8650–11–C–7158. Approved for Public Release, Distribution Unlimited.	2015	David M. Bortz
+	Inverse Problems for a Class of Conditional Probability Measure-Dependent Evolution Equations	2015	David M. Bortz Erin Byrne Inom Mirzaev
+	The effects of MAPK activity on cell-cell adhesion during wound healing	2015	John T. Nardini Douglas A. Chapnick Xuedong Liu David M. Bortz
+	Stability of steady states for a class of flocculation equations with growth and removal	2015	Inom Mirzaev David M. Bortz
+	Criteria for linearized stability for a size-structured population model	2015	Inom Mirzaev David M. Bortz
+ PDF Chat	Determining equilibrium osmolarity in poly(ethylene glycol)/chondrotin sulfate gels mimicking articular cartilage	2014	Sarthok Sircar Elizabeth A. Aisenbrey Stephanie J. Bryant David M. Bortz
+ PDF Chat	Determination of personalized diabetes treatment plans using a two-delay model	2014	Stephen M. Kissler Cody Cichowitz Sriram Sankaranarayanan David M. Bortz
+	Generalized sensitivity functions for size-structured population models	2014	Dustin D. Keck David M. Bortz
+	ANALYTICAL EQUILIBRIUM SOLUTIONS OF BIOCHEMICAL SYSTEMS WITH SYNTHESIS AND DEGRADATION	2014	Inom Mirzaev David M. Bortz
+	Determination of personalized diabetes treatment plans using a two-delay model	2014	Stephen M. Kissler Cody Cichowitz Sriram Sankaranarayanan David M. Bortz
+	Analytical Equilibrium Solutions of Biochemical Systems with Synthesis and Degradation	2014	Inom Mirzaev David M. Bortz
+	Generalized sensitivity functions for size-structured population models	2014	Dustin D. Keck David M. Bortz
+	Numerical simulation of solutions and moments of the smoluchowski coagulation equation	2013	Dustin D. Keck David M. Bortz
+	Determining equilibrium osmolarity in Poly(ethylene glycol) / Chondrotin sulfate gels mimicking articular cartilage	2013	Sarthok Sircar Elizabeth A. Aisenbrey Stephanie J. Bryant David M. Bortz
+	Spatially Heterogeneous Biofilm Simulations using an Immersed Boundary Method with Lagrangian Nodes Defined by Bacterial Locations	2013	Jason F. Hammond Elizabeth Stewart John G. Younger Michael J. Solomon David M. Bortz
+	Sticky Surfaces: Sphere-Sphere Adhesion Dynamics	2013	Sarthok Sircar John G. Younger David M. Bortz
+	Spatially Heterogeneous Biofilm Simulations using an Immersed Boundary Method with Lagrangian Nodes Defined by Bacterial Locations	2013	Jason F. Hammond Elizabeth Stewart John G. Younger Michael J. Solomon David M. Bortz
+	Numerical simulation of solutions and moments of the smoluchowski coagulation equation	2013	Dustin D. Keck David M. Bortz
+	Sticky Surfaces: Sphere-Sphere Adhesion Dynamics	2013	Sarthok Sircar John G. Younger David M. Bortz
+	Determining equilibrium osmolarity in Poly(ethylene glycol) / Chondrotin sulfate gels mimicking articular cartilage	2013	Sarthok Sircar Elizabeth A. Aisenbrey Stephanie J. Bryant David M. Bortz
+ PDF Chat	Propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion	2012	Christopher W. Curtis David M. Bortz
+	Eigenvalues for Two-Lag Linear Delay Differential Equations	2012	David M. Bortz
+	Analytical solutions to Fisher’s equation with time-variable coefficients	2011	Jason F. Hammond David M. Bortz
+	Scandalously Parallelizable Mesh Generation	2011	David M. Bortz Andrew Christlieb
+	Model Selection and Mixed-Effects Modeling of HIV Infection Dynamics	2006	David M. Bortz Patrick W. Nelson
+ PDF Chat	Inverse problems for a class of measure dependent dynamical systems	2005	H. T. Banks David M. Bortz
+ PDF Chat	A Parameter Sensitivity Methodology in the Context of HIV Delay Equation Models	2002	H. T. Banks David M. Bortz
+ PDF Chat	The Simplex Gradient and Noisy Optimization Problems	1998	David M. Bortz C. T. Kelley

Common Coauthors

Coauthor	Papers Together
Daniel A. Messenger	21
Inom Mirzaev	11
Vanja Dukić	7
Jacqueline Wentz	7
John T. Nardini	6
Dustin D. Keck	5
Xiaolong He	5
Youngsoo Choi	5
Xuedong Liu	5
Jay A. Stotsky	5
Sarthok Sircar	5
John G. Younger	5
Jason F. Hammond	4
April Tran	4
Jeffrey C. Cameron	3
Stephanie J. Bryant	3
April Tran	3
Elizabeth Stewart	3
Douglas A. Chapnick	3
Zhiyong Jason Ren	3
Andrew Christlieb	3
Elizabeth A. Aisenbrey	3
Harry J. Dudley	3
Alexander Mendenhall	2
Brian W. O’Shea	2
jimi adams	2
Andrea G. Buchwald	2
Graycen E. Wheeler	2
Erin Byrne	2
Michael J. Solomon	2
Elizabeth J. Carlton	2
J. W. Burby	2
Gina Vasey	2
Sriram Sankaranarayanan	2
H. T. Banks	2
Cody Cichowitz	2
Stephen M. Kissler	2
Seth Minor	1
Jane Evans	1
Jude Bayham	1
Olivia Zarella	1
Kathryn Colborn	1
William Fries	1
Victoria Gershuny	1
E. P. Kightley	1
A. Pearson	1
Yeonjong Shin	1
Brian P. Ziemba	1
Jonathan M. Samet	1
C. T. Kelley	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Discovering governing equations from data by sparse identification of nonlinear dynamical systems	2016	Steven L. Brunton Joshua L. Proctor J. Nathan Kutz	16
+	Weak SINDy for partial differential equations	2021	Daniel A. Messenger David M. Bortz	14
+ PDF Chat	Weak SINDy: Galerkin-Based Data-Driven Model Selection	2021	Daniel A. Messenger David M. Bortz	14
+ PDF Chat	Data-driven discovery of partial differential equations	2017	Samuel Rudy Steven L. Brunton Joshua L. Proctor J. Nathan Kutz	12
+	Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control	2022	Urban Fasel J. Nathan Kutz Bingni W. Brunton Steven L. Brunton	9
+	Learning mean-field equations from particle data using WSINDy	2022	Daniel A. Messenger David M. Bortz	9
+ PDF Chat	Learning partial differential equations for biological transport models from noisy spatio-temporal data	2020	John Lagergren John T. Nardini G. Michael Lavigne Erica M. Rutter Kevin Flores	8
+ PDF Chat	Modeling aggregation and growth processes in an algal population model: analysis and computations	1997	Azmy S. Ackleh Ben Fitzpatrick	7
+	Learning anisotropic interaction rules from individual trajectories in a heterogeneous cellular population	2022	Daniel A. Messenger Graycen E. Wheeler Xuedong Liu David M. Bortz	6
+ PDF Chat	Robust and optimal sparse regression for nonlinear PDE models	2019	Daniel R. Gurevich Patrick A. K. Reinbold Roman O. Grigoriev	6
+ PDF Chat	Coagulation, fragmentation and growth processes in a size structured population	2009	Jacek Banasiak Wilson Lamb	5
+ PDF Chat	Learning sparse nonlinear dynamics via mixed-integer optimization	2023	Dimitris Bertsimas Wes Gurnee	5
+	Variational system identification of the partial differential equations governing the physics of pattern-formation: Inference under varying fidelity and noise	2019	Z. Wang Xun Huan Krishna Garikipati	5
+ PDF Chat	Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics	2023	David M. Bortz Daniel A. Messenger Vanja Dukić	5
+ PDF Chat	On the Convergence of the SINDy Algorithm	2019	Linan Zhang Hayden Schaeffer	5
+	Criteria for linearized stability for a size-structured population model	2015	Inom Mirzaev David M. Bortz	5
+ PDF Chat	Dynamical Scaling in Smoluchowski’s Coagulation Equations: Uniform Convergence	2006	Govind Menon Robert L. Pego	4
+ PDF Chat	Data-driven discovery of coordinates and governing equations	2019	Kathleen Champion Bethany Lusch J. Nathan Kutz Steven L. Brunton	4
+	Transformation semigroups andL 1-approximation for size structured population models	1989	H. T. Banks Franz Kappel	4
+	Steady states in hierarchical structured populations with distributed states at birth	2012	József Z. Farkas Peter Hinow	4
+ PDF Chat	A unified approach for sparse dynamical system inference from temporal measurements	2018	Yannis Pantazis Ioannis Tsamardinos	4
+	Stability and regularity results for a size-structured population model	2006	József Z. Farkas Thomas Hagen	4
+ PDF Chat	Learning partial differential equations via data discovery and sparse optimization	2017	Hayden Schaeffer	4
+	Identification of significant host factors for HIV dynamics modelled by non‐linear mixed‐effects models	2002	Hulin Wu Lang Wu	4
+ PDF Chat	EIGENELEMENTS OF A GENERAL AGGREGATION-FRAGMENTATION MODEL	2010	Marie Doumic Pierre Gabriel	4
+	Stability of steady states for a class of flocculation equations with growth and removal	2015	Inom Mirzaev David M. Bortz	4
+	Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems	2008	Randall J. LeVeque	4
+	Learning interaction kernels in heterogeneous systems of agents from multiple trajectories	2021	Fei Lu Mauro Maggioni Sui Tang	4
+	Statistical methods for model comparison in parameter estimation problems for distributed systems	1990	H. T. Banks Ben Fitzpatrick	4
+ PDF Chat	Using noisy or incomplete data to discover models of spatiotemporal dynamics	2020	Patrick A. K. Reinbold Daniel R. Gurevich Roman O. Grigoriev	4
+	Discovery of Dynamics Using Linear Multistep Methods	2019	Rachael T. Keller Qiang Du	3
+	Multi-scale modeling of a wound-healing cell migration assay	2006	Anna Q. Cai Kerry A. Landman Barry D. Hughes	3
+ PDF Chat	Deterministic and Stochastic Models for Coalescence (Aggregation and Coagulation): A Review of the Mean-Field Theory for Probabilists	1999	David Aldous	3
+ PDF Chat	Boundedness and Large-Time Behavior Results for a Diffusive Epidemic Model	2007	Lamine Melkemi Ahmed Zerrouk Mokrane Amar Youkana	3
+ PDF Chat	Generalized sensitivity functions for size-structured population models	2015	Dustin D. Keck David M. Bortz	3
+ PDF Chat	Exact Recovery of Chaotic Systems from Highly Corrupted Data	2017	Giang Tran Rachel Ward	3
+	Handbook of Mathematical Functions	1972	Milton Abramowitz I. A. Stegun	3
+ PDF Chat	DIFFERENTIAL-DIFFERENCE EQUATIONS	1987	Kenneth L. Cooke	3
+	Blow-up of solutions to some coagulation and fragmentation equations with growth	2011	Jacek Banasiak	3
+	IDENT: Identifying Differential Equations with Numerical Time evolution	2019	Sung Ha Kang Wenjing Liao Yingjie Liu	3
+ PDF Chat	Perturbation Theory for Linear Operators	1995	Tosio Kato	3
+ PDF Chat	Stability and Lyapunov Functions for Reaction-Diffusion Systems	1997	W. B. Fitzgibbon Selwyn Hollis Jeffrey J. Morgan	3
+ PDF Chat	PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network	2019	Zichao Long Yiping Lu Bin Dong	3
+ PDF Chat	Machine learning of linear differential equations using Gaussian processes	2017	Maziar Raissi Paris Perdikaris George Em Karniadakis	3
+	Boundedness and Decay Results for Reaction-Diffusion Systems	1990	Jeffrey R. Morgan	3
+ PDF Chat	Modeling keratinocyte wound healing dynamics: Cell–cell adhesion promotes sustained collective migration	2016	John T. Nardini Douglas A. Chapnick Xuedong Liu David M. Bortz	3
+ PDF Chat	Deep learning of dynamics and signal-noise decomposition with time-stepping constraints	2019	Samuel Rudy J. Nathan Kutz Steven L. Brunton	3
+ PDF Chat	Using Experimental Data and Information Criteria to Guide Model Selection for Reaction–Diffusion Problems in Mathematical Biology	2019	David J. Warne Ruth E. Baker Matthew J. Simpson	3
+	Swarm dynamics and equilibria for a nonlocal aggregation model	2011	Razvan C. Fetecau Yanghong Huang Théodore Kolokolnikov	3
+	SUNDIALS	2005	A.C. Hindmarsh Peter N. Brown Keith Eric Grant Steven L. Lee Radu Serban Dan Shumaker Carol S. Woodward	3