Publications

Publications from the Weak Form Scientific Machine Learning (WSciML) group, listed in reverse chronological order. Accepted papers that are not yet in print appear under “Forthcoming”; works not yet accepted are listed under “Preprints.”

 

Forthcoming

  • N. Rummel, D. A. Messenger, S. Becker, V. Dukic, and D. M. Bortz, “WENDy for Nonlinear-in-Parameters ODEs,” SIAM J. Sci. Comput., 2026 (to appear). arXiv:2502.08881
  • S. Minor, V. Dukic, and D. M. Bortz, “Learning Effective Soliton Dynamics from Scattering Data,” J. Nonlinear Waves, 2026 (to appear). arXiv:2607.01545
  • 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,” in Computational Approaches to Scientific Discovery, Lecture Notes in Computer Science, Springer, 2026 (to appear). arXiv:2403.10748

 

2026

  • C. López, M. Partridge, S. De Pascuale, J. Lore, A. J. Christlieb, S. Becker, and D. M. Bortz, “WSINDy for Model Predictive Control with Applications to Fusion, Drones, and Chaos,” Proc. R. Soc. A, 482:20260413, 2026. doi:10.1098/rspa.2026.0413
  • S. Minor, B. D. Elderd, B. Van Allen, D. M. Bortz, and V. Dukic, “Weak Form Learning for Mean-Field Partial Differential Equations: An Application to Insect Movement,” SIAM J. Life Sci., 1(3):444–484, 2026. doi:10.1137/25M1812038
  • A. Tran and D. M. Bortz, “Weak Form Scientific Machine Learning: Test Function Construction for System Identification,” SIAM J. Sci. Comput., 48(4):C890–C915, 2026. doi:10.1137/25M1776020
  • N. Heitzman-Breen, V. Dukic, and D. M. Bortz, “A Practical Identifiability Criterion Leveraging Weak-Form Parameter Estimation,” Bull. Math. Biol., 88:70, 2026. doi:10.1007/s11538-026-01639-x
  • A. Chawla, D. M. Bortz, and V. Dukic, “Bias and Coverage Properties of the WENDy-IRLS Algorithm,” in B. Sriraman (ed.), Handbook of Visual, Experimental and Computational Mathematics: Bridges through Data, Springer Nature, 2026, pp. 1639–1746. doi:10.1007/978-3-032-16368-4_86

 

2025

  • J. W. Burby, I. A. Maldonado, M. Ruth, D. A. Messenger, and L. Carbajal, “Nonperturbative Guiding Center Model for Magnetized Plasmas,” Phys. Rev. Lett., 134(17):175101, 2025. doi:10.1103/PhysRevLett.134.175101
  • 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, 2025. doi:10.1002/nme.7634
  • R. Lyons, V. Dukic, and D. M. Bortz, “Learning Structured Population Models from Data with WSINDy,” PLOS Comput. Biol., 21(12):e1013742, 2025. doi:10.1371/journal.pcbi.1013742
  • D. A. Messenger and D. M. Bortz, “Asymptotic Consistency of the WSINDy Algorithm in the Limit of Continuum Data,” IMA J. Numer. Anal., 45(6):3264–3312, 2025. doi:10.1093/imanum/drae086
  • S. Minor, D. A. Messenger, V. Dukic, and D. M. Bortz, “Learning Physically Interpretable Atmospheric Models from Data with WSINDy,” J. Geophys. Res. Mach. Learn. Comput., 2(3):e2025JH000602, 2025. doi:10.1029/2025JH000602
  • 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, 2025. doi:10.1016/j.jcp.2025.113719
  • R. R. W. Wang and D. A. Messenger, “Physics-Guided Weak-Form Discovery of Reduced-Order Models for Trapped Ultracold Hydrodynamics,” Phys. Rev. A, 111(3):033311, 2025. doi:10.1103/PhysRevA.111.033311

 

2024

  • 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 (eds.), Numerical Analysis Meets Machine Learning, Handbook of Numerical Analysis, vol. 25, pp. 53–82, Elsevier, 2024. doi:10.1016/bs.hna.2024.05.002
  • D. A. Messenger, J. W. Burby, and D. M. Bortz, “Coarse-Graining Hamiltonian Systems Using WSINDy,” Sci. Rep., 14:14457, 2024. doi:10.1038/s41598-024-64730-0
  • D. A. Messenger, G. Dwyer, and V. Dukic, “Weak-Form Inference for Hybrid Dynamical Systems in Ecology,” J. R. Soc. Interface, 21(221):20240376, 2024. doi:10.1098/rsif.2024.0376
  • D. A. Messenger, A. Tran, V. Dukic, and D. M. Bortz, “The Weak Form Is Stronger Than You Think,” SIAM News, 57(8), 2024. SIAM News article · arXiv:2409.06751
  • 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:10.1016/j.ifacol.2024.10.120
  • 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, 2024. doi:10.1016/j.cma.2024.116998

 

2023

  • 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:10.1007/s11538-023-01208-6
  • G. Vasey, B. O’Shea, A. Christlieb, D. Messenger, and D. M. Bortz, “Influence of Initial Conditions on Data-Driven Model Identification for Ideal MHD Test Problems,” in 2023 IEEE Int. Conf. Plasma Sci. (ICOPS), Santa Fe, NM, 2023. doi:10.1109/ICOPS45740.2023.10481488

 

2022

  • D. A. Messenger and D. M. Bortz, “Learning Mean-Field Equations from Particle Data Using WSINDy,” Physica D, 439:133406, 2022. doi:10.1016/j.physd.2022.133406
  • 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., PMLR 190:241–256, 2022. PMLR
  • 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, 2022. doi:10.1098/rsif.2022.0412

 

2021

  • D. A. Messenger and D. M. Bortz, “Weak SINDy: Galerkin-Based Data-Driven Model Selection,” Multiscale Model. Simul., 19(3):1474–1497, 2021. doi:10.1137/20M1343166
  • D. A. Messenger and D. M. Bortz, “Weak SINDy for Partial Differential Equations,” J. Comput. Phys., 443:110525, 2021. doi:10.1016/j.jcp.2021.110525

 

Preprints

  • R. Lyons, V. Dukic, and D. M. Bortz, “From Individual Trajectories to Population Densities: Weak-Form Inference of Heterogeneous Growth Laws,” 2026. arXiv:2609.31955
  • W. Houser, V. Dukic, and D. M. Bortz, “Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics,” 2026. arXiv:2609.09434
  • C. W. Curtis and D. M. Bortz, “Weak-form Extended Dynamic Mode Decomposition,” 2026. arXiv:2607.25950
  • N. Heitzman-Breen, R. Lyons, P. Jain, M. K. Jolly, and D. M. Bortz, “Weak form Scientific Machine Learning for Systems Biology: A Tutorial on WENDy,” bioRxiv, 2026. doi:10.64898/2026.07.02.735880
  • M. Tian, D. A. Messenger, V. Dukic, N. Rodríguez, and D. M. Bortz, “Learning Effective Models from Network Dynamics Data with Multiple Initial Conditions Using Weak Form SINDy,” 2026. arXiv:2605.30432
  • A. Tran, T. Haut, D. M. Bortz, and Y. Choi, “Time-Dependent PDE-Constrained Optimization via Weak-Form Latent Dynamics,” 2026. arXiv:2605.20639
  • N. Heitzman-Breen, S. L. Atlus, j. adams, A. G. Buchwald, V. Dukic, B. K. Fosdick, D. Ghosh, J. Samet, E. J. Carlton, and D. M. Bortz, “Waning Immunity and Partial Vaccination Coverage Lead to Transitions in the Source of Daily Incidence,” medRxiv, 2026. doi:10.64898/2026.03.12.26348258