Recorded here is a list of publications, current through 8/2026.

Journal Articles

1. Preprint _{Irina Tezaur, Eric Parish, Anthony Gruber, Ian Moore, Christopher Wentland, Alejandro Mota.
   Hybrid coupling with operator inference and the overlapping Schwarz alternating method.
   Int. J. Numer. Methods Eng. (to appear).}

2. Preprint _{Arjun Vijaywargia, Shane A. McQuarrie, Anthony Gruber.
   Tensor Parametric Hamiltonian Operator Inference.
   SIAM J. Appl. Dyn. Sys. (to appear).}

3. Preprint _{Xiaolong He, Yeonjong Shin, Anthony Gruber, Sohyeon Jung, Kookjin Lee, Youngsoo Choi.
   Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems. TMLR (2026).}

4. Preprint _{Anthony Gruber, Irina Tezaur.
   Variationally Consistent Hamiltonian Model Reduction.
   SIAM J. Appl. Dyn. Sys. (2025).}

5. Preprint _{Anthony Gruber, Irina Tezaur.
   Canonical and Noncanonical Hamiltonian Operator Inference.
   Comput. Methods Appl. Mech. Eng. (2023).}

6. Preprint _{Anthony Gruber, Álvaro Pámpano, Magdalena Toda.
   Instability of Closed p-Elastic Curves in \(S^2\).
   Anal. Appl. (2023).}

7. Preprint _{Anthony Gruber, Álvaro Pámpano, Magdalena Toda.
   On p-Willmore Disks with Boundary Energies.
   Differ. Geom. Appl. (2023).}

8. Preprint _{Anthony Gruber.
   Parallel Codazzi tensors with submanifold applications.
   Math. Nachr. (2023).}

9. Preprint _{Yuankai Teng, Zhu Wang, Lili Ju, Anthony Gruber, Guannan Zhang.
   Learning Level Sets with Pseudo-Reversible Neural Networks for Nonlinear Dimension Reduction in Function Approximation.
   SIAM J. Sci. Comput. (2023).}

10. Here _{Anthony Gruber, Max Gunzburger, Lili Ju, Rihui Lan, Zhu Wang.
    Multifidelity Monte Carlo Estimation for Efficient Uncertainty Quantification in Climate-Related Modeling.
    Geosci. Model Dev. (2023).}

11. Preprint _{Anthony Gruber, Max Gunzburger, Lili Ju, Zhu Wang.
    Energetically Consistent Model Reduction for Metriplectic Systems.
    Comput. Methods Appl. Mech. Eng. (2022).}

12. Preprint _{Anthony Gruber, Max Gunzburger, Lili Ju, Zhu Wang.
    A Multifidelity Monte Carlo Method for Realistic Computational Budgets.
    J. Sci. Comput. (2022).}

13. Preprint _{Anthony Gruber, Magdalena Toda, Hung Tran.
    Stationary surfaces with boundaries.
    Ann. Glob. Anal. Geom. (2022).}

14. Preprint _{Anthony Gruber, Max Gunzburger, Lili Ju, Zhu Wang.
    A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling.
    Comput. Methods Appl. Mech. Eng. (2022).}

15. Preprint _{Anthony Gruber.
    Planar Immersions with Prescribed Curl and Jacobian Determinant are Unique.
    Bull. Aust. Math. Soc. (2021).}

16. Preprint _{Anthony Gruber, Max Gunzburger, Lili Ju, Yuankai Teng, Zhu Wang.
    Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations.
    Numer. Math. Theory Methods Appl. (2021).}

17. Preprint _{Anthony Gruber, Álvaro Pámpano, Magdalena Toda.
    Regarding the Euler-Plateau Problem with Elastic Modulus.
    Ann. Mat. Pura. Appl. (2021).}

18. Here _{Anthony Gruber, Eugenio Aulisa.
    Computational p-Willmore Flow with Conformal Penalty.
    ACM Trans. Graph. (2020)}

19. Preprint _{Anthony Gruber, Magdalena Toda, Hung Tran.
    On the variation of curvature functionals in a space form with application to a generalized Willmore energy.
    Ann. Glob. Anal. Geom. (2019)}

Articles in Refereed Conference Proceedings

1. Preprint _{Cheng Jing, Uvini Balasuriya Mudiyanselage, Woojin Cho, Minju Jo, Anthony Gruber, Kookjin Lee.
   Meta-Learning Structure-Preserving Dynamics
   43rd ICML Proceedings (2026).}

2. Preprint _{Anthony Gruber, Kookjin Lee, Haksoo Lim, Noseong Park, Nathaniel Trask.
   Efficiently Parameterized Neural Metriplectic Systems
   13th ICLR Proceedings (2025).}

3. Preprint _{Eugenio Aulisa, Anthony Gruber, Magdalena Toda.
   Generalized Willmore Energies and Applications.
   Geom. Integr. Quantization, vol. 29 (2024).}

4. Preprint _{Mingu Kang, Dongseok Lee, Woojin Cho, Jaehyeon Park, Kookjin Lee, Anthony Gruber, Youngjoon Hong, Noseong Park.
   Can we pre-train ICL-based SFMs for the zero-shot inference of the 1D CDR problem with noisy data?
   NeurIPS FM4Science Workshop (2024).}

5. Preprint _{Anthony Gruber, Kookjin Lee, Nathaniel Trask.
   Reversible and Irreversible Bracket-Based Dynamics for Deep Graph Neural Networks.
   17th NeurIPS Proceedings (2023).}

6. Preprint _{Anthony Gruber, Eugenio Aulisa.
   Quaternionic Remeshing During Surface Evolution.
   AIP Conference Proceedings 2425, 330003 (2022).}

7. Preprint _{Anthony Gruber, Magdalena Toda, Hung Tran.
   Willmore-Stable Minimal Surfaces.
   AIP Conference Proceedings 2425, 330004 (2022).}

8. Preprint _{Eugenio Aulisa, Anthony Gruber, Magdalena Toda, Hung Tran.
   New Developments on the p-Willmore Energy of Surfaces.
   Geom. Integr. Quantization, vol. 21 (2019).}

9. Here _{Robert A. Bridges, Anthony D. Gruber, Christopher Felder, Miki Verma, Chelsey Hoff.
   Active Manifolds: A non-linear analogue to Active Subspaces.
   36th ICML Proceedings, PMLR 97:764-772 (2019).}

Others

1. Here _{Anthony Gruber, Gianluca Geraci, Patrick J. Blonigan, Eric Parish, Michael Eldred.
   Advancements in Reduced Order Model-Based Multifidelity Uncertainty Quantification for High-Speed Flows.
   AIAA Proceedings (2026).}

2. Here _{Ritoban Roy-Chowdhury, Irina Tezaur, Nathan M. Urban, Anthony Gruber.
   Onsager’s variational principle for solving inverse problems.
   CSRI Summer Proceedings (2025).}

3. Here _{Tage T. Burnett, Anthony Gruber, Eric C. Cyr.
   Towards Structure-Preserving Reduced Order Modeling of Particle in Cell Simulations.
   CSRI Summer Proceedings (2025).}

4. Here _{Adrienne M. Propp, Mauro Perego, Eric C. Cyr, Anthony Gruber, Amanda A. Howard, Alexander Heinlein, Panos Stinis, Daniel M. Tartakovsky.
   Scalable ice sheet surrogate modeling via domain-decomposed, physics- inspired graph neural networks.
   CSRI Summer Proceedings (2025).}

5. Here _{Cameron Rodriguez, Irina Tezaur, Alejandro Mota, Anthony Gruber, Eric Parish, Christopher Wentland.
   Transmission Conditions for the Non-Overlapping Schwarz Coupling of Full Order and Operator Inference Models.
   CSRI Summer Proceedings (2025).}

6. Here _{Anthony Gruber.
   Learning Operators for Structure-Informed Surrogate Models.
   tech. rep., Sandia National Lab. (SNL-NM), Albuquerque, NM (United States) (2024).}

7. Here _{Arjun Vijaywargia, Shane A. McQuarrie, Anthony Gruber.
   Tensor Parametric Operator Inference with Hamiltonian Structure.
   CSRI Summer Proceedings (2024).}

8. Here _{Ian R. Moore, Christopher Wentland, Anthony Gruber, Irina Tezaur.
   Domain decomposition-based coupling of Operator Inference Reduced Order Models via the Schwarz alternating method.
   CSRI Summer Proceedings (2024).}

9. Here _{Anthony Gruber.
   Curvature functionals and p-Willmore energy.
   TTU Electronic Thesis and Dissertation Repository (2019).}

Submitted Articles

1. Preprint _{Ritoban Roy-Chowdhury, Mohammad Sina Nabizadeh, Oliver Gross, Anthony Gruber, Albert Chern.
   Vakonomic Fluids.
   (under review).}

2. Preprint _{Anthony Gruber, Ritoban Roy-Chowdhury, Irina Tezaur, Nathan M. Urban.
   Flexible and Stable Dynamics Discovery with Onsager’s Variational Principle.
   (under review).}

3. Preprint _{Arjun Vijaywargiya, Eric C. Cyr, Anthony Gruber.
   Structure-Aware Tensorial Model Reduction.
   (under review).}

4. Preprint _{Eric Parish, Anthony Gruber, Patrick Blonigan, Irina Tezaur.
   NN-OpInf: an operator inference approach using structure-preserving composable neural networks.
   (under review).}

5. Preprint _{Adrienne M. Propp, Mauro Perego, Eric C. Cyr, Anthony Gruber, Amanda A. Howard, Alexander Heinlein, Panos Stinis, Daniel M. Tartakovsky.
   Domain-Decomposed Graph Neural Network Surrogate Modeling for Ice Sheets.
   (under review).}

6. Preprint _{Sanghyun Hong, Fan Wu, Anthony Gruber, Kookjin Lee.
   Rethinking privacy in neural networks through continuous-time dynamics.
   (under review).}

7. Preprint _{Jaehyeon Park, Mingu Kang, Dongseok Lee, Woojin Cho, Kookjin Lee, Anthony Gruber, Youngjoon Hong, Noseong Park.
   PDE-PFN: Prior-Data Fitted Neural PDE Solver.
   (under review).}

8. Preprint _{Jonas A. Actor, Anthony Gruber, Eric C. Cyr, Nathaniel Trask.
   Gaussian Variational Schemes on Bounded and Unbounded Domains.
   (under review).}

9. Preprint _{Anthony Gruber, Eugenio Aulisa.
   Quasiconformal Mappings with Surface Domains.
   (under review).}

Corrigenda to Published Works

All Arxiv preprints are (eventually…) kept up-to-date with this list. If you notice any typos or suspected errors in the above publications, e-mail notifications are appreciated.

In Canonical and Noncanonical Hamiltonian Operator Inference.

• Section 3, Equation (5):

                    \(\hat{\mathbf{J}}\hat{\mathbf{A}}\hat{\mathbf{X}} + \hat{\nabla}f(\hat{\mathbf{X}})\) \(\,\,\longrightarrow\,\,\) \(\hat{\mathbf{J}}\left(\hat{\mathbf{A}}\hat{\mathbf{X}} + \hat{\nabla}f(\hat{\mathbf{X}})\right)\) .

In Planar Immersions with Prescribed Curl and Jacobian Determinant are Unique.

• Section 2, Paragraph 1:

                    \(\mathbf{v} \otimes \mathbf{v} - 2|\mathbf{v}|^2\,1\) \(\,\,\longrightarrow\,\,\) \(\mathbf{v} \otimes \mathbf{v} - |\mathbf{v}|^2\,1\) .

In On the variation of curvature functionals in a space form with application to a generalized Willmore energy.

• Equation (22), line 2:

                    \(\frac{1}{2}\langle \nabla |h|^2, \nabla f\rangle\) \(\,\,\longrightarrow\,\,\) \(\frac{1}{2}u \langle \nabla |h|^2, \nabla f\rangle\) .

• Equation (35), line 3:

                    \(- h^{ij}(\delta\Gamma^k_{ij})f_k + h^{ij}g^{kl}(u_ih_{jl}+u_jh_{il}-u_lh_{ij})f_k\) \(\,\,\longrightarrow\,\,\) \(-h^{ij}(\delta\Gamma^k_{ij})f_k\) .