Recorded here is a list of publications, current through 1/2025.

Journal Articles

1. Preprint _{Anthony Gruber, Irina Tezaur.
   Variationally Consistent Hamiltonian Model Reduction.
   SIAM J. Appl. Dyn. Sys. (2024).}

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

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

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

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

6. 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).}

7. 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).}

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

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

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

11. 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).}

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

13. 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).}

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

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

16. 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 _{Anthony Gruber, Kookjin Lee, Haksoo Lim, Noseong Park, Nathaniel Trask.
   Efficiently Parameterized Neural Metriplectic Systems
   Proceedings of the 13th ICML (2025).}

2. Preprint _{Eugenio Aulisa, Anthony Gruber, Magdalena Toda.
   Generalized Willmore Energies and Applications.
   Geometry, Integrability and Quantization, vol. 29 (2024).}

3. 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 Workshop on Foundation Models for Science: Progress, Opportunities, and Challenges (2024).}

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

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

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

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

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

Others

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

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

3. 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).}

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

Submitted Articles

1. Preprint _{Sanghyun Hong, Fan Wu, Anthony Gruber, Kookjin Lee.
   Understanding and Mitigating Membership Inference Risks of Neural Ordinary Differential Equations.
   (under review).}

2. Preprint _{Mingu Kang, Dongseok Lee, Woojin Cho, Jaehyeon Park, Kookjin Lee, Anthony Gruber, Youngjoon Hong, Noseong Park.
   MaD-Scientist: AI-based scientist solving convection-diffusion-reaction equations using massive PINN-based prior data.
   (under review).}

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

4. 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:

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