Publications

Recorded here is a list of publications, current through 9/2022.

Journal Articles

  1. Preprint Anthony Gruber, Max Gunzburger, Lili Ju, Zhu Wang.
    Energetically Consistent Model Reduction for Metriplectic Systems.
    Comput. Methods Appl. Mech. Eng. (to appear).

  2. Preprint Anthony Gruber, Max Gunzburger, Lili Ju, Zhu Wang.
    A Multifidelity Monte Carlo Method for Realistic Computational Budgets.
    J. Sci. Comput. (to appear).

  3. Preprint Anthony Gruber.
    Parallel Codazzi tensors with submanifold applications.
    Math. Nachr. (to appear).

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

  5. 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).

  6. Preprint Anthony Gruber.
    Planar Immersions with Prescribed Curl and Jacobian Determinant are Unique.
    Bull. Aust. Math. Soc. 1-6 (2021).

  7. 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).

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

  9. Here Anthony Gruber, Eugenio Aulisa.
    Computational p-Willmore Flow with Conformal Penalty.
    ACM Trans. Graph. 39, 5, Article 161 (September 2020), 16 pages.

  10. 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) 56: 147.

Articles in Refereed Conference Proceedings

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

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

  3. Preprint Eugenio Aulisa, Anthony Gruber, Magdalena Toda, Hung Tran.
    New Developments on the p-Willmore Energy of Surfaces.
    Proceedings of the XXIst GIQ, BAS - Varna (2019).

  4. 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.
    Curvature functionals and p-Willmore energy.
    TTU Electronic Thesis and Dissertation Repository (2019).

Submitted Articles

  1. Preprint Anthony Gruber, Álvaro Pámpano, Magdalena Toda.
    Instability of p-Elastic Curves in \(S^2\).
    (under review).

  2. Preprint Anthony Gruber, Max Gunzburger, Lili Ju, Rihui Lan, Zhu Wang.
    Multifidelity Monte Carlo Estimation for Efficient Uncertainty Quantification in Climate-Related Modeling.
    (under review).

  3. Preprint Anthony Gruber, Eugenio Aulisa.
    Quasiconformal Mappings with Surface Domains.
    (under review).

  4. 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.
    (under review).

  5. Preprint Anthony Gruber, Álvaro Pámpano, Magdalena Toda.
    On p-Willmore Disks with Boundary Energies.
    (under review).

 

Corrigenda to Published Works


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

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:

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