Ralf Zimmermann

Søgeresultater

• 2024

  Adaptive data-driven probabilistic reduced-order models for parameterized dynamical system

  Cheng, K. & Zimmermann, R., 15. okt. 2024, (Accepteret/In press) I: SIAM Journal on Scientific Computing. s. 1 38 s.

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  Fil

  • Dynamical System 100%
  • Dynamic Models 33%
  • Numerical Example 33%
  • Kriging 33%
  • Adaptive Sampling 33%
  52 Downloads (Pure)

• A Grassmann manifold handbook: basic geometry and computational aspects

  Bendokat, T., Zimmermann, R. & Absil, P. A., feb. 2024, I: Advances in Computational Mathematics. 50, 1, 51 s., 6.

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  • Manifold 100%
  • Grassmann 100%
  • Computational Aspects 100%
  • Matrix (Mathematics) 50%
  • Orthogonal Projector 50%
  66 Downloads (Pure)

• An efficient algorithm for the Riemannian logarithm on the Stiefel manifold for a family of Riemannian metrics

  Mataigne, S., Zimmermann, R. & Miolane, N., 19. mar. 2024, (Afsendt) I: SIAM Journal on Matrix Analysis and Applications. s. 1-20 20 s.

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  Fil

  • Stiefel Manifold 100%
  • Parameter Family 66%
  • Statistics 33%
  • Matrix (Mathematics) 33%
  • Seminal Paper 33%
  16 Downloads (Pure)

• High curvature means low-rank: On the sectional curvature of Grassmann and Stiefel manifolds and the underlying matrix trace inequalities

  Zimmermann, R. & Stoye, J., 5. mar. 2024, 23 s. arXiv.

  Publikation: Andet › Andet bidrag › Forskning

  • Stiefel Manifold 100%
  • Matrix (Mathematics) 100%
  • Manifold 100%
  • Mean Curvature 100%
  • Sectional Curvature 100%

• Multivariate Hermite Interpolation On Riemannian Manifolds

  Zimmermann, R. & Bergmann, R., apr. 2024, I: SIAM Journal on Scientific Computing. 46, 2, s. 1276-1297

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  • Tangent Space 100%
  • Hermite Interpolation 100%
  • Riemannian Manifolds 100%
  • Base Point 50%
  • Weight Function 25%
  72 Downloads (Pure)

• On the Injectivity Radius of the Stiefel Manifold: Numerical investigations and an explicit construction of a cut point at short distance

  Stoye, J. & Zimmermann, R., 6. mar. 2024, 15 s.

  Publikation: Andet › Andet bidrag › Forskning

  • Stiefel Manifold 100%
  • Cut Point 100%
  • Matrix (Mathematics) 20%
  • Open Question 20%
  • Manifold 20%

• Randomized greedy magic point selection schemes for nonlinear model reduction

  Zimmermann, R. & Cheng, K., aug. 2024, I: Advances in Computational Mathematics. 50, 4, 26 s., 81.

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  • Point Estimation 100%
  • Computational Cost 100%
  • Nonlinear Model 100%
  • Nonlinearity 100%
  66 Downloads (Pure)

• Riemannian optimization on the symplectic Stiefel manifold using second-order information

  Jensen, R. & Zimmermann, R., 12. apr. 2024, (Afsendt) I: SIAM Jounal on Optimization. s. 1 24 s.

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  • Stiefel Manifold 100%
  • Matrix (Mathematics) 66%
  • Manifold 66%
  • Trust Region Method 66%
  • Retraction 33%

• The injectivity radius of the compact Stiefel manifold under the Euclidean metric

  Zimmermann, R. & Stoye, J., 2024, (Accepteret/In press) I: SIAM Journal on Matrix Analysis and Applications.

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  • Stiefel Manifold 100%
  • Manifold 100%
  • Matrix (Mathematics) 33%
  • Wide Range 33%
  • Normal Coordinate 33%
• 2023

  Gradient-enhanced Kriging for high-dimensional Bayesian optimization with linear embedding

  Cheng, K. & Zimmermann, R., nov. 2023, I: AIAA Journal. 61, 11, s. 4946-4959

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

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  • Active Subspace 100%
  • Kriging 100%
  • Bayesian Optimization 100%
  • Kriging Model 100%
  • Objective Function 50%
  8 Downloads (Pure)

• Gradient-enhanced polynomial chaos expansion for high-dimensional function approximation

  Cheng, K. & Zimmermann, R., 2023, The 13th International Conference on Structural Safety and Reliability : ICOSSAR 2021.

  Publikation: Kapitel i bog/rapport/konference-proceeding › Konferencebidrag i proceedings › Forskning › peer review

  • Polynomial 100%
  • Approximation Function 100%
  • Gaussian Distribution 16%
  • Likelihood Function 16%
  • Numerical Experiment 16%

• Sliced gradient-enhanced Kriging for high-dimensional function approximation

  Zimmermann, R. & Cheng, K., 2023, I: SIAM Journal on Scientific Computing. 45, 6, s. A2858-A2885

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  • Kriging 100%
  • Approximation Function 100%
  • Dimensional Function 100%
  • Correlation Matrix 60%
  • Likelihood Function 40%
• 2022

  Computing the Riemannian Logarithm on the Stiefel manifold: Metrics, methods and performance

  Zimmermann, R. & Hüper, K., 2022, I: SIAM Journal on Scientific Computing. 43, 2, s. 953-980

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  • Stiefel Manifold 100%
  • Normal Coordinate 66%
  • Exponential Matrix 66%
  • Matrix (Mathematics) 33%
  • Numerical Example 33%
  133 Downloads (Pure)

• Geometric optimization for structure-preserving model reduction of Hamiltonian systems

  Bendokat, T. & Zimmermann, R., 2022, 10th Vienna International Conference on Mathematical Modelling: MATHMOD 2022. 20 udg. Elsevier, Bind 55. s. 457-462 (IFAC-PapersOnLine).

  Publikation: Kapitel i bog/rapport/konference-proceeding › Konferencebidrag i proceedings › Forskning › peer review

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  • Manifold 100%
  • Hamiltonian Systems 100%
  • Matrix (Mathematics) 50%
  • Numerical Example 25%
  • Classical Model 25%
  141 Downloads (Pure)
• 2021

  A geometric approach to subspace updates and orthogonal matrix decompositions under rank-one modifications

  Zimmermann, R., 2021, I: Mathematics of Computation. 90, 328, s. 671-688

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  • Matrix (Mathematics) 100%
  • Orthogonal Matrix 100%
  • Matrix Decomposition 100%
  • Factorization 66%
  • Closed Form 33%
  15 Downloads (Pure)

• Efficient Quasi-Geodesics on the Stiefel Manifold

  Bendokat, T. & Zimmermann, R., 14. jul. 2021, Geometric Science of Information: 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings. Nielsen, F. & Barbaresco, F. (red.). Springer, s. 763-771 (Lecture Notes in Computer Science, Bind 12829).

  Publikation: Kapitel i bog/rapport/konference-proceeding › Konferencebidrag i proceedings › Forskning › peer review

  Fil

  • Stiefel Manifold 100%
  • Manifold 50%
  • Covariant 50%
  • Constant Speed 50%
  • Orthonormal Frame 50%
  53 Downloads (Pure)

• Manifold interpolation

  Zimmermann, R., 8. nov. 2021, Model Order Reduction: Volume 1 System- and Datat Driven Methods and Algorithms. Benner, P. (red.). De Gruyter, Bind 1. s. 229-274

  Publikation: Kapitel i bog/rapport/konference-proceeding › Kapitel i bog › Forskning › peer review

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  • Orthogonal Basis 100%
  • Model Reduction 100%
  • System Matrix 100%
  • Positive Definite 100%
  • Matrix (Mathematics) 100%
  176 Downloads (Pure)

• Model Reduction of Complex Dynamical Systems

  Benner, P. (Redaktør), Breiten, T. (Redaktør), Faßbender, H. (Redaktør), Hinze, M. (Redaktør), Stykel, T. (Redaktør) & Zimmermann, R. (Redaktør), 2021, Birkhäuser Verlag. 415 s. (International Series of Numerical Mathematics, Bind 171).

  Publikation: Bog/rapport › Antologi › Forskning › peer review

  • Dynamical System 100%

• The real symplectic Stiefel and Grassmann manifolds: metrics, geodesics and applications

  Bendokat, T. & Zimmermann, R., 27. aug. 2021, arXiv, 32 s.

  Publikation: Working paper › Forskning

  Fil

  • Manifold 100%
  • Grassmann 100%
  • Retraction 33%
  • Stiefel Manifold 16%
  • Matrix (Mathematics) 16%
  38 Downloads (Pure)
• 2020

  Hermite Interpolation and data processing errors on Riemannian Matrix Manifolds

  Zimmermann, R., 2020, I: SIAM Journal on Scientific Computing. 42, 5, s. A2593–A2619

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  • Matrix (Mathematics) 100%
  • Manifold 100%
  • Hermite Interpolation 100%
  • Orthogonal Matrix 50%
  • Stiefel Manifold 25%
  78 Downloads (Pure)
• 2019

  Manifold interpolation and model reduction

  Zimmermann, R., 11. feb. 2019, I: arxiv.org. 37 s.

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  • Matrix (Mathematics) 100%
  • Manifold 100%
  • Model Reduction 100%
  • Orthogonal Basis 33%
  • System Matrix 33%

• Parametric model reduction via interpolating orthonormal bases

  Zimmermann, R. & Debrabant, K., 5. jan. 2019, Numerical Mathematics and Advanced Applications: ENUMATH 2017. Radu, F. A., Kumar, K., Berre, I., Nordbotten, J. M. & Pop, I. S. (red.). Springer, s. 683-691 (Lecture Notes in Computational Science and Engineering, Bind 126).

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  • Parametric Model 100%
  • Orthonormal Basis 100%
  • Model Reduction 100%
  • Orthogonal Coordinate 66%
  • Operating Condition 66%
  241 Downloads (Pure)
• 2018

  Geometric subspace updates with applications to online adaptive nonlinear model reduction

  Zimmermann, R., Peherstorfer, B. & Willcox, K., 2018, I: SIAM Journal on Matrix Analysis and Applications. 39, 1, s. 234–261

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  • Least Squares Method 100%
  • Image Processing 100%
  • Nonlinear Model 100%
  • Least Square 100%
  • Geodesics 50%
  387 Downloads (Pure)

• Model reduction of complex dynamical systems: Editorial of the special issue corresponding to a workshop held at SDU Odense, Denmark, January 11–13, 2017

  Benner, P., Faßbender, H., Hinze, M., Stykel, T. & Zimmermann, R., dec. 2018, I: Advances in Computational Mathematics. 44, 6, s. 1687-1691

  Publikation: Bidrag til tidsskrift › Leder › peer review

• Theoretical investigations of the new Cokriging method for variable-fidelity surrogate modeling: Well-posedness and maximum likelihood training

  Bertram, A. & Zimmermann, R., dec. 2018, I: Advances in Computational Mathematics. 44, 6, s. 1693-1716

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  • Theoretical Investigation 100%
  • Maximum Likelihood 100%
  • Posedness 100%
  • Positive Definite 100%
  • Surrogate Modeling 100%
  222 Downloads (Pure)

• Towards real-time vehicle aerodynamic design via multi-fidelity data-driven reduced order modeling

  Bertram, A., Othmery, C. & Zimmermannz, R., 2018, AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials. 210049 udg. American Institute of Aeronautics and Astronautics, s. 1-11

  Publikation: Kapitel i bog/rapport/konference-proceeding › Konferencebidrag i proceedings › Forskning › peer review

  • Computational Cost 100%
  • Proper Orthogonal Decomposition 100%
  • Design Process 100%
  • Passenger Cars 100%
  • Reynolds-Averaged Navier-Stokes 100%
• 2017

  Adaptive Sampling for Nonlinear Dimensionality Reduction Based on Manifold Learning

  Franz, T., Zimmermann, R. & Goertz, S., 2017, Model Reduction of Parametrized Systems. Rozza, G., Patera, A., Ohlberger, M., Urban, K. & Benner, P. (red.). Springer, s. 255-269 (Modeling, Simulation & Applications, Bind 17).

  Publikation: Kapitel i bog/rapport/konference-proceeding › Kapitel i bog › Forskning › peer review

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  • Dimensionality 100%
  • Manifold 100%
  • Dimensionality Reduction 100%
  • Adaptive Sampling 100%
  • Stokes Flow 100%
  524 Downloads (Pure)

• A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel manifold under the canonical metric

  Zimmermann, R., 2017, I: SIAM Journal on Matrix Analysis and Applications. 38, 2, s. 322-342

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  • Stiefel Manifold 100%
  • Matrix (Mathematics) 100%
  547 Downloads (Pure)
• 2016

  An Accelerated Greedy Missing Point Estimation Procedure

  Zimmermann, R. & Willcox, K., 7. sep. 2016, I: SIAM Journal on Scientific Computing. 38, 5, s. A2827-A2850

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  • Point Estimation 100%
  • Eigenvalue Problem 100%
  • Minimizes 50%
  • Eigenvalue 50%
  • Combinatorial Problem 50%
  223 Downloads (Pure)

• Local Parametrization of Subspaces on Matrix Manifolds via Derivative Information

  Zimmermann, R., dec. 2016, Numerical Mathematics and Advanced Applications: ENUMATH 2015. Karasozen, B., Manguoğlu, M., Tezer-Sezgin, M., Göktepe, S. & Uğur, Ö. (red.). Springer, Bind 112. s. 379-387 (Lecture Notes in Computational Science and Engineering, Bind 112).

  Publikation: Kapitel i bog/rapport/konference-proceeding › Konferencebidrag i proceedings › Forskning › peer review

  • Matrix (Mathematics) 100%
  • Manifold 100%
  • Parametric Model 66%
  • Parametric 33%
  • Numerical Experiment 33%
• 2015

  An improved estimate for the condition number anomaly of univariate Gaussian correlation matrices

  Zimmermann, R., 2015, I: The Electronic Journal of Linear Algebra. 30, s. 592-598

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  • Gaussians 100%
  • Condition Number 100%
  • Correlation Matrix 100%
  • Gaussian Distribution 100%
  • Euclidean Distance 25%

• On the condition number anomaly of Gaussian correlation matrices

  Zimmermann, R., 2015, I: Linear Algebra and Its Applications. 466, s. 512-526

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  • Gaussian Distribution 100%
  • Matrix (Mathematics) 100%
  • Correlation Matrix 100%
  • Gaussians 100%
  • Condition Number 100%
  42 Downloads (Pure)
• 2014

  A locally parametrized reduced order model for the linear frequency domain approach to time-accurate computational fluid dynamics

  Zimmermann, R., 2014, I: SIAM Journal on Scientific Computing. 36, 3, s. B508-B537

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  • Frequency Domain 100%
  • Computational Fluid Dynamics 100%
  • Reduced Order Model 100%
  • Transonic Flow 40%
  • Parametric 40%

• Erratum: Asymptotic behavior of the likelihood function of covariance matrices of spatial gaussian processes

  Zimmermann, R., 2014, I: Journal of Applied Mathematics. 2014, 1 s., 321932.

  Publikation: Bidrag til tidsskrift › Kommentar/debat › Formidling

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• Interpolation-based reduced-order modelling for steady transonic flows via manifold learning

  Franz, T., Zimmermann, R., Goertz, S. & Karcher, N., 1. mar. 2014, I: International Journal of Computational Fluid Dynamics. 28, 3-4, s. 106-121 16 s.

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  • Computational Fluid Dynamics 100%
  • Transonic Flow 100%
  • Reduced Order Model 100%
  • Two Dimensional 25%
  • Proper Orthogonal Decomposition 25%

• Model order reduction for steady aerodynamics of high-lift configurations

  Vendl, A., Faßbender, H., Goertz, S., Zimmermann, R. & Mifsud, M., 2014, I: CEAS Aeronautical Journal. 5, 4, s. 487-500 14 s.

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  • Proper Orthogonal Decomposition 100%
  • Control Volume 50%
  • Model Reduction 25%
  • Computational Grid 25%
  • Grid Point 25%

• Reduced order modeling of steady flows subject to aerodynamic constraints

  Zimmermann, R., Vendl, A. & Goertz, S., 2014, I: AIAA Journal. 52, 2, s. 255-266 12 s.

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  • Proper Orthogonal Decomposition 100%
  • Least Square Problem 100%
  • Computational Fluid Dynamics 100%
  • Aerodynamic Load 100%
  • Steady Flow 100%
  667 Downloads (Pure)

• Speeding-up the computation of high-lift aerodynamics using a residual-based reduced-order model

  Mifsud, M., Zimmermann, R. & Goertz, S., 2014, I: CEAS Aeronautical Journal. 6, 1, s. 3-16 14 s.

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  • Reduced Order Model 100%
  • Aerodynamic Lift 100%
  • Angle-of-Attack 71%
  • Basis Vector 42%
  • Proper Orthogonal Decomposition 28%
• 2013

  Gradient-Enhanced Surrogate Modeling Based on Proper Orthogonal Decomposition

  Zimmermann, R., 2013, I: Journal of Computational and Applied Mathematics. 237, 1, s. 403-418

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  • Surrogate Modeling 100%
  • Proper Orthogonal Decomposition 100%
  • Partial Differential Equation 50%
  • Adjoints 50%
  • Input Value 50%
  77 Downloads (Pure)

• Improving variable-fidelity surrogate modeling via gradient-enhanced kriging and a generalized hybrid bridge function

  Han, Z. H., Goertz, S. & Zimmermann, R., mar. 2013, I: Aerospace Science and Technology. 25, 1, s. 177-189 13 s.

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  • Computational Fluid Dynamics 100%
  • Airfoil 100%
  • Computational Expense 100%
  • Aerodynamic Coefficient 100%
  • Analytical Function 100%

• On the maximum likelihood training of gradient-enhanced spatial Gaussian processes

  Zimmermann, R., 2013, I: SIAM Journal on Scientific Computing. 35, 6, s. A2554–A2574 21 s.

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  • Gaussian Process 100%
  • Kriging 100%
  • Maximum Likelihood 100%
  • Crosscorrelation 50%
  • Function Value 25%

• Variable-fidelity and reduced-order models for aero data for loads predictions

  Goertz, S., Zimmermann, R. & Han, Z. H., 2013, Computational Flight Testing: Results of the Closing Symposium of the German Research Initiative ComFliTe, Braunschweig, Germany, June 11th-12th, 2012. Kroll, N., Radespiel, R., Burg, J. W. & Sørensen, K. (red.). s. 99-112 (Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Bind 123).

  Publikation: Kapitel i bog/rapport/konference-proceeding › Konferencebidrag i proceedings › Forskning › peer review

  • Computational Fluid Dynamics 100%
  • Reduced Order Model 100%
  • Proper Orthogonal Decomposition 25%
  • Flow Condition 25%
  • Transonic Flow 25%
• 2012

  Alternative cokriging model for variable-fidelity surrogate modeling

  Han, Z. H., Zimmermann, R. & Goertz, S., 2012, I: AIAA Journal. 50, 5, s. 1205-1210

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  • Airfoil 100%
  • Aerodynamic Coefficient 100%
  • Covariance Matrix 100%
  • Kriging Model 100%
  • Moment Coefficient 100%

• Improved extrapolation of steady turbulent aerodynamics using a non-linear POD-based reduced order model

  Zimmermann, R. & Goertz, S., okt. 2012, I: Aeronautical Journal. 116, 1184, s. 1079-1100

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  • Proper Orthogonal Decomposition 100%
  • Reduced Order Model 100%
  • Computational Fluid Dynamics 45%
  • Least Square 9%
  • Optimisation Problem 9%
• 2011

  A POD-based Reduced Order Modeling Approach for the Efficient Computation of High-Lift Aerodynamics

  Mifsud, M., Zimmermann, R., Sippli, J. & Goertz, S., sep. 2011, volutionary and Deterministic Methods for Design, Optimization and Control. Poloni, C., Quagliarella, D., Périaux, J., Gauger, N. & Giannakoglou, K. (red.). CIRA, Centro italiano ricerche aerospaziali, s. 213-225

  Publikation: Kapitel i bog/rapport/konference-proceeding › Konferencebidrag i proceedings › Forskning › peer review

• Towards best practice guidelines for POD-based reduced order models

  Zimmermann, R., 14. sep. 2011, EUROGEN, Evolutionary and deterministic methods for design, optimization and control. Poloni, C., Quagliarella, D., Périaux, J., Gauger, N. & Giannakoglou, K. (red.). CIRA, Centro italiano ricerche aerospaziali, s. 326-341

  Publikation: Kapitel i bog/rapport/konference-proceeding › Konferencebidrag i proceedings › Forskning › peer review
• 2010

  A new cokriging method for variable-fidelity surrogate modeling of aerodynamic data

  Han, Z. H., Zimmermann, R. & Goertz, S., 2010, 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. 2010-1225

  Publikation: Kapitel i bog/rapport/konference-proceeding › Konferencebidrag i proceedings › Forskning › peer review

  • Computational Fluid Dynamics 100%
  • Numerical Implementation 20%
  • Design Optimization 20%
  • Numerical Example 20%
  • Auxiliary Variable 20%

• Asymptotic behavior of the likelihood function of covariance matrices of spatial Gaussian processes

  Zimmermann, R., 2010, I: Journal of Applied Mathematics. 2010, 17 s., 494070.

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

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  • Likelihood Function 100%
  • Asymptotic Behavior 100%
  • Gaussian Process 100%
  • Kriging 100%
  • Maximum Likelihood 100%

• Complete embedded minimal surfaces of finite total curvature with planar ends of smallest possible order

  Zimmermann, R., 2010, I: Mathematische Annalen. 346, s. 85-105

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  • Total Curvature 100%
  • Minimal Surface 100%
  • Algebraic Equation 33%
  • Several Complex Variables 33%
  • Implicit Function Theorem 33%
  59 Downloads (Pure)

• Non-linear reduced order models for steady aerodynamics

  Zimmermann, R. & Goertz, S., 2010, I: Procedia Computer Science. 1, 1, s. 165-174

  Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

  Åben adgang

  • Proper Orthogonal Decomposition 100%
  • Reduced Order Model 100%
  • Computational Fluid Dynamics 40%
  • Least Square 20%
  • Optimisation Problem 20%