# Publications

List of publications

### 2023

- V. Mehrmann and B. Unger, “Control of port-Hamiltonian differential-algebraic systems and applications,”
*Acta Numerica*, vol. 32, pp. 395–515, 2023, doi: 10.1017/S0962492922000083. - T. Holicki, J. Nicodemus, P. Schwerdtner, and B. Unger, “Energy matching in reduced passive and port-Hamiltonian systems,” 2023.
- R. Morandin, J. Nicodemus, and B. Unger, “Port-Hamiltonian Dynamic Mode Decomposition,”
*SIAM Journal on Scientific Computing*, vol. 45, no. 4, Art. no. 4, Jul. 2023, doi: 10.1137/22m149329x.

### 2022

- F. Black, P. Schulze, and B. Unger, “Modal Decomposition of Flow Data via Gradient-Based Transport Optimization,” in
*Active Flow and Combustion Control 2021*, R. King and D. Peitsch, Eds., in Active Flow and Combustion Control 2021. Cham: Springer International Publishing, 2022, pp. 203–224. doi: 10.1007/978-3-030-90727-3_13. - V. Mehrmann and B. Unger, “Control of port-Hamiltonian differential-algebraic systems and applications,”
*ArXiv e-print 2201.06590*, 2022, [Online]. Available: http://arxiv.org/abs/2201.06590 - T. Breiten, D. Hinsen, and B. Unger, “Towards a modeling class for port-Hamiltonian systems with time-delay,” 2022. doi: 10.48550/arXiv.2211.10687.
- D. Frank, D. A. Latif, M. Muehlebach, B. Unger, and S. Staab, “Robust Recurrent Neural Network to Identify Ship Motion in Open Water with Performance Guarantees,” Publication, 2022. doi: 10.48550/arXiv.2212.05781.
- B. Hillebrecht and B. Unger, “Certified machine learning: A posteriori error estimation for physics-informed neural networks,”
*ArXiv e-print 2203.17055*, 2022, [Online]. Available: http://arxiv.org/abs/2203.17055 - J. Heiland and B. Unger, “Identification of Linear Time-Invariant Systems with Dynamic Mode Decomposition,”
*Mathematics*, vol. 10, no. 3, Art. no. 3, 2022, doi: 10.3390/math10030418. - B. Hillebrecht and B. Unger, “Certified machine learning: Rigorous a posteriori error bounds for PDE defined PINNs,” 2022.
- T. Breiten and B. Unger, “Passivity preserving model reduction via spectral factorization,”
*Automatica*, vol. 142, p. 110368, Aug. 2022, doi: 10.1016/j.automatica.2022.110368. - R. Morandin, J. Nicodemus, and B. Unger, “Port-Hamiltonian Dynamic Mode Decomposition,”
*ArXiv e-print 2204.13474*, 2022, doi: 10.48550/arXiv.2204.13474. - R. Altmann, R. Maier, and B. Unger, “Semi-explicit integration of second order for weakly coupled poroelasticity,”
*ArXiv e-print 2203.16664*, 2022, [Online]. Available: http://arxiv.org/abs/2203.16664 - J. Nicodemus, J. Kneifl, J. Fehr, and B. Unger, “Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators,”
*IFAC-PapersOnLine*, vol. 55, no. 20, Art. no. 20, 2022, doi: 10.1016/j.ifacol.2022.09.117.

### 2021

- R. Altmann, R. Maier, and B. Unger, “Semi-explicit discretization schemes for weakly coupled elliptic-parabolic problems,”
*Mathematics of Computation*, vol. 90, no. 329, Art. no. 329, 2021, doi: 10.1090/mcom/3608. - F. Black, P. Schulze, and B. Unger, “Decomposition of flow data via gradient-based transport optimization,”
*ArXiv e-print 2107.03481*, 2021, [Online]. Available: https://arxiv.org/abs/2107.03481 - I. Ahrens and B. Unger, “A simple success check for delay differential-algebraic equations,” in
*Proceedings in Applied Mathematics and Mechanics 2020*, in Proceedings in Applied Mathematics and Mechanics 2020, vol. 20. Wiley, 2021, p. e202000270. doi: 10.1002/pamm.202000270. - F. Black, P. Schulze, and B. Unger, “Efficient Wildland Fire Simulation via Nonlinear Model Order Reduction,”
*Fluids*, vol. 6, no. 8, Art. no. 8, 2021, doi: 10.3390/fluids6080280. - I. V. Gosea, S. Gugercin, and B. Unger, “Parametric model reduction via rational interpolation along parameters,” in
*2021 60th IEEE Conference on Decision and Control (CDC)*, in 2021 60th IEEE Conference on Decision and Control (CDC). 2021, pp. 6895–6900. doi: 10.1109/CDC45484.2021.9682841. - R. Altmann, V. Mehrmann, and B. Unger, “Port-Hamiltonian formulations of poroelastic network models,”
*Mathematical and Computer Modelling of Dynamical Systems*, vol. 27, no. 1, Art. no. 1, 2021, doi: 10.1080/13873954.2021.1975137. - J. Heiland and B. Unger, “Identification of linear time-invariant systems with Dynamic Mode Decomposition,”
*ArXiv e-print 2109.06765*, 2021, [Online]. Available: https://arxiv.org/abs/2109.06765 - F. Black, P. Schulze, and B. Unger, “Model order reduction with dynamically transformed modes for the wave equation,” in
*Proceedings in Applied Mathematics and Mechanics 2020*, in Proceedings in Applied Mathematics and Mechanics 2020, vol. 20. Wiley, 2021, p. e202000321. doi: 10.1002/pamm.202000321. - J. Nicodemus, J. Kneifl, J. Fehr, and B. Unger, “Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators,”
*ArXiv e-print 2109.10793*, 2021, [Online]. Available: https://arxiv.org/abs/2109.10793 - S. Trenn and B. Unger, “Unimodular transformations for DAE initial trajectory problems,” in
*Proceedings in Applied Mathematics and Mechanics 2020*, in Proceedings in Applied Mathematics and Mechanics 2020, vol. 20. Wiley, 2021, p. e202000322. doi: 10.1002/pamm.202000322. - R. Altmann, R. Maier, and B. Unger, “A semi-explicit integration scheme for weakly-coupled poroelasticity with nonlinear permeability,” in
*Proceedings in Applied Mathematics and Mechanics 2020*, in Proceedings in Applied Mathematics and Mechanics 2020, vol. 20. Wiley, 2021, p. e202000061. doi: 10.1002/pamm.202000061. - T. Breiten and B. Unger, “Passivity preserving model reduction via spectral factorization,”
*ArXiv e-print 2103.13194*, 2021, [Online]. Available: https://arxiv.org/abs/2103.13194

### 2020

- I. Ahrens and B. Unger, “The Pantelides algorithm for delay differential-algebraic equations,”
*Transactions of Mathematics and Its Application*, vol. 4, no. 1, Art. no. 1, 2020, doi: 10.1093/imatrm/tnaa003. - R. Altmann, R. Maier, and B. Unger, “Semi-explicit discretization schemes for weakly coupled elliptic-parabolic problems,”
*Mathematics of Computation*, p. 1, Oct. 2020, doi: 10.1090/mcom/3608. - R. Altmann, V. Mehrmann, and B. Unger, “Port-Hamiltonian formulations of poroelastic network models,”
*ArXiv e-print 2012.01949*, Dec. 2020, [Online]. Available: https://arxiv.org/abs/2012.01949 - F. Black, P. Schulze, and B. Unger, “Projection-based model reduction with dynamically transformed modes,”
*ESAIM: Mathematical Modelling and Numerical Analysis*, vol. 54, no. 6, Art. no. 6, Oct. 2020, doi: 10.1051/m2an/2020046. - B. Unger, “Delay differential-algebraic equations in real-time dynamic substructuring,”
*ArXiv e-print 2003.10195*, Mar. 2020, [Online]. Available: https://arxiv.org/abs/2003.10195

### 2019

- S. Trenn and B. Unger, “Delay regularity of differential-algebraic equations,” in
*2019 IEEE 58th Conference on Decision and Control (CDC)*, in 2019 IEEE 58th Conference on Decision and Control (CDC). Dec. 2019, pp. 989–994. doi: 10.1109/CDC40024.2019.9030146. - E. Fosong, P. Schulze, and B. Unger, “From Time-Domain Data to Low-Dimensional Structured Models,”
*ArXiv e-print 1902.05112*, Feb. 2019, [Online]. Available: https://arxiv.org/abs/1902.05112 - B. Unger and S. Gugercin, “Kolmogorov n-widths for linear dynamical systems,”
*Advances in Computational Mathematics*, vol. 45, no. 5, Art. no. 5, Dec. 2019, doi: 10.1007/s10444-019-09701-0. - D. Kern, M. Bartelt, and B. Unger, “How to write an article for GAMMAS and a longer title,”
*GAMM Archive for Students*, vol. 1, no. 1, Art. no. 1, Feb. 2019, doi: 10.14464/gammas.v1i1.417.

### 2018

- P. Schulze, B. Unger, Christopher. Beattie, and S. Gugercin, “Data-driven Structured Realization,”
*Linear Algebra and its Applications*, vol. 537, pp. 250–286, 2018, doi: 10.1016/j.laa.2017.09.030. - P. Schulze and B. Unger, “Model reduction for linear systems with low-rank switching.,”
*SIAM J. Control and Optimization*, vol. 56, no. 6, Art. no. 6, 2018, doi: 10.1137/18M1167887. - B. Unger, “Discontinuity Propagation in Delay Differential-Algebraic Equations,”
*The Electronic Journal of Linear Algebra*, vol. 34, pp. 582–601, Feb. 2018, doi: 10.13001/1081-3810.3759.

### 2016

- P. Schulze and B. Unger, “Data-driven interpolation of dynamical systems with delay.,”
*Systems Control Lett.*, vol. 97, pp. 125–131, 2016, doi: 10.1016/j.sysconle.2016.09.007.

### 2015

- V. Mehrmann and B. Unger, “Index preserving polynomial representation of nonlinear differential-algebraic systems,” Institut für Mathematik, TU Berlin, Str. des 17. Juni 136, D-10623 Berlin, FRG, Preprint 2--2015, 2015. [Online]. Available: http://www3.math.tu-berlin.de/cgi-bin/IfM/show_abstract.cgi?Report-02-2015.rdf.html

### 2013

- B. Unger, “Impact of Discretization Techniques on Nonlinear Model Reduction and Analysis of the Structure of the POD Basis,” Master’s Thesis, Virginia Polytechnic and State University, Blacksburg, Virginia, USA, 2013. [Online]. Available: https://vtechworks.lib.vt.edu/handle/10919/24197