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Jonas Nicodemus

Doctoral researcher

Contact

Universitätsstraße 32
70569 Stuttgart
Deutschland
Room: 226B

Subject

Data-Integrated Low-Dimensional Surrogate Models with Guarantees
We study the identification of port-Hamiltonian systems from given data. Port-Hamiltonian systems guarantee physical properties such as passivity, which leads to the preservation of the physical behavior when the systems are coupled. We also develop novel structure-preserving model order reduction strategies to enable rapid evaluation of the identified models.

Publications

T. Holicki, J. Nicodemus, P. Schwerdtner, and B. Unger, “Energy matching in reduced passive and port-Hamiltonian systems,” arXiv, 2023. doi: 10.48550/ARXIV.2309.05778.
- BibTeX
BibTeX
@preprint{https://doi.org/10.48550/arxiv.2309.05778, author = {Holicki, Tobias and Nicodemus, Jonas and Schwerdtner, Paul and Unger, Benjamin}, copyright = {Creative Commons Attribution 4.0 International}, doi = {10.48550/ARXIV.2309.05778}, publisher = {arXiv}, title = {Energy matching in reduced passive and port-Hamiltonian systems}, url = {https://arxiv.org/abs/2309.05778}, year = 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.
- BibTeX
BibTeX
@article{Morandin_2023, author = {Morandin, Riccardo and Nicodemus, Jonas and Unger, Benjamin}, doi = {10.1137/22m149329x}, journal = {{SIAM} Journal on Scientific Computing}, month = {07}, number = 4, pages = {A1690--A1710}, publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})}, title = {Port-Hamiltonian Dynamic Mode Decomposition}, url = {https://doi.org/10.1137%2F22m149329x}, volume = 45, year = 2023 }
R. Morandin, J. Nicodemus, and B. Unger, “Port-Hamiltonian Dynamic Mode Decomposition,” ArXiv e-print 2204.13474, 2022, doi: 10.48550/arXiv.2204.13474.
- Abstract
- BibTeX
Abstract
We present a novel physics-informed system identification method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the input, state, and output of a system in the time domain, we find a realization that approximates the data well while guaranteeing that the energy functional satisfies a dissipation inequality. To this end, we use the framework of port-Hamiltonian (pH) systems and modify the dynamic mode decomposition to be feasible for continuous-time pH systems. We propose an iterative numerical method to solve the corresponding least-squares minimization problem. We construct an effective initialization of the algorithm by studying the least-squares problem in a weighted norm, for which we present the analytical minimum-norm solution. The efficiency of the proposed method is demonstrated with several numerical examples.
BibTeX
@article{MorNU22, abstract = {We present a novel physics-informed system identification method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the input, state, and output of a system in the time domain, we find a realization that approximates the data well while guaranteeing that the energy functional satisfies a dissipation inequality. To this end, we use the framework of port-Hamiltonian (pH) systems and modify the dynamic mode decomposition to be feasible for continuous-time pH systems. We propose an iterative numerical method to solve the corresponding least-squares minimization problem. We construct an effective initialization of the algorithm by studying the least-squares problem in a weighted norm, for which we present the analytical minimum-norm solution. The efficiency of the proposed method is demonstrated with several numerical examples.}, author = {Morandin, Riccardo and Nicodemus, Jonas and Unger, Benjamin}, doi = {10.48550/arXiv.2204.13474}, journal = {ArXiv e-print 2204.13474}, pubdate = {2022-04-28}, title = {Port-Hamiltonian Dynamic Mode Decomposition}, year = 2022 }
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
- Abstract
- BibTeX
Abstract
We discuss nonlinear model predictive control (NMPC) for multi-body dynamics via physics-informed machine learning methods. Physics-informed neural networks (PINNs) are a promising tool to approximate (partial) differential equations. PINNs are not suited for control tasks in their original form since they are not designed to handle variable control actions or variable initial values. We thus present the idea of enhancing PINNs by adding control actions and initial conditions as additional network inputs. The high-dimensional input space is subsequently reduced via a sampling strategy and a zero-hold assumption. This strategy enables the controller design based on a PINN as an approximation of the underlying system dynamics. The additional benefit is that the sensitivities are easily computed via automatic differentiation, thus leading to efficient gradient-based algorithms. Finally, we present our results using our PINN-based MPC to solve a tracking problem for a complex mechanical system, a multi-link manipulator.
BibTeX
@article{NicKFU21, abstract = {We discuss nonlinear model predictive control (NMPC) for multi-body dynamics via physics-informed machine learning methods. Physics-informed neural networks (PINNs) are a promising tool to approximate (partial) differential equations. PINNs are not suited for control tasks in their original form since they are not designed to handle variable control actions or variable initial values. We thus present the idea of enhancing PINNs by adding control actions and initial conditions as additional network inputs. The high-dimensional input space is subsequently reduced via a sampling strategy and a zero-hold assumption. This strategy enables the controller design based on a PINN as an approximation of the underlying system dynamics. The additional benefit is that the sensitivities are easily computed via automatic differentiation, thus leading to efficient gradient-based algorithms. Finally, we present our results using our PINN-based MPC to solve a tracking problem for a complex mechanical system, a multi-link manipulator.}, author = {Nicodemus, Jonas and Kneifl, Jonas and Fehr, Jörg and Unger, Benjamin}, journal = {ArXiv e-print 2109.10793}, pubdate = {2021-09-23}, title = {Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators}, url = {https://arxiv.org/abs/2109.10793}, year = 2021 }

Vita

2021 Master of Science in Engineering Cybernetics, University of Stuttgart
2015 - 2021 Research Associate at the Institute of Engineering and Computational Mechanics, University of Stuttgart
2018 - 2020 Working Student Bosch SoftTec GmbH, Berlin
2018 Bachelor of Science in Engineering Cybernetics, University of Stuttgart
2014 - 2016 Working Student Robert-Bosch Start-up GmbH, Ludwigsburg

Talks

Invited Talks

Towards Dynamic Mode Decomposition and Port-Hamiltonian Systems in pyMOR
pyMOR school 2022 (online), Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, August 2022.

Minisymposium Talks

Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators
MATHMOD 2022, 10th Vienna International Conference on Mathematical Modelling, Vienna, July 2022.

Selected other talks and poster

Data-driven Discovery of Linear Time-Invariant Port-Hamiltonian Systems
GAMM Annual Meeting 2022, Aachen, August 2022.
Towards the Identification of Port-Hamiltonian Systems
Young Mathematicians in Model Order Reduction, Mathematics Münster, July 2022.
Identification of Passive Linear Time-Invariant Systems from Time Domain Data (Poster)
Workshop "Trends on Dissipativity in Systems and Control”, UniDistance Suisse, Brig, May 2022.
Physics-Informed Neural Networks-based Model Predictive Control
Advanced Topics in Simulation Science Seminar, University of Stuttgart, November 2021.

Channels

Find me on GitHub, Google scholar, ResearchGate

Jonas Nicodemus

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Jonas Nicodemus

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