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PreprintCC BY 4.0arXiv

Mathematical modeling, simulation and optimization via (port-Hamiltonian) differential-algebraic equations

  • Volker Mehrmann
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Abstract

Differential-algebraic equations (DAEs) present a ubiquitous model class in the automated modeling, simulation, control and optimization of complex finite or infinite dimensional dynamical systems, in particular in the construction of digital twins. When combined with adequate space and time discretization methods they present the work-horse of developments in many engineering domains. However, this approach comes with certain challenges for the numerical methods and in particular in the coupling of systems from different physical domains with different scales or regularity requirements. We survey the modeling with DAEs and address how to overcome some of the challenges via the framework of port-Hamiltonian differential-algebraic systems (pHDAEs) and their simulation and optimization with space-time-model adaptive methods.

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Cite

BibTeXRIS
BibTeX
@misc{mehrmann2026mathematical,
  title = {{Mathematical modeling, simulation and optimization via (port-Hamiltonian) differential-algebraic equations}},
  author = {Volker Mehrmann},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33954},
  eprint = {2609.33954},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33954},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Mathematical modeling, simulation and optimization via (port-Hamiltonian) differential-algebraic equations
AU  - Volker Mehrmann
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.33954
UR  - https://arxiv.org/abs/2609.33954
AB  - Differential-algebraic equations (DAEs) present a ubiquitous model class in the automated modeling, simulation, control and optimization of complex finite or infinite dimensional dynamical systems, in particular in the construction of digital twins. When combined with adequate space and time discretization methods they present the work-horse of developments in many engineering domains. However, this approach comes with certain challenges for the numerical methods and in particular in the coupling of systems from different physical domains with different scales or regularity requirements. We survey the modeling with DAEs and address how to overcome some of the challenges via the framework of port-Hamiltonian differential-algebraic systems (pHDAEs) and their simulation and optimization with space-time-model adaptive methods.
ER  -