Index Analysis
DAEs are no ODEs. Actually, Differential agebraic equations (DAEs) are a mixture of ordinary differential equations (ODEs) and algebraic relations. This may create difficulties, which are not seen at the first sight. The analysis shows that due this mixture hidden differentiation might occur. Recalling from analysis that differentiation is not an unbounded operator, such a process is much more difficult to handle than the integrals used for solving ODEs. E.g. imagine a sinosoidal signal of small amplitude but with high frequency, such as a numerical error, the derivative is of much larger magnitude.
Clearly, the more derivatives involved in the exact solution of a DAE, the more one needs to be careful in numerical computations. The index is a measure for this difficutly. That is why it is important to know the index before simulation.
Group members working on that field
- Andreas Bartel
- Michael Günther
Cooperations
- Giuseppe Ali (Academia)
- Sascha Baumanns (Academia)
- Caren Tischendorf (Academia)
Publications
- 2024
5291.
Klamroth, Kathrin; Stiglmayr, Michael; Totzeck, Claudia
Consensus-Based Optimization for Multi-Objective Problems: A Multi-Swarm Approach
Journal of Global Optimization
20245290.
Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain
Mathematics of Control, Signals, and Systems, 36 (4) :957–977
2024
Herausgeber: Springer London5289.
Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain
Mathematics of Control, Signals, and Systems, 36 (4) :957–977
2024
Herausgeber: Springer London5288.
Günther, M.; Jacob, B.; Totzeck, C.
Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain
Math. Control Signals Syst., 36 :957–977
20245287.
Günther, M.; Jacob, Birgit; Totzeck, Claudia
Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain
Math. Control Signals Syst.
20245286.
Zaspel, Peter; Günther, Michael
Data-driven identification of port-Hamiltonian DAE systems by Gaussian processes
Preprint
20245285.
Zaspel, Peter; Günther, Michael
Data-driven identification of port-Hamiltonian DAE systems by Gaussian processes
Preprint
20245284.
Zaspel, Peter; Günther, Michael
Data-driven identification of port-Hamiltonian DAE systems by Gaussian processes.
20245283.
Kapllani, Lorenc; Teng, Long
Deep learning algorithms for solving high-dimensional nonlinear backward stochastic differential equations
Discrete and continuous dynamical systems - B, 29 (4) :1695–1729
2024
Herausgeber: AIMS Press5282.
Ackermann, Julia; Jentzen, Arnulf; Kuckuck, Benno; Padgett, Joshua Lee
Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations
arXiv:2406.10876 :64 pages
20245281.
Kossaczká, Tatiana; Jagtap, Ameya D; Ehrhardt, Matthias
Deep smoothness weighted essentially non-oscillatory method for two-dimensional hyperbolic conservation laws: A deep learning approach for learning smoothness indicators
Physics of Fluids, 36 (3)
2024
Herausgeber: AIP Publishing5280.
Kossaczká, Tatiana; Jagtap, Ameya D; Ehrhardt, Matthias
Deep smoothness WENO method for two-dimensional hyperbolic conservation laws: A deep learning approach for learning smoothness indicators
Physics of Fluid, 36 (3) :036603
2024
Herausgeber: AIP Publishing5279.
Kossaczká, Tatiana; Jagtap, Ameya D; Ehrhardt, Matthias
Deep smoothness WENO method for two-dimensional hyperbolic conservation laws: A deep learning approach for learning smoothness indicators
Physics of Fluid, 36 (3) :036603
2024
Herausgeber: AIP Publishing5278.
Stiglmayr, Michael; Uhlemeyer, Svenja; Uhlemeyer, Björn; Zdrallek, Markus
Determining Cost-Efficient Controls of Electrical Energy Storages Using Dynamic Programming
Journal of Mathematics in Industry
20245277.
Ehrhardt, M.; Kruse, T.; Tordeux, A.
Dynamics of a Stochastic port-{H}amiltonian Self-Driven Agent Model in One Dimension
ESAIM: Math. Model. Numer. Anal.
20245276.
Itzenhäuser, Patricia; Wachter, Ferdinand Max; Lehmann, Laura; Rajkovic, Michelle; Benter, Thorsten; Wissdorf, Walter
Dynamics of the Aspiration of Charged Droplets into a LC-ESI-MS System
Journal of the American Society for Mass Spectrometry :jasms.4c00238
September 2024
ISSN: 1044-0305, 1879-11235275.
Efficient and Simple Extraction Protocol for Triterpenic Acids from Apples
Journal of Chemical Education, 101 :2087-2093
April 2024
Herausgeber: ACS5274.
Santos, Daniela Scherer; Klamroth, Kathrin; Martins, Pedro; Paquete, Luís
Ensuring connectedness for the Maximum Quasi-clique and Densest $k$-subgraph problems
20245273.
Holzenkamp, Matthias; Lyu, Dongyu; Kleinekathöfer, Ulrich; Zaspel, Peter
Evaluation of uncertainty estimations for Gaussian process regression based machine learning interatomic potentials.
20245272.
Gaul, Daniela
Exact and Heuristic Methods for Dial-a-Ride Problems
Dissertation
Dissertation
Bergische Universität Wuppertal
20245271.
Lyu, Dongyu; Holzenkamp, Matthias; Vinod, Vivin; Holtkamp, Yannick M.; Maity, Sayan; Salazar, Carlos R.; Kleinekathöfer, Ulrich; Zaspel, Peter
Excitation Energy Transfer between Porphyrin Dyes on a Clay Surface: A study employing Multifidelity Machine Learning.
20245270.
Kienitz, Jörg
Exciting times are ahead - Gaussian views and yield curve extrapolation
Wilmott, 2024 (134) :46–50
2024
Herausgeber: Wilmott Magazine5269.
[german] Zeller, Diana; Bohrmann-Linde, Claudia
Falschinformationen in Videos? Mit dem Konzept KriViNat die Kompetenz der Informationsbewertung stärken
In Bohrmann-Linde, C.; Gökkus, Y.; Meuter, N.; Zeller, D., Editor, Band Netzwerk Digitalisierter Chemieunterricht. Sammelband NeDiChe-Treff 2022
Seite 9-15
Herausgeber: Chemiedidaktik. Bergische Universität Wuppertal
2024
9-155268.
Bartel, Andreas; Schaller, Manuel
Goal-oriented time adaptivity for port-{H}amiltonian systems
20245267.
Schäfers, Kevin; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco
Hessian-free force-gradient integrators
2024