Publikationen

F. Heldmann, M. Ehrhardt and K. Klamroth, "PINN training using biobjective optimization: The trade-off between data loss and residual loss", Journal of Computational Physics, vol. 488, pp. 112211, 2023. Academic Press.

DOI: 10.1016/j.jcp.2023.112211

K. S. Matyokubov and M. Ehrhardt, "Manakov system on metric graphs: Modeling the reflectionless propagation of vector solitons in networks", Physics Letters, Section A, vol. 479, pp. 128928, 2023. North-Holland.

DOI: 10.1016/j.physleta.2023.128928

M. Ehrhardt, "Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons", Physics Letters, Section A, vol. 459, pp. 128611, 2023. North-Holland.

DOI: 10.1016/j.physleta.2022.128611

M. Ehrhardt, "Experimental observation and theoretical analysis of the low-frequency source interferogram and hologram in shallow water", Journal of Sound and Vibration, vol. 544, pp. 117388, 2023. Academic Press.

DOI: 10.1016/j.jsv.2022.117388

H. Fatoorehchi and M. Ehrhardt, "A new method for stability analysis of linear time-invariant systems and continuous-time nonlinear systems with application to process dynamics and control", Preprint IMACM, 2023.

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M. Ehrhardt, "Use of interference patterns to control sound field focusing in shallow water", Journal of Marine Science and Engineering, vol. 11, no. 3, pp. 559, 2023. MDPI.

DOI: 10.3390/jmse11030559

L. Di Persio and M. Ehrhardt, "Electricity price forecasting via statistical and deep learning approaches: The German case", AppliedMath, vol. 3, no. 2, pp. 316–342, 2023. MDPI.

DOI: 10.3390/appliedmath3020018

H. Fatoorehchi and M. Ehrhardt, "A combined method for stability analysis of linear time invariant control systems based on Hermite-Fujiwara matrix and Cholesky decomposition", The Canadian Journal of Chemical Engineering, vol. 101, no. 12, pp. 7043–7052, 2023. John Wiley & Sons.

DOI: 10.1002/cjce.24962

M. Muniz, M. Ehrhardt, M. Günther and R. Winkler, "Strong stochastic Runge-Kutta-Munthe-Kaas methods for nonlinear Itô SDEs on manifolds", Applied Numerical Mathematics, vol. 193, pp. 196–203, 2023. North-Holland.

DOI: 10.1016/j.apnum.2023.07.024

T. Kossaczká, M. Ehrhardt and M. Günther, "Deep FDM: Enhanced finite difference methods by deep learning", Franklin Open, vol. 4, pp. 100039, 2023. Elsevier.

DOI: 10.1016/j.fraope.2023.100039

M. Ehrhardt, "Three-dimensional modeling of sound field holograms of a moving source in the presence of internal waves causing horizontal refraction", Journal of Marine Science and Engineering, vol. 11, no. 10, pp. 1922, 2023. MDPI.

DOI: 10.3390/jmse11101922

T. Kossaczká, M. Ehrhardt and M. Günther, "Deep finite difference method for solving Asian option pricing problems", Preprint IMACM, 2023. Bergische Universität Wuppertal.

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M. Ehrhardt and S. B. Kozitskiy, "On a generalization of the split-step Padé method to the case of unknown vector-functions", Preprint IMACM, 2023. Bergische Universität Wuppertal.

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M. Ehrhardt and K. S. Matyokubov, "Driven transparent quantum graphs", Preprint, 2023.

DOI: 10.48550/arXiv.2312.01448

M. Clemens and M. Günther, "Stability of Transient Coupled Multi-Model Discrete Electromagnetic Field Formulations Using the Port-Hamiltonian System Framework" in 2023 International Conference on Electromagnetics in Advanced Applications (ICEAA), IEEE, 2023, pp. 1–1.

DOI: 10.1109/ICEAA57318.2023.10297842

K. Schäfers, M. Günther and A. Sandu, "Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems", Preprint, 2023.

DOI: 10.48550/arXiv.2306.04389

A. Frommer, M. Günther, B. Liljegren-Sailer and N. Marheineke, "Operator splitting for port-Hamiltonian systems", Preprint, 2023.

DOI: 10.48550/arXiv.2304.01766

M. Hutzenthaler, A. Jentzen, T. Kruse and T. Anh Nguyen, "Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations", Journal of Numerical Mathematics, vol. 31, no. 1, pp. 1–28, 2023. De Gruyter.

DOI: 10.1515/jnma-2021-0111

J. Ackermann, A. Jentzen, T. Kruse, B. Kuckuck and J. L. Padgett, "Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the Lp-sense", Preprint, 2023.

DOI: 10.48550/arXiv.2309.13722

F. Klass, A. Gabbana and A. Bartel, "A non-reflecting boundary condition for multispeed lattice Boltzmann methods" in Progress in Industrial Mathematics at ECMI 2021, Ehrhardt, Matthias and Günther, Michael, Eds. Springer Cham, 2022, pp. 447–453.

DOI: 10.1007/978-3-031-11818-0_58