Page 373 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 373
TIONAL APPROXIMATION FOR DATA-DRIVEN MODELING AND COMPLEXITY
REDUCTION OF LINEAR AND NONLINEAR DYNAMICAL SYSTEMS (MS-69)
of the matrix A in the state space model. On the other hand, this connection could potentially
also lead us to a theory of model order reduction for neural networks. In the presentation,
we will review the artificial networks, establish the 1-1 connection and discuss the resulting
implications.
Structured Realization Based on Time-Domain Data
Philipp Schulze, pschulze@math.tu-berlin.de
Technische Universität Berlin, Germany
Coauthors: Elliot Fosong, Benjamin Unger
In this talk we present a method for constructing a continuous-time linear time-invariant sys-
tem based on discrete samples of an input/output trajectory of the system. Especially, our
approach allows to impose different structures on the constructed system including structures
like second-order systems, systems with time-delay in the state, and fractional systems. The
proposed method consists of first using the measured time-domain data to estimate the transfer
function at selected points in the frequency domain by using a modified version of the empir-
ical transfer function estimation presented in [Peherstorfer, Gugercin, Willcox, SIAM J. Sci.
Comput., 39(5):2152–2178, 2017]. Afterward, we construct a structured realization based on
the estimated frequency data such that the transfer function of the obtained realization interpo-
lates the frequency data. The effectiveness of this new approach is illustrated by means of a
numerical example.
Structure Preserving Model Order Reduction by Parameter Optimization
Paul Schwerdtner, schwerdt@math.tu-berlin.de
TU Berlin, Germany
Coauthor: Matthias Voigt
We present a framework for structure-preserving model order reduction (MOR) based on direct
parameter optimization as introduced in [1]. We explain how our method can be applied to
compute reduced order models for linear port-Hamiltonian (pH) systems. For that, we first
describe how we fully parametrize pH systems such that all structural constraints regarding
the system matrices are automatically satisfied. After that, we give insights into the specific
optimization problem we set up to find a good approximation with respect to the H-infinity
norm. Finally, we highlight the effectiveness of our method by comparing it to other structure
preserving MOR algorithms [2, 3] on a pH benchmark system from [2].
References
[1] P. Schwerdtner and M. Voigt, "Structure Preserving Model Order Reduction by Parameter
Optimization", https://arxiv.org/pdf/2011.07567.pdf
[2] S. Gugercin, R. V. Polyuga, C. Beattie, and A. van der Schaft, "Structure-preserving tan-
gential interpolation for model reduction of port-Hamiltonian systems," Automatica, vol.
48, no. 9, pp. 1963-1974, 2012.
371
REDUCTION OF LINEAR AND NONLINEAR DYNAMICAL SYSTEMS (MS-69)
of the matrix A in the state space model. On the other hand, this connection could potentially
also lead us to a theory of model order reduction for neural networks. In the presentation,
we will review the artificial networks, establish the 1-1 connection and discuss the resulting
implications.
Structured Realization Based on Time-Domain Data
Philipp Schulze, pschulze@math.tu-berlin.de
Technische Universität Berlin, Germany
Coauthors: Elliot Fosong, Benjamin Unger
In this talk we present a method for constructing a continuous-time linear time-invariant sys-
tem based on discrete samples of an input/output trajectory of the system. Especially, our
approach allows to impose different structures on the constructed system including structures
like second-order systems, systems with time-delay in the state, and fractional systems. The
proposed method consists of first using the measured time-domain data to estimate the transfer
function at selected points in the frequency domain by using a modified version of the empir-
ical transfer function estimation presented in [Peherstorfer, Gugercin, Willcox, SIAM J. Sci.
Comput., 39(5):2152–2178, 2017]. Afterward, we construct a structured realization based on
the estimated frequency data such that the transfer function of the obtained realization interpo-
lates the frequency data. The effectiveness of this new approach is illustrated by means of a
numerical example.
Structure Preserving Model Order Reduction by Parameter Optimization
Paul Schwerdtner, schwerdt@math.tu-berlin.de
TU Berlin, Germany
Coauthor: Matthias Voigt
We present a framework for structure-preserving model order reduction (MOR) based on direct
parameter optimization as introduced in [1]. We explain how our method can be applied to
compute reduced order models for linear port-Hamiltonian (pH) systems. For that, we first
describe how we fully parametrize pH systems such that all structural constraints regarding
the system matrices are automatically satisfied. After that, we give insights into the specific
optimization problem we set up to find a good approximation with respect to the H-infinity
norm. Finally, we highlight the effectiveness of our method by comparing it to other structure
preserving MOR algorithms [2, 3] on a pH benchmark system from [2].
References
[1] P. Schwerdtner and M. Voigt, "Structure Preserving Model Order Reduction by Parameter
Optimization", https://arxiv.org/pdf/2011.07567.pdf
[2] S. Gugercin, R. V. Polyuga, C. Beattie, and A. van der Schaft, "Structure-preserving tan-
gential interpolation for model reduction of port-Hamiltonian systems," Automatica, vol.
48, no. 9, pp. 1963-1974, 2012.
371
