51 citations · 204 across the 20 of their papers we have counts for
21 papers
Towards a modeling class for port-Hamiltonian systems with time-delay
Tobias Breiten, Dorothea Hinsen, Benjamin Unger
The framework of port-Hamiltonian (pH) systems is a powerful and broadly applicable modeling paradigm. In this paper, we extend the scope of pH systems to time-delay systems. Our d…
Certified machine learning: Rigorous a posteriori error bounds for PDE defined PINNs
Birgit Hillebrecht, Benjamin Unger
Prediction error quantification in machine learning has been left out of most methodological investigations of neural networks, for both purely data-driven and physics-informed app…
Port-Hamiltonian Dynamic Mode Decomposition
Riccardo Morandin, Jonas Nicodemus, Benjamin Unger
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, measu…
Certified machine learning: A posteriori error estimation for physics-informed neural networks
Birgit Hillebrecht, Benjamin Unger
Physics-informed neural networks (PINNs) are one popular approach to incorporate a priori knowledge about physical systems into the learning framework. PINNs are known to be robust…
Semi-explicit integration of second order for weakly coupled poroelasticity
R. Altmann, R. Maier, B. Unger
We introduce a semi-explicit time-stepping scheme of second order for linear poroelasticity satisfying a weak coupling condition. Here, semi-explicit means that the system, which n…
Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators
Jonas Nicodemus, Jonas Kneifl, Jörg Fehr +1
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…
Identification of linear time-invariant systems with Dynamic Mode Decomposition
Jan Heiland, Benjamin Unger
Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identificati…
Decomposition of flow data via gradient-based transport optimization
Felix Black, Philipp Schulze, Benjamin Unger
We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to…
Efficient Wildland Fire Simulation via Nonlinear Model Order Reduction
Felix Black, Philipp Schulze, Benjamin Unger
We propose a new hyper-reduction method for a recently introduced nonlinear model reduction framework based on dynamically transformed basis functions and especially well-suited fo…
Parametric model reduction via rational interpolation along parameters
Ion Victor Gosea, Serkan Gugercin, Benjamin Unger
We present a novel projection-based model reduction framework for parametric linear time-invariant systems that allows interpolating the transfer function at a given frequency poin…
Passivity preserving model reduction via spectral factorization
Tobias Breiten, Benjamin Unger
We present a novel model-order reduction (MOR) method for linear time-invariant systems that preserves passivity and is thus suited for structure-preserving MOR for port-Hamiltonia…
Port-Hamiltonian formulations of poroelastic network models
Robert Altmann, Volker Mehrmann, Benjamin Unger
We investigate an energy-based formulation of the two-field poroelasticity model and the related multiple-network model as they appear in geosciences or medical applications. We pr…
Delay differential-algebraic equations in real-time dynamic substructuring
Benjamin Unger
Hybrid numerical-experimental testing is a standard approach for complex dynamical structures that are, on the one hand, not easy to model due to complexity and parameter uncertain…
Projection-Based Model Reduction with Dynamically Transformed Modes
Felix Black, Philipp Schulze, Benjamin Unger
We propose a new model reduction framework for problems that exhibit transport phenomena. As in the moving finite element method (MFEM), our method employs time-dependent transform…
Semi-explicit discretization schemes for weakly-coupled elliptic-parabolic problems
Robert Altmann, Roland Maier, Benjamin Unger
We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled.…
The Pantelides algorithm for delay differential-algebraic equations
Ines Ahrens, Benjamin Unger
We present a graph-theoretical approach that can detect which equations of a delay differential-algebraic equation (DDAE) need to be differentiated or shifted to construct a soluti…
From Time-Domain Data to Low-Dimensional Structured Models
Elliot Fosong, Philipp Schulze, Benjamin Unger
We present a framework for constructing a structured realization of a linear time-invariant dynamical system solely from a discrete sampling of an input and output trajectory of th…
Kolmogorov -widths for linear dynamical systems
Benjamin Unger, Serkan Gugercin
Kolmogorov -widths and Hankel singular values are two commonly used concepts in model reduction. Here we show that for the special case of linear time-invariant dynamical (LTI)…
Discontinuity propagation in delay differential-algebraic equations
Benjamin Unger
The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Based on the (quasi-) Weierstraß form f…
Model reduction for linear systems with low-rank switching
Philipp Schulze, Benjamin Unger
We introduce a novel model order reduction method for large-scale linear switched systems (LSS) where the coefficient matrices are affected by a low-rank switching. The key idea is…
Data-driven Structured Realization
Philipp Schulze, Benjamin Unger, Christopher Beattie +1
We present a framework for constructing structured realizations of linear dynamical systems having transfer functions of the form where $h_1,h_2,\…