12 citations · 16 across the 6 of their papers we have counts for
8 papers
A quadratic decoder approach to nonintrusive reduced-order modeling of nonlinear dynamical systems
Peter Benner, Pawan Goyal, Jan Heiland +1
Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated…
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…
Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows
Peter Benner, Pawan Goyal, Jan Heiland +1
Reduced-order modeling has a long tradition in computational fluid dynamics. The ever-increasing significance of data for the synthesis of low-order models is well reflected in the…
Space and Chaos-Expansion Galerkin POD Low-order Discretization of PDEs for Uncertainty Quantification
Peter Benner, Jan Heiland
The quantification of multivariate uncertainties in partial differential equations can easily exceed any computing capacity unless proper measures are taken to reduce the complexit…
Convergence of Coprime Factor Perturbations for Robust Stabilization of Oseen Systems
Jan Heiland
Linearization based controllers for incompressible flows have been proven to work in theory and in simulations. To realize such a controller numerically, the infinite dimensional s…
Invariant Galerkin Ansatz Spaces and Davison-Maki Methods for the Numerical Solution of Differential Riccati Equations
Maximilian Behr, Peter Benner, Jan Heiland
The differential Riccati equation appears in different fields of applied mathematics like control and system theory. Recently Galerkin methods based on Krylov subspaces were develo…