activity
20172022
most citedExample Setups of Navier-Stokes Equations with Control and Observation: Spatial Discretization and Representation via Linear-quadratic Matrix Coefficients

12 citations · 16 across the 6 of their papers we have counts for

collaborators

8 papers

math.DS20221 cited

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…

math.NA2021

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…

math.DS2020

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…

math.DS2020

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…

math.DS2019

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…

math.NA20193 cited

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…