Related papers: Adaptive Frequency-limited H2-Model Order Reductio…
In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed from local solutions of the partial differential equation…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
This note presents a method that provides optimal monotone conditional error functions for a large class of adaptive two stage designs. The presented method builds on a previously developed general theory for optimal adaptive two stage…
Projection-based model order reduction on nonlinear manifolds has been recently proposed for problems with slowly decaying Kolmogorov n-width such as advection-dominated ones. These methods often use neural networks for manifold learning…
Considering the use of dynamical systems in practical applications, often only limited regions in the time or frequency domain are of interest. Therefor, it usually pays off to compute local approximations of the used dynamical systems in…
We introduce a filtering technique for Discontinuous Galerkin approximations of hyperbolic problems. Following an approach already proposed for the Hamilton-Jacobi equations by other authors, we aim at reducing the spurious oscillations…
This paper considers the distributed robust suboptimal consensus control problem of linear multi-agent systems, with both H2 and H_infty performance requirements. A novel two-step complementary design approach is proposed. In the first…
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…
In this paper, synchronization of fractional order Coullet system with precise and also unknown parameters are studied. The proposed method which is based on the adaptive backstepping, has been developed to synchronize two chaotic systems…
We study the Hamiltonian truncation for the two-dimensional $\lambda\phi^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms…
An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…
This work proposes A$^2$GD, a novel adaptive accelerated gradient descent method for convex and composite optimization. Smoothness and convexity constants are updated via Lyapunov analysis. Inspired by stability analysis in ODE solvers, the…
We propose a model order reduction approach to speed up the computation of seismograms, i.e. the solution of the seismic wave equation evaluated at a receiver location, for different model parameters. Our approach achieves a reduction of…
We present an adaptive sampling strategy for the optimization-based structure preserving model order reduction (MOR) algorithm developed in [Schwerdtner, P. and Voigt, M. (2020). Structure preserving model order reduction by parameter…
A single-step high-order implicit time integration scheme with controllable numerical dissipation at high frequencies is presented for the transient analysis of structural dynamic problems. The amount of numerical dissipation is controlled…
This paper deals with the exponential stability of systems made of a hyperbolic PDE coupled with an ODE with different time scales, the dynamics of the PDE being much faster than that of the ODE. Such a difference of time scales is modeled…
Data-driven reduced order modeling of chaotic dynamics can result in systems that either dissipate or diverge catastrophically. Leveraging non-linear dimensionality reduction of autoencoders and the freedom of non-linear operator inference…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
We analyze a structure-preserving model order reduction technique for delay and stochastic delay equations based on the balanced truncation method and provide a system theoretic interpretation. Transferring error bounds based on Hankel…