Related papers: Data-Driven Model Order Reduction for Problems wit…
Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for…
We propose in this paper an adaptive reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus…
In this paper, balancing based model order reduction (MOR) for large-scale linear discrete-time time-invariant systems in prescribed finite time intervals is studied. The first main topic is the development of error bounds regarding the…
Model Order Reduction (MOR) methods enable the generation of real-time-capable digital twins, which can enable various novel value streams in industry. While traditional projection-based methods are robust and accurate for linear problems,…
We provide a unifying framework for $\mathcal{L}_2$-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive…
This contribution describes the implementation of a data--driven shape optimization pipeline in a naval architecture application. We adopt reduced order models (ROMs) in order to improve the efficiency of the overall optimization, keeping a…
Given a set of solution snapshots of a hyperbolic PDE, we are interested in learning a reduced order model (ROM). To this end, we propose a novel decompose then learn approach. We decompose the solution by expressing it as a composition of…
Generally, reduced order models of fluid flows are obtained by projecting the Navier-Stokes equations onto a reduced subspace spanned by vector functions that carry the meaningful information of the dynamics. A common method to generate…
This work introduces an empirical quadrature-based hyperreduction procedure and greedy training algorithm to effectively reduce the computational cost of solving convection-dominated problems with limited training. The proposed approach…
This work introduces a novel approach for data-driven model reduction of time-dependent parametric partial differential equations. Using a multi-step procedure consisting of proper orthogonal decomposition, dynamic mode decomposition and…
A non-intrusive model order reduction (MOR) method that combines features of the dynamic mode decomposition (DMD) and the radial basis function (RBF) network is proposed to predict the dynamics of parametric nonlinear systems. In many…
A new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method,…
We introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients based on model order reduction techniques and the Laplace…
We present a modified model order reduction (MOR) technique for the FFT-based simulation of composite microstructures. It utilizes the earlier introduced MOR technique (Kochmann et al. [2019]), which is based on solving the…
Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…
In this contribution we present an accelerated optimization-based approach for combined state and parameter reduction of a parametrized linear control system which is then used as a surrogate model in a Bayesian inverse setting. Following…
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…
Here, we focus on Model Order Reduction (MOR) of non-parametric second-order dynamical systems. In these MOR algorithms, sequences of large and sparse linear systems arise during the model reduction process. Solving such linear systems is…
This work investigates model order reduction for time-dependent parametrized variational inequalities, with a focus on discrete contact problems. As a prototypical example, we consider an agent-based crowd model [Maury et al., 2011] in…
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…