Related papers: Dynamical model reduction method for solving param…
An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear time-invariant systems but differ in their output equations,…
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…
Training nonlinear parametrizations such as deep neural networks to numerically approximate solutions of partial differential equations is often based on minimizing a loss that includes the residual, which is analytically available in…
Probabilistic variants of Model Order Reduction (MOR) methods have recently emerged for improving stability and computational performance of classical approaches. In this paper, we propose a probabilistic Reduced Basis Method (RBM) for the…
In gradient-based time domain topology optimization, design sensitivity analysis (DSA) of the dynamic response is essential, and requires high computational cost to directly differentiate, especially for high-order dynamic system. To…
In this work, we propose to efficiently solve time dependent parametrized optimal control problems governed by parabolic partial differential equations through the certified reduced basis method. In particular, we will exploit an error…
In this work a stabilised and reduced Galerkin projection of the incompressible unsteady Navier-Stokes equations for moderate Reynolds number is presented. The full-order model, on which the Galerkin projection is applied, is based on a…
These notes present preliminary results regarding two different approximations of linear infinite-horizon optimal control problems arising in model predictive control. Input and state trajectories are parametrized with basis functions and a…
We present a model reduction approach for the real-time solution of time-dependent nonlinear partial differential equations (PDEs) with parametric dependencies. The approach integrates several ingredients to develop efficient and accurate…
For affine linear parameter-varying (LPV) systems, this paper develops two parameter reduction methods for reducing the dimension of the parameter space. The first method achieves the complexity reduction by transforming the affine LPV…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
We present a low-order modeling technique for actuated flows based on the regularization of an inverse problem. The inverse problem aims at minimizing the error between the model predictions and some reference simulations. The parameters to…
In this contribution we are concerned with tight a posteriori error estimation for projection based model order reduction of $\inf$-$\sup$ stable parameterized variational problems. In particular, we consider the Reduced Basis Method in a…
An interior penalty discontinuous Galerkin method is devised to approximate minimizers of a linear folding model by discontinuous isoparametric finite element functions that account for an approximation of a folding arc. The numerical…
Model order reduction through the POD-Galerkin method can lead to dramatic gains in terms of computational efficiency in solving physical problems. However, the applicability of the method to non linear high-dimensional dynamical systems…
In this contribution we present a survey of concepts in localized model order reduction methods for parameterized partial differential equations. The key concept of localized model order reduction is to construct local reduced spaces that…
This paper proposes a data-driven model reduction approach on the basis of noisy data. Firstly, the concept of data reduction is introduced. In particular, we show that the set of reduced-order models obtained by applying a Petrov-Galerkin…
We deal with the numerical solution of the time-dependent partial differential equations using the adaptive space-time discontinuous Galerkin (DG) method. The discretization leads to a nonlinear algebraic system at each time level, the size…
An adaptive scheme to generate reduced-order models for parametric nonlinear dynamical systems is proposed. It aims to automatize the POD-Greedy algorithm combined with empirical interpolation. At each iteration, it is able to adaptively…
This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…