Related papers: Localized model reduction for parameterized proble…
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…
Reduced order models, in particular the reduced basis method, rely on empirically built and problem dependent basis functions that are constructed during an off-line stage. In the on-line stage, the precomputed problem-dependent solution…
To efficiently tackle parametrized multi and/or large scale problems, we propose an adaptive localized model order reduction framework combining both local offline training and local online enrichment with localized error control. For the…
Finite element based simulation of phenomena governed by partial differential equations is a standard tool in many engineering workflows today. However, the simulation of complex geometries is computationally expensive. Many engineering…
Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…
In this contribution, we introduce and numerically evaluate a certified and adaptive localized reduced basis method as a local model in a trust-region optimization method for parameter optimization constrained by partial differential…
This thesis presents recent advances in model order reduction methods with the primary aim to construct online-efficient reduced surrogate models for parameterized multiscale phenomena and accelerate large-scale PDE-constrained parameter…
In this contribution we present first results towards localized model order reduction for spatially resolved, three-dimensional lithium-ionbattery models. We introduce a localized reduced basis scheme based on non-conforming local…
We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized {nonlinear} elliptic partial differential equations (PDEs). CB-pMOR is designed to deal with large-scale problems for which full-order…
This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient…
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…
Locally adapted parameterizations of a model (such as locally weighted regression) are expressive but often suffer from high variance. We describe an approach for reducing the variance, based on the idea of estimating simultaneously a…
In this paper, a local-global model reduction method is presented to solve stochastic optimal control problems governed by partial differential equations (PDEs). If the optimal control problems involve uncertainty, we need to use a few…
We extend a localized model order reduction method for the distributed finite element solution of elliptic boundary value problems in the cloud. We give a computationally efficient technique to compute the required inner product matrices…
We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…
We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…
In this paper, we propose a model reduction method for solving multiscale elliptic PDEs with random coefficients in the multiquery setting using an optimization approach. The optimization approach enables us to construct a set of localized…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
In this work we combine the framework of the Reduced Basis method (RB) with the framework of the Localized Orthogonal Decomposition (LOD) in order to solve parametrized elliptic multiscale problems. The idea of the LOD is to split a high…
Projection based model order reduction has become a mature technique for simulation of large classes of parameterized systems. However, several challenges remain for problems where the solution manifold of the parameterized system cannot be…