Related papers: A novel model reduction method to solve inverse pr…
A parametric model order reduction (MOR) approach for simulating the high dimensional models arising in financial risk analysis is proposed on the basis of the proper orthogonal decomposition (POD) approach to generate small model…
In this paper we study the approximation of an optimal control problem for linear para\-bolic PDEs with model order reduction based on Proper Orthogonal Decomposition (POD-MOR). POD-MOR is a Galerkin approach where the basis functions are…
Recently, researchers have investigated the relationship between proper orthogonal decomposition (POD), difference quotients (DQs), and pointwise in time error bounds for POD reduced order models of partial differential equations. In a…
The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures…
The Probability Of Detection (POD) curve is a standard tool in several industries to evaluate the performance of Non Destructive Testing (NDT) procedures for the detection of harmful defects for the inspected structure. Due to new…
In this paper, we present a new nonintrusive reduced basis method when a cheap low-fidelity model and expensive high-fidelity model are available. The method relies on proper orthogonal decomposition (POD) to generate the high-fidelity…
In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation.…
In this paper we discuss a projection model order reduction (MOR) method for a class of parametric linear evolution PDEs, which is based on the application of the Laplace transform. The main advantage of this approach consists in the fact…
This paper focuses on the efficient numerical algorithms of a three-field Biot's consolidation model. The approach begins with the introduction of innovative monolithic and global-in-time iterative decoupled algorithms, which incorporate…
We are interested in the numerical solution of coupled nonlinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take advantage of the Kronecker structure arising in standard…
Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are two complementary singular-value decomposition (SVD) techniques that are widely used to construct reduced-order models (ROMs) in a variety of fields of science…
We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical…
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
In this work, the dual-weighted residual (DWR) method is applied to obtain a certified incremental proper orthogonal decomposition (POD) based reduced order model. A novel approach called MORe DWR (Model Order Rduction with Dual-Weighted…
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…
Temporal or spatial structures are readily extracted from complex data by modal decompositions like Proper Orthogonal Decomposition (POD) or Dynamic Mode Decomposition (DMD). Subspaces of such decompositions serve as reduced order models…
Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low order models of complex phenomena. In this work, we analyze 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…
Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…
We propose a reduced basis method to solve time-dependent partial differential equations based on the Laplace transform. Unlike traditional approaches, we start by applying said transform to the evolution problem, yielding a…