scholarly journals Comparison of Reduced-Basis techniques for the model order reduction of parametric incompressible fluid flows

2020 ◽  
Vol 130 ◽  
pp. 103551
Author(s):  
Péter German ◽  
Mauricio Tano ◽  
Jean C. Ragusa ◽  
Carlo Fiorina
Keyword(s):  
Incompressible Fluid ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Fluid Flows ◽  
Reduced Basis ◽  
Model Order ◽  
Incompressible Fluid Flows

scholarly journals Model order reduction for the simulation of parametric interest rate models in financial risk analysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Andreas Binder ◽  
Onkar Jadhav ◽  
Volker Mehrmann
Keyword(s):  
Model Order Reduction ◽  
Financial Risk ◽  
Large Scale ◽  
Order Reduction ◽  
Parametric Models ◽  
Diffusion Reaction ◽  
High Dimensional ◽  
Reduced Basis ◽  
Model Order ◽  
Reduction Approach

AbstractThis paper presents a model order reduction approach for large scale high dimensional parametric models arising in the analysis of financial risk. To understand the risks associated with a financial product, one has to perform several thousand computationally demanding simulations of the model which require efficient algorithms. We establish a model reduction approach based on a variant of the proper orthogonal decomposition method to generate small model approximations for the high dimensional parametric convection-diffusion-reaction partial differential equations. This approach requires to solve the full model at some selected parameter values to generate a reduced basis. We propose an adaptive greedy sampling technique based on surrogate modeling for the selection of the sample parameter set. The new technique is analyzed, implemented, and tested on industrial data of a floater with cap and floor under the Hull–White model. The results illustrate that the reduced model approach works well for short-rate models.

scholarly journals Model Order Reduction of Nonlinear Magnetodynamics with Manifold Interpolation

2015 ◽  
Author(s):  
Y. Paquay ◽  
O. Brüls ◽  
C. Geuzaine
Keyword(s):  
Model Order Reduction ◽  
Interpolation Method ◽  
Order Reduction ◽  
Nonlinear Problems ◽  
Single Shot ◽  
Reduced Basis ◽  
Model Order ◽  
Core System ◽  
Input Parameters ◽  
Speed Up

In the model order reduction community, linear systems have been widely studied and reduced thanks to various techniques. Proper Orthogonal Decomposition (POD) in particular has been very successful, and has recently been gaining popularity in computational electromagnetics. However, the efficiency of POD degrades considerably for nonlinear problems, in particular for nonlinear magnetodynamic models---necessary for designing most of today's electrical machines and drives. We propose to investigate an algorithm which first applies the POD to construct reduced order models of nonlinear magnetodynamic problems for discrete sets of values of the input parameters. Then, for a new set of values of the input parameters, a nonlinear interpolation on manifolds is performed to determine the reduced basis. This interpolation method is based on the theory previously studied for aerodynamic problems. The goal here is not to speed up single shot calculations, but to be able to determine efficiently reduced models for nonlinear problems based on previous offline computations. As a simple application, we apply the procedure to a nonlinear inductor-core system, solved using a classical finite element method. In order to gauge the interest of manifold interpolation we compare the proposed approach to the direct use of a precomputed reduced basis, as well as with the use of standard Lagrange interpolation.

Separated Representations of Incremental Elastoplastic Simulations

2015 ◽  
Vol 651-653 ◽  
pp. 1285-1293 ◽  
Author(s):  
Mohamed Aziz Nasri ◽  
Jose Vicente Aguado ◽  
Amine Ammar ◽  
Elias Cueto ◽  
Francisco Chinesta ◽  
...  
Keyword(s):  
Model Order Reduction ◽  
Mechanical Systems ◽  
Order Reduction ◽  
Fast Simulation ◽  
Reduced Basis ◽  
Model Order ◽  
Reduction Techniques ◽  
Separated Representations ◽  
Separated Representation

Forming processes usually involve irreversible plastic transformations. The calculation in that case becomes cumbersome when large parts and processes are considered. Recently Model Order Reduction techniques opened new perspectives for an accurate and fast simulation of mechanical systems, however nonlinear history-dependent behaviors remain still today challenging scenarios for the application of these techniques. In this work we are proposing a quite simple non intrusive strategy able to address such behaviors by coupling a separated representation with a POD-based reduced basis within an incremental elastoplastic formulation.

scholarly journals Model Order Reduction with Neural Networks: Application to Laminar and Turbulent Flows

2021 ◽  
Vol 2 (6) ◽  
Author(s):  
Kai Fukami ◽  
Kazuto Hasegawa ◽  
Taichi Nakamura ◽  
Masaki Morimoto ◽  
Koji Fukagata
Keyword(s):  
Neural Networks ◽  
Turbulent Flows ◽  
Model Order Reduction ◽  
Experimental Studies ◽  
Order Reduction ◽  
Fluid Flows ◽  
Turbulent Channel Flow ◽  
Cylinder Wake ◽  
Cross Sectional ◽  
Model Order

AbstractWe investigate the capability of neural network-based model order reduction, i.e., autoencoder (AE), for fluid flows. As an example model, an AE which comprises of convolutional neural networks and multi-layer perceptrons is considered in this study. The AE model is assessed with four canonical fluid flows, namely: (1) two-dimensional cylinder wake, (2) its transient process, (3) NOAA sea surface temperature, and (4) a cross-sectional field of turbulent channel flow, in terms of a number of latent modes, the choice of nonlinear activation functions, and the number of weights contained in the AE model. We find that the AE models are sensitive to the choice of the aforementioned parameters depending on the target flows. Finally, we foresee the extensional applications and perspectives of machine learning based order reduction for numerical and experimental studies in the fluid dynamics community.

scholarly journals Localized Reduced Basis Methods for Time Harmonic Maxwell’s Equations

2018 ◽  
Author(s):  
Andreas Buhr ◽  
Mario Ohlberger ◽  
Stephan Rave
Keyword(s):  
Electromagnetic Fields ◽  
Model Order Reduction ◽  
Maxwell's Equations ◽  
Order Reduction ◽  
Reduced Basis Method ◽  
Galerkin Projection ◽  
Reduced Basis ◽  
Model Order ◽  
Time Harmonic ◽  
Basis Method

Localized model order reduction methods have attracted significant attention during the last years. They have favorable parallelization properties and promise to perform well on cloud architectures, which become more and more commonplace. We introduced ArbiLoMod, a localized reduced basis method targeted at the important use case of changing problem definition, wherein the changes are of local nature. This is a common situation in simulation software used by engineers optimizing a CAD model. An especially interesting application is the simulation of electromagnetic fields in printed circuit boards, which is necessary to design high frequency electronics. The simulation of the electromagnetic fields can be done by solving the time-harmonic Maxwell’s equations, which results in a parameterized, inf-sup stable problem which has to be solved for many parameters. In this multi-query setting, the reduced basis method can perform well. Experiments have shown two dimensional time-harmonic Maxwell’s to be amenable to localized model reduction. However, Galerkin projection of an inf-sup stable problem is not guaranteed to be stable. Existing stabilization methods for the reduced basis method involve global computations and are thus not applicable in a localized setting. Replacing the Galerkin projection with the minimization of a localized a posteriori error estimator provides a stable reduction for inf-sup stable projects which retains all the advantageous properties of localized model order reduction. It allows for an offline-online decomposition and requires no global computations in the unreduced space.

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