A local multiple proper generalized decomposition based on the partition of unity

Ibáñez, Rubén; Abisset-Chavanne, Emmanuelle; Chinesta, Francisco; Huerta, Antonio

doi:10.1002/nme.6128

Cited by 9 publications

(8 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The just described procedure defines a powerful nonlinear regression called rPGD. Following our recent works on multi-local-PGD representations [26], local approximations ensuring continuity could be defined.…”

Section: Pgd-based Regression (Rpgd) and Sparse Pgd (Spgd)mentioning

confidence: 99%

See 1 more Smart Citation

Virtual, Digital and Hybrid Twins: A New Paradigm in Data-Based Engineering and Engineered Data

Chinesta

Cueto

Abisset-Chavanne

et al. 2018

Arch Computat Methods Eng

Self Cite

193

143

View full text Add to dashboard Cite

Engineering is evolving in the same way than society is doing. Nowadays, data is acquiring a prominence never imagined. In the past, in the domain of materials, processes and structures, testing machines allowed extract data that served in turn to calibrate state-of-the-art models. Some calibration procedures were even integrated within these testing machines. Thus, once the model had been calibrated, computer simulation takes place. However, data can offer much more than a simple state-of-the-art model calibration, and not only from its simple statistical analysis, but from the modeling and simulation viewpoints. This gives rise to the the family of so-called twins: the virtual, the digital and the hybrid twins. Moreover, as discussed in the present paper, not only data serve to enrich physically-based models. These could allow us to perform a tremendous leap forward, by replacing big-data-based habits by the incipient smart-data paradigm.

show abstract

Section: Pgd-based Regression (Rpgd) and Sparse Pgd (Spgd)mentioning

confidence: 99%

“…In a similar way rPGD can be replaced by a multiple local PGD-based nonlinear regression while ensuring continuity thanks to its consideration within the partition of unity (PU) framework [26].…”

Section: Model Learnersmentioning

confidence: 99%

Virtual, Digital and Hybrid Twins: A New Paradigm in Data-Based Engineering and Engineered Data

Chinesta

Cueto

Abisset-Chavanne

et al. 2018

Arch Computat Methods Eng

Self Cite

193

143

View full text Add to dashboard Cite

show abstract

“…They are therefore, harder to approximate. To overcome this issue, improved PGD approximations can be employed, such as local‐PGD approximations, for instance 40,41 …”

Section: The Correction Proceduresmentioning

confidence: 99%

Digital twins that learn and correct themselves

Moya

Badías

Alfaro

et al. 2020

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

Digital twins can be defined as digital representations of physical entities that employ real-time data to enable understanding of the operating conditions of these entities.Here we present a particular type of digital twin that involves a combination of computer vision, scientific machine learning and augmented reality. This novel digital twin is able, therefore, to see, to interpret what it sees-and, if necessary, to correct the model it is equipped with-and presents the resulting information in the form of augmented reality.The computer vision capabilities allow the twin to receive data continuously. As any other digital twin, it is equipped with one or more models so as to assimilate data. However, if persistent deviations from the predicted values are found, the proposed methodology is able to correct on the fly the existing models, so as to accommodate them to the measured reality.Finally, the suggested methodology is completed with augmented reality capabilities so as to render a completely new type of digital twin. These concepts are tested against a proof-of-concept model consisting on a non-linear, hyperelastic beam subjected to moving loads whose exact position is to be determined.

show abstract

“…Similarly, Niroomandi et al [20] combined global ROM with the Generalized Finite Element Method (GFEM), introduced locally in a patch near simulated surgical cut, in order to capture localized solution characteristics efficiently. Using Partition of Unity (PU) [21], underlying the previously mentioned GFEM approaches, Ibáñez et al [22] recently proposed a local variant of Proper Generalized Decomposition.…”

Section: Local Reduced Modelsmentioning

confidence: 99%

Microstructure-informed reduced modes synthesized with Wang tiles and the Generalized Finite Element Method

Doškář

Zeman

Krysl

et al. 2020

Preprint

View full text Add to dashboard Cite

A recently introduced representation by a set of Wang tiles-a generalization of the traditional Periodic Unit Cell based approach-serves as a reduced geometrical model for materials with stochastic heterogeneous microstructure, enabling an efficient synthesis of microstructural realizations. To facilitate macroscopic analyses with a fully resolved microstructure generated with Wang tiles, we develop a reduced order modelling scheme utilizing pre-computed characteristic features of the tiles.In the offline phase, inspired by the computational homogenization, we extract continuous fluctuation fields from the compressed microstructural representation as responses to generalized loading represented by the first-and second-order macroscopic gradients. In the online phase, using the ansatz of the Generalized Finite Element Method, we combine these fields with a coarse finite element discretization to create microstructure-informed reduced modes specific for a given macroscopic problem.Considering a two-dimensional scalar elliptic problem, we demonstrate that our scheme delivers less than a 3% error in both the relative L 2 and energy norms with only 0.01% of the unknowns when compared to the fully resolved problem. Accuracy can be further improved by locally refining the macroscopic discretization and/or employing more pre-computed fluctuation fields. Finally, unlike the standard snapshot-based reduced-order approaches, our scheme handles significant changes in the macroscopic geometry or loading without the need for recalculating the offline phase, because the fluctuation fields are extracted without any prior knowledge on the macroscopic problem.

show abstract

A local multiple proper generalized decomposition based on the partition of unity

Cited by 9 publications

References 32 publications

Virtual, Digital and Hybrid Twins: A New Paradigm in Data-Based Engineering and Engineered Data

Virtual, Digital and Hybrid Twins: A New Paradigm in Data-Based Engineering and Engineered Data

Digital twins that learn and correct themselves

Microstructure-informed reduced modes synthesized with Wang tiles and the Generalized Finite Element Method

Contact Info

Product

Resources

About