Towards a pancreatic surgery simulator based on model order reduction

Mena, A.; Bel, David; Alfaro, Icíar; González, David; Chinesta, Francisco

doi:10.1186/s40323-015-0049-1

Cited by 10 publications

(9 citation statements)

References 30 publications

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“…Literature shows that the PGD framework is particularly suitable for many challenging problems in biomechanics such as real‐time simulation and multiparameter identification. In a comprehensive ageing society, osteoporosis is one of the common diseases for the elders.…”

Section: Application In Biomechanical Problems: Human Proximal Femurmentioning

confidence: 99%

A nonintrusive proper generalized decomposition scheme with application in biomechanics

Zou

Conti

Dı́ez

et al. 2017

Numerical Meth Engineering

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Summary Proper generalized decomposition (PGD) is often used for multiquery and fast‐response simulations. It is a powerful tool alleviating the curse of dimensionality affecting multiparametric partial differential equations. Most implementations of PGD are intrusive extensions based on in‐house developed FE solvers. In this work, we propose a nonintrusive PGD scheme using off‐the‐shelf FE codes (such as certified commercial software) as an external solver. The scheme is implemented and monitored by in‐house flow‐control codes. A typical implementation is provided with downloadable codes. Moreover, a novel parametric separation strategy for the PGD resolution is presented. The parametric space is split into two‐ or three‐dimensional subspaces, to allow PGD technique solving problems with constrained parametric spaces, achieving higher convergence ratio. Numerical examples are provided. In particular, a practical example in biomechanics is included, with potential application to patient‐specific simulation.

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Section: Application In Biomechanical Problems: Human Proximal Femurmentioning

confidence: 99%

A nonintrusive proper generalized decomposition scheme with application in biomechanics

Zou

Conti

Dı́ez

et al. 2017

Numerical Meth Engineering

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“…surgical simulation involving haptic devices involving contact, cutting, etc.) [52], material homogenization [39], real-time process optimization [26,27], inverse analysis and simulation-based control [29]. They where also employed in dynamic data driven application systems.…”

Section: Proper Generalized Decompositionmentioning

confidence: 99%

kPCA-Based Parametric Solutions Within the PGD Framework

González

Aguado

Cueto

et al. 2016

Arch Computat Methods Eng

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Parametric solutions make possible fast and reliable real-time simulations which, in turn allow real time optimization, simulation-based control and uncertainty propagation. This opens unprecedented possibilities for robust and efficient design and real-time decision making. The construction of such parametric solutions was addressed in our former works in the context of models whose parameters were easily identified and known in advance. In this work we address more complex scenarios in which the parameters do not appear explicitly in the model-complex microstructures, for instance. In these circumstances the parametric model solution requires combining a technique to find the relevant model parameters and a solution procedure able to cope with high-dimensional models, avoiding the well-known curse of dimensionality. In this work, kPCA (kernel Principal Component Analysis) is used for extracting the hidden model parameters, whereas the PGD (Proper Generalized Decomposition) is used for calculating the resulting parametric solution.

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“…[9][10][11][12] These methods compute the basis function on the fly, that is to say, by means of a greedy algorithm that enriches successively the basis until the desired precision is achieved. This methodology has proven to be very effective for a wide variety of high-dimensional problems ranging from the resolution of Fokker-Planck equation 13 to patient-specific liver responses, 14,15 structural dynamics, 16 computational rheology, 17 or, more generally, to any parametric problem that could be written in separate form. 13 There are situations, however, when the solution is highly nonseparable.…”

Section: Introductionmentioning

confidence: 99%

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

Ibáñez

Abisset-Chavanne

Chinesta

et al. 2019

Numerical Meth Engineering

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Summary It is well known that model order reduction techniques that project the solution of the problem at hand onto a low‐dimensional subspace present difficulties when this solution lies on a nonlinear manifold. To overcome these difficulties (notably, an undesirable increase in the number of required modes in the solution), several solutions have been suggested. Among them, we can cite the use of nonlinear dimensionality reduction techniques or, alternatively, the employ of linear local reduced order approaches. These last approaches usually present the difficulty of ensuring continuity between these local models. Here, a new method is presented, which ensures this continuity by resorting to the paradigm of the partition of unity while employing proper generalized decompositions at each local patch.

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Towards a pancreatic surgery simulator based on model order reduction

Cited by 10 publications

References 30 publications

A nonintrusive proper generalized decomposition scheme with application in biomechanics

A nonintrusive proper generalized decomposition scheme with application in biomechanics

kPCA-Based Parametric Solutions Within the PGD Framework

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

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