kPCA-Based Parametric Solutions Within the PGD Framework

doi:10.1007/s11831-016-9173-4

kPCA-Based Parametric Solutions Within the PGD Framework

2016-03-21

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AI

Emmanuelle Abisset‐Chavanne

F

F. Chinesta

DOI：10.1007/s11831-016-9173-4

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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.

Keywords:

PROPER GENERALIZED DECOMPOSITION

PARTIAL-DIFFERENTIAL-EQUATIONS

REAL-TIME SIMULATION

MODEL-REDUCTION

COMPLEX FLUIDS

EMPIRICAL INTERPOLATION

SHAPE OPTIMIZATION

FAMILY

IDENTIFICATION

MULTISCALE

kPCA-Based Parametric Solutions Within the PGD Framework

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