Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Algorithms for Numerical Analysis in High Dimensions
SIAM Journal on Scientific Computing
Original article: Proper Generalized Decomposition based dynamic data driven inverse identification
Mathematics and Computers in Simulation
A dedicated multiparametric strategy for the fast construction of a cokriging metamodel
Computers and Structures
The use of partially converged simulations in building surrogate models
Advances in Engineering Software
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This paper focuses on the efficient solution of models defined in high dimensional spaces. Those models involve numerous numerical challenges because of their associated curse of dimensionality. It is well known that in mesh-based discrete models the complexity (degrees of freedom) scales exponentially with the dimension of the space. Many models encountered in computational science and engineering involve numerous dimensions called configurational coordinates. Some examples are the models encountered in biology making use of the chemical master equation, quantum chemistry involving the solution of the Schrodinger or Dirac equations, kinetic theory descriptions of complex systems based on the solution of the so-called Fokker-Planck equation, stochastic models in which the random variables are included as new coordinates, financial mathematics, etc. This paper revisits the curse of dimensionality and proposes an efficient strategy for circumventing such challenging issue. This strategy, based on the use of a Proper Generalized Decomposition, is specially well suited to treat the multidimensional parametric equations.