A non-intrusive B-splines Bézier elements-based method for uncertainty propagation

Abdedou, Azzedine; Soulaïmani, Azzeddine

doi:10.1016/j.cma.2018.10.047

Cited by 13 publications

(9 citation statements)

References 42 publications

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“…In a real case scenario, we launch several hundred simulations by sampling the parameters, such as the inflow rate or Manning's number. The goal is to build a database and then perform statistical studies like those in Abdedou and Soulaimani (2018). This database can also be used to train machine learning algorithms, as in Jacquier et al (2021).…”

Section: Visualization Of the Flood Linesmentioning

confidence: 99%

Multi-GPU implementation of a time-explicit finite volume solver using CUDA and a CUDA-Aware version of OpenMPI with application to shallow water flows

Delmas

Soulaïmani

2022

Computer Physics Communications

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Section: Visualization Of the Flood Linesmentioning

confidence: 99%

Multi-GPU implementation of a time-explicit finite volume solver using CUDA and a CUDA-Aware version of OpenMPI with application to shallow water flows

Delmas

Soulaïmani

2022

Computer Physics Communications

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“…This approach belongs to the multi-element techniques that use local piecewise bases expressed as a function of input random parameters. It is worth noting that the basic framework of the BSBEM in its full-order version has been presented in detail in [33,34]. Thus, only a summary description of its fundamental aspects is outlined in the following.…”

Section: Regression-based Non-intrusive B-splines Bézier Elements Met...mentioning

confidence: 99%

“…where e stands for the e th Bézier element I e and p i denotes the polynomial order of the univariate B-splines basis function ψ i (ξ i ). Details of the construction of the B-splines basis and their extraction from the local Bernstein's functions can be found in [33,34,36]. In each Bézier element, a set of n e s ≥ n b collocation points are selected ξ e(r) ∈ I e ; r = 1, .…”

Section: Let Us Considermentioning

confidence: 99%

“…This work presents a non-intrusive reduced order model for stochastic time-dependent problems. The method, referred to as the POD-BSBEM, combines the advantages of the POD and the B-splines Bézier element method (BSBEM) [33,34] to extract the reduced basis and to build a stochastic expansion over the random space, respectively. A two-level POD is applied to the snapshot matrix obtained by the collection of time-trajectory high-fidelity solutions for each given value of the random parametric vector.…”

Section: Introductionmentioning

confidence: 99%

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A non-intrusive reduced-order modelling for uncertainty propagation of time-dependent problems using a B-splines Bézier elements-based method and Proper Orthogonal Decomposition: application to dam-break flows

Abdedou,

Soulaïmani

2021

Preprint

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A proper orthogonal decomposition-based B-splines Bézier elements method (POD-BSBEM) is proposed as a non-intrusive reduced-order model for uncertainty propagation analysis for stochastic time-dependent problems. The method uses a two-step proper orthogonal decomposition (POD) technique to extract the reduced basis from a collection of high-fidelity solutions called snapshots.A third POD level is then applied on the data of the projection coefficients associated with the reduced basis to separate the time-dependent modes from the stochastic parametrized coefficients.These are approximated in the stochastic parameter space using B-splines basis functions defined in the corresponding Bézier element. The accuracy and the efficiency of the proposed method are assessed using benchmark steady-state and time-dependent problems and compared to the reducedorder model-based artificial neural network (POD-ANN) and to the full-order model-based polynomial chaos expansion (Full-PCE). The POD-BSBEM is then applied to analyze the uncertainty propagation through a flood wave flow stemming from a hypothetical dam-break in a river with a complex bathymetry. The results confirm the ability of the POD-BSBEM to accurately predict the statistical moments of the output quantities of interest with a substantial speed-up for both offline and online stages compared to other techniques.

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“…Finally, B-splines basis functions have also been used for uncertainty propagation to overcome the limitations of classical approaches in the presence of discontinuities (see e.g. [33,34]).…”

Section: Introductionmentioning

confidence: 99%

Multi-element flow-driven spectral chaos (ME-FSC) method for uncertainty quantification of dynamical systems

Esquivel,

Prakash,

Lin

2022

Preprint

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The flow-driven spectral chaos (FSC) is a recently developed method for tracking and quantifying uncertainties in the long-time response of stochastic dynamical systems using the spectral approach. The method uses a novel concept called enriched stochastic flow maps as a means to construct an evolving finite-dimensional random function space that is both accurate and computationally efficient in time. In this paper, we present a multi-element version of the FSC method (the ME-FSC method for short) to tackle (mainly) those dynamical systems that are inherently discontinuous over the probability space. In ME-FSC, the random domain is partitioned into several elements, and then the problem is solved separately on each random element using the FSC method. Subsequently, results are aggregated to compute the probability moments of interest using the law of total probability. To demonstrate the effectiveness of the ME-FSC method in dealing with discontinuities and long-time integration of stochastic dynamical systems, four representative numerical examples are presented in this paper, including the Van-der-Pol oscillator problem and the Kraichnan-Orszag three-mode problem. Results show that the ME-FSC method is capable of solving problems that have strong nonlinear dependencies over the probability space, both reliably and at low computational cost.

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A non-intrusive B-splines Bézier elements-based method for uncertainty propagation

Cited by 13 publications

References 42 publications

Multi-GPU implementation of a time-explicit finite volume solver using CUDA and a CUDA-Aware version of OpenMPI with application to shallow water flows

Multi-GPU implementation of a time-explicit finite volume solver using CUDA and a CUDA-Aware version of OpenMPI with application to shallow water flows

A non-intrusive reduced-order modelling for uncertainty propagation of time-dependent problems using a B-splines Bézier elements-based method and Proper Orthogonal Decomposition: application to dam-break flows

Multi-element flow-driven spectral chaos (ME-FSC) method for uncertainty quantification of dynamical systems

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