Automatic selection of basis-adaptive sparse polynomial chaos expansions for engineering applications

@article{Luthen2021AutomaticSO,
  title={Automatic selection of basis-adaptive sparse polynomial chaos expansions for engineering applications},
  author={Nora Luthen and Stefano Paolo Marelli and Bruno Sudret},
  journal={International Journal for Uncertainty Quantification},
  year={2021}
}
Sparse polynomial chaos expansions (PCE) are an efficient and widely used surrogate modeling method in uncertainty quantification for engineering problems with computationally expensive models. To make use of the available information in the most efficient way, several approaches for so-called basis-adaptive sparse PCE have been proposed to determine the set of polynomial regressors (“basis”) for PCE adaptively. The goal of this paper is to help practitioners identify the most suitable methods… 
On efficient algorithms for computing near-best polynomial approximations to high-dimensional, Hilbert-valued functions from limited samples
TLDR
A novel restarted version of the primal-dual iteration for solving weighted (cid:96) 1 -minimization problems in Hilbert spaces and establishes error bounds for these algorithms which provably achieve the same algebraic or exponential rates as those of the best s -term approximation.
Global sensitivity analysis using derivative-based sparse Poincar\'e chaos expansions
TLDR
The Poincaré basis is the unique orthonormal basis with the property that partial derivatives of the basis form again an orthogonal basis with respect to the same measure as the original basis, which makes PoinCE ideally suited for incorporating derivative information into the surrogate modelling process.
Towards optimal sampling for learning sparse approximation in high dimensions
TLDR
This chapter discusses recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vectoror even Hilbert space-valued, and describes a general construction of sampling measures that improves over standard Monte Carlo sampling.
A spectral surrogate model for stochastic simulators computed from trajectory samples
TLDR
A surrogate model for stochastic simulators based on spectral expansions that approximates the marginals and the covariance function, and allows to obtain new realizations at low computational cost is proposed.
Bayesian tomography with prior-knowledge-based parametrization and surrogate modeling
We present a Bayesian tomography framework operating with prior-knowledge-based parametrization that is accelerated by surrogate models. Standard high-fidelity forward solvers (e.g.,

References

SHOWING 1-10 OF 51 REFERENCES
Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark
TLDR
It is found that the choice of sparse regression solver and sampling scheme for the computation of a sparse PCE surrogate can make a significant difference, of up to several orders of magnitude in the resulting mean-square error.
Sequential Design of Experiment for Sparse Polynomial Chaos Expansions
TLDR
A novel sequential adaptive strategy where the ED is enriched sequentially by capitalizing on the sparsity of the underlying metamodel is introduced, which maximizes the accuracy of the surrogate model over the whole input space within a given computational budget.
Adaptive sparse polynomial chaos expansion based on least angle regression
Basis adaptive sample efficient polynomial chaos (BASE-PC)
Adaptive Sparse Polynomial Chaos Expansions via Leja Interpolation
TLDR
This work suggests an interpolation-based stochastic collocation method for the non-intrusive and adaptive construction of sparse polynomial chaos expansions (PCEs) and relies on the use of Leja sequence points as interpolation nodes.
Sparse polynomial chaos expansions via compressed sensing and D-optimal design
Hierarchical adaptive polynomial chaos expansions
TLDR
A novel approach to SPCE is proposed, which allows one to exploit the model's hierarchical structure using the so-called principle of heredity, and can reduce the computational burden related to a large pre-defined candidate set while obtaining higher accuracy with the same computational budget.
Efficient computation of global sensitivity indices using sparse polynomial chaos expansions
...
...