This paper aims at handling high dimensional uncertainty propagation problems by proposing a tensor product approximation method based on regression techniques. The underlying assumption is that the model output functional can be well represented in a separated form, as a sum of elementary tensors in the stochastic tensor product space. The proposed method consists in constructing a tensor basis with a greedy algorithm and then in computing an approximation in the generated approximation space using regression with sparse regularization. Using appropriate regularization techniques, the regression problems are well posed for only few sample evaluations and they provide accurate approximations of model outputs.
A Regression Based Non-Intrusive Method Using Separated Representation for Uncertainty Quantification
Rai, P, Chevreuil, M, Nouy, A, & Sen Gupta, J. "A Regression Based Non-Intrusive Method Using Separated Representation for Uncertainty Quantification." Proceedings of the ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. Volume 1: Advanced Computational Mechanics; Advanced Simulation-Based Engineering Sciences; Virtual and Augmented Reality; Applied Solid Mechanics and Material Processing; Dynamical Systems and Control. Nantes, France. July 2–4, 2012. pp. 167-174. ASME. https://doi.org/10.1115/ESDA2012-82301
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