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Title: Data-driven regression and uncertainty quantification by polynomial chaos expansions and copulas Authors:  Emiliano Torre - ETH Zurich (Switzerland) [presenting]
Stefano Marelli - ETH Zurich (Switzerland)
Paul Embrechts - ETH Zurich (Switzerland)
Bruno Sudret - ETH Zurich (Switzerland)
Abstract: A regression method is presented for data driven problems based on polynomial chaos expansion (PCE). PCE is an established uncertainty quantification method, typically used to replace a computationally expensive (e.g., a finite element) model subject to random inputs with an inexpensive-to-evaluate multivariate polynomial. The metamodel enables a reliable estimation of the response statistics, provided that a suitable probabilistic model of the input is used. In classical machine learning (ML) regression settings, instead, the system is only known through observations of its inputs and output, and the interest lies in obtaining accurate point predictions of the latter. Here, we show that a PCE metamodel purely trained on input and output data, with input dependencies modelled through copulas, can yield point predictions whose accuracy is comparable to that of other ML methods, such as neural networks. Additionally though, the methodology enables to quantify the output uncertainty accurately, and is robust to noise. Furthermore, it enjoys additional desirable properties, such as high performance also for small training sets, and simplicity of construction, with only little parameter tuning required. In the presence of coupled inputs, we investigate two alternative ways to build the PCE, and show through simulations the superiority of one approach in the stated settings.