Polynomial chaos and regression models comparison based on the Kolmogorov — Gabor polynomials

Authors: Pham Quoc Viet
Published in issue: #8(85)/2023
DOI: 10.18698/2541-8009-2023-8-926
Category: Mathematics | Chapter: Computational Mathematics
Keywords: рolynomial chaos, Askey — Wiener scheme, elastic network, non-intrusive spectral projection, polynomial neural network, method of the arguments group accounting, Kolmogorov — Gabor polynomials, Ishigami function
Published: 27.08.2023

The paper considers the polynomial chaos generalized expansion applied to the regression model analysis problem. The polynomial chaos coefficients were calculated by the non-intrusive methods, including the least squares and the elastic network methods. Kolmogorov — Gabor polynomials were used as a reference function in the method of the arguments group accounting. Methods were compared with the Ishigami function. It is shown that at the wide range of variation in the random variables values, the polynomial chaos models are providing the best result and stay insensitive to the multicollinearity. The paper demonstrates that models based on the Kolmogorov — Gabor polynomials are providing unstable error range at the slower execution speed, but are preferable at the large input data dimensions.

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