Sparsity for parametric PDEs with log-gamma random inputs and applications
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| author | Dũng, Dinh Nguyen, Van Kien Hoang, Viet Ha |
| author_facet | Dũng, Dinh Nguyen, Van Kien Hoang, Viet Ha |
| contents | We propose a novel method for establishing the sparsity of the coefficients of the Laguerre generalized polynomial chaos expansion of solutions to parametric elliptic PDEs with log-gamma inputs on $\mathbb{R}_+^\infty$. The established sparsity is quantified by $\ell_p$-summability and weighted $\ell_2$-summability of the coefficients. Building on these sparsity results, we derive convergence rates for semi-discrete approximations in the parametric variables. These rates apply to sparse-grid polynomial interpolations, extended least-squares approximations and the associated semi-discrete quadrature rules. Moreover, a counterpart of our method for parametric elliptic PDEs with log-normal inputs yields a significant improvement in the sufficient condition for $\ell_p$-summability when the component functions in the log-normal representation of the parametric diffusion coefficients have global support, compared with results obtained in prior works. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14813 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sparsity for parametric PDEs with log-gamma random inputs and applications Dũng, Dinh Nguyen, Van Kien Hoang, Viet Ha Numerical Analysis 60H35, 65C30, 65D32, 65N35, 41A25 We propose a novel method for establishing the sparsity of the coefficients of the Laguerre generalized polynomial chaos expansion of solutions to parametric elliptic PDEs with log-gamma inputs on $\mathbb{R}_+^\infty$. The established sparsity is quantified by $\ell_p$-summability and weighted $\ell_2$-summability of the coefficients. Building on these sparsity results, we derive convergence rates for semi-discrete approximations in the parametric variables. These rates apply to sparse-grid polynomial interpolations, extended least-squares approximations and the associated semi-discrete quadrature rules. Moreover, a counterpart of our method for parametric elliptic PDEs with log-normal inputs yields a significant improvement in the sufficient condition for $\ell_p$-summability when the component functions in the log-normal representation of the parametric diffusion coefficients have global support, compared with results obtained in prior works. |
| title | Sparsity for parametric PDEs with log-gamma random inputs and applications |
| topic | Numerical Analysis 60H35, 65C30, 65D32, 65N35, 41A25 |
| url | https://arxiv.org/abs/2603.14813 |