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Physics-informed neural networks with Poincaré-Lighthill-Kuo method for singular perturbation problems 认领 引用
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作者 Qingyong Luo Lei Zhang Guowei He 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2026年第6期211-222,共12页
Physics-informed neural networks(PINNs)have recently emerged as a powerful tool to solve differential equations for nonlinear mechanics.However,PINNs struggle with singular perturbation problems due to their locally a... Physics-informed neural networks(PINNs)have recently emerged as a powerful tool to solve differential equations for nonlinear mechanics.However,PINNs struggle with singular perturbation problems due to their locally abrupt behavior and singularities.The Poincaré-Lighthill-Kuo(PLK)method has been efficiently used to address these problems by applying perturbation expansions to both dependent and independent variables.This paper proposes a combination of the PLK method and PINNs,termed PLK-PINNs.The PLK-PINNs employ a parametric expression through two neural networks:one representing the mapping from parametric variables to independent variables,and the other approximating the solution of dependent variables with respect to parametric variables.Moreover,an auxiliary loss term is proposed to constrain the Jacobian determinant of the mapping within a constant sign interval to ensure the bijectivity of the mapping.The effectiveness of the proposed method is demonstrated through tests on typical singularity-shift and secular-term problems,with conventional PINNs in comparison. 展开更多
关键词 Physics-informed neural networks Singular perturbation problems Poincaré-Lighthill-Kuo method Parametric expressions
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The Enumeration of General Rooted Planar Maps 认领 引用 被引量：3
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作者 JunLiangCAI YahPeiLIU 《Acta Mathematica Sinica,English Series》 SCIE 2005年第1期215-224,共10页
This paper provides some functional equations satisfied by the generatingfunctions for enumerating general rooted planar maps with up to three parameters. Furthermore, thegenerating functions can be obtained explicitl... This paper provides some functional equations satisfied by the generatingfunctions for enumerating general rooted planar maps with up to three parameters. Furthermore, thegenerating functions can be obtained explicitly by employing the Lagrangian inversion. This is alsoan answer to an open problem in 1989. 展开更多
关键词 Planar map Functional equation Parametric expression Lagrangian inversion
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