A Regularization Homotopy Strategy for the Constrained Parameter Inversion of Partial Differential Equations

The main difficulty posed by the parameter inversion of partial differential equations lies in the presence of numerous local minima in the cost function. Inversion fails to converge to the global minimum point unless the initial estimate is close to the exact solution. Constraints can improve the c...

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Autores principales:	Tao Liu, Runqi Xue, Chao Liu, Yunfei Qi
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	parameter inversion partial differential equation Tikhonov regularization homotopy method constraints Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/ccdd0e50fc6f4c899e88f50f54864ee3
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id	oai:doaj.org-article:ccdd0e50fc6f4c899e88f50f54864ee3
record_format	dspace
spelling	oai:doaj.org-article:ccdd0e50fc6f4c899e88f50f54864ee32021-11-25T17:29:59ZA Regularization Homotopy Strategy for the Constrained Parameter Inversion of Partial Differential Equations10.3390/e231114801099-4300https://doaj.org/article/ccdd0e50fc6f4c899e88f50f54864ee32021-11-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1480https://doaj.org/toc/1099-4300The main difficulty posed by the parameter inversion of partial differential equations lies in the presence of numerous local minima in the cost function. Inversion fails to converge to the global minimum point unless the initial estimate is close to the exact solution. Constraints can improve the convergence of the method, but ordinary iterative methods will still become trapped in local minima if the initial guess is far away from the exact solution. In order to overcome this drawback fully, this paper designs a homotopy strategy that makes natural use of constraints. Furthermore, due to the ill-posedness of inverse problem, the standard Tikhonov regularization is incorporated. The efficiency of the method is illustrated by solving the coefficient inversion of the saturation equation in the two-phase porous media.Tao LiuRunqi XueChao LiuYunfei QiMDPI AGarticleparameter inversionpartial differential equationTikhonov regularizationhomotopy methodconstraintsScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1480, p 1480 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	parameter inversion partial differential equation Tikhonov regularization homotopy method constraints Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	parameter inversion partial differential equation Tikhonov regularization homotopy method constraints Science Q Astrophysics QB460-466 Physics QC1-999 Tao Liu Runqi Xue Chao Liu Yunfei Qi A Regularization Homotopy Strategy for the Constrained Parameter Inversion of Partial Differential Equations
description	The main difficulty posed by the parameter inversion of partial differential equations lies in the presence of numerous local minima in the cost function. Inversion fails to converge to the global minimum point unless the initial estimate is close to the exact solution. Constraints can improve the convergence of the method, but ordinary iterative methods will still become trapped in local minima if the initial guess is far away from the exact solution. In order to overcome this drawback fully, this paper designs a homotopy strategy that makes natural use of constraints. Furthermore, due to the ill-posedness of inverse problem, the standard Tikhonov regularization is incorporated. The efficiency of the method is illustrated by solving the coefficient inversion of the saturation equation in the two-phase porous media.
format	article
author	Tao Liu Runqi Xue Chao Liu Yunfei Qi
author_facet	Tao Liu Runqi Xue Chao Liu Yunfei Qi
author_sort	Tao Liu
title	A Regularization Homotopy Strategy for the Constrained Parameter Inversion of Partial Differential Equations
title_short	A Regularization Homotopy Strategy for the Constrained Parameter Inversion of Partial Differential Equations
title_full	A Regularization Homotopy Strategy for the Constrained Parameter Inversion of Partial Differential Equations
title_fullStr	A Regularization Homotopy Strategy for the Constrained Parameter Inversion of Partial Differential Equations
title_full_unstemmed	A Regularization Homotopy Strategy for the Constrained Parameter Inversion of Partial Differential Equations
title_sort	regularization homotopy strategy for the constrained parameter inversion of partial differential equations
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/ccdd0e50fc6f4c899e88f50f54864ee3
work_keys_str_mv	AT taoliu aregularizationhomotopystrategyfortheconstrainedparameterinversionofpartialdifferentialequations AT runqixue aregularizationhomotopystrategyfortheconstrainedparameterinversionofpartialdifferentialequations AT chaoliu aregularizationhomotopystrategyfortheconstrainedparameterinversionofpartialdifferentialequations AT yunfeiqi aregularizationhomotopystrategyfortheconstrainedparameterinversionofpartialdifferentialequations AT taoliu regularizationhomotopystrategyfortheconstrainedparameterinversionofpartialdifferentialequations AT runqixue regularizationhomotopystrategyfortheconstrainedparameterinversionofpartialdifferentialequations AT chaoliu regularizationhomotopystrategyfortheconstrainedparameterinversionofpartialdifferentialequations AT yunfeiqi regularizationhomotopystrategyfortheconstrainedparameterinversionofpartialdifferentialequations
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A Regularization Homotopy Strategy for the Constrained Parameter Inversion of Partial Differential Equations

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