DIAS: A Data-Informed Active Subspace Regularization Framework for Inverse Problems
This paper presents a regularization framework that aims to improve the fidelity of Tikhonov inverse solutions. At the heart of the framework is the data-informed regularization idea that only data-uninformed parameters need to be regularized, while the data-informed parameters, on which data and fo...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/10/3/38 |
| _version_ | 1827649523065815040 |
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| author | Hai Nguyen Jonathan Wittmer Tan Bui-Thanh |
| author_facet | Hai Nguyen Jonathan Wittmer Tan Bui-Thanh |
| author_sort | Hai Nguyen |
| collection | DOAJ |
| description | This paper presents a regularization framework that aims to improve the fidelity of Tikhonov inverse solutions. At the heart of the framework is the data-informed regularization idea that only data-uninformed parameters need to be regularized, while the data-informed parameters, on which data and forward model are integrated, should remain untouched. We propose to employ the active subspace method to determine the data-informativeness of a parameter. The resulting framework is thus called a data-informed (DI) active subspace (DIAS) regularization. Four proposed DIAS variants are rigorously analyzed, shown to be robust with the regularization parameter and capable of avoiding polluting solution features informed by the data. They are thus well suited for problems with small or reasonably small noise corruptions in the data. Furthermore, the DIAS approaches can effectively reuse any Tikhonov regularization codes/libraries. Though they are readily applicable for nonlinear inverse problems, we focus on linear problems in this paper in order to gain insights into the framework. Various numerical results for linear inverse problems are presented to verify theoretical findings and to demonstrate advantages of the DIAS framework over the Tikhonov, truncated SVD, and the TSVD-based DI approaches. |
| first_indexed | 2024-03-09T19:58:54Z |
| format | Article |
| id | doaj.art-56de7512a9144c9090fa6c257b5cb314 |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-09T19:58:54Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-56de7512a9144c9090fa6c257b5cb3142023-11-24T00:49:59ZengMDPI AGComputation2079-31972022-03-011033810.3390/computation10030038DIAS: A Data-Informed Active Subspace Regularization Framework for Inverse ProblemsHai Nguyen0Jonathan Wittmer1Tan Bui-Thanh2Department of Aerospace Engineering and Engineering Mechanics, UT Austin, Austin, TX 78712, USAThe Oden Institute of Computational Engineering and Sciences, UT Austin, Austin, TX 78712, USADepartment of Aerospace Engineering and Engineering Mechanics, The Oden Institute for Computational Engineering and Sciences, UT Austin, Austin, TX 78712, USAThis paper presents a regularization framework that aims to improve the fidelity of Tikhonov inverse solutions. At the heart of the framework is the data-informed regularization idea that only data-uninformed parameters need to be regularized, while the data-informed parameters, on which data and forward model are integrated, should remain untouched. We propose to employ the active subspace method to determine the data-informativeness of a parameter. The resulting framework is thus called a data-informed (DI) active subspace (DIAS) regularization. Four proposed DIAS variants are rigorously analyzed, shown to be robust with the regularization parameter and capable of avoiding polluting solution features informed by the data. They are thus well suited for problems with small or reasonably small noise corruptions in the data. Furthermore, the DIAS approaches can effectively reuse any Tikhonov regularization codes/libraries. Though they are readily applicable for nonlinear inverse problems, we focus on linear problems in this paper in order to gain insights into the framework. Various numerical results for linear inverse problems are presented to verify theoretical findings and to demonstrate advantages of the DIAS framework over the Tikhonov, truncated SVD, and the TSVD-based DI approaches.https://www.mdpi.com/2079-3197/10/3/38inverse problemsregularizationactive subspacesdata-informed regularization |
| spellingShingle | Hai Nguyen Jonathan Wittmer Tan Bui-Thanh DIAS: A Data-Informed Active Subspace Regularization Framework for Inverse Problems Computation inverse problems regularization active subspaces data-informed regularization |
| title | DIAS: A Data-Informed Active Subspace Regularization Framework for Inverse Problems |
| title_full | DIAS: A Data-Informed Active Subspace Regularization Framework for Inverse Problems |
| title_fullStr | DIAS: A Data-Informed Active Subspace Regularization Framework for Inverse Problems |
| title_full_unstemmed | DIAS: A Data-Informed Active Subspace Regularization Framework for Inverse Problems |
| title_short | DIAS: A Data-Informed Active Subspace Regularization Framework for Inverse Problems |
| title_sort | dias a data informed active subspace regularization framework for inverse problems |
| topic | inverse problems regularization active subspaces data-informed regularization |
| url | https://www.mdpi.com/2079-3197/10/3/38 |
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