DIAS: A Data-Informed Active Subspace Regularization Framework for Inverse Problems

Nguyen, Hai; Wittmer, Jonathan; Bui-Thanh, Tan

doi:10.3390/computation10030038

DIAS: A Data-Informed Active Subspace Regularization Framework for Inverse Problems

Journal Article · Fri Mar 11 00:00:00 EST 2022 · Computation

DOI:https://doi.org/10.3390/computation10030038· OSTI ID:1854406

Nguyen, Hai; Wittmer, Jonathan; Bui-Thanh, Tan

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.

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Sponsoring Organization:: USDOE

OSTI ID:: 1854406

Journal Information:: Computation, Journal Name: Computation Journal Issue: 3 Vol. 10; ISSN 2079-3197; ISSN COMPGT

Publisher:: MDPI AGCopyright Statement

Country of Publication:: Switzerland

Language:: English

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