Work

Efficient identification of geometric inverse sources of parabolic problems by model order reduction

Year: 2025

Type: article

Abstract: This article investigates reduced-order models for efficiently solving geometric inverse source problems in parabolic equations. To reconstruct source supports in diffusion processes, a reduced-order approach combining proper orthogonal decomposition and incremental singular value decomposition is proposed. This method significantly reduces the computational complexity and storage requirements typically associated with numerical shape and topology optimization. Numerical experiments are conducted to validate the effectiveness and efficiency of the proposed methodology.

Source: Inverse Problems

DOI: 10.1088/1361-6420/add17d

Authors: Xindi Hu, Yangwen Zhang, Shengfeng Zhu

Institutions: East China Normal University, University of Louisiana at Lafayette

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funders: National Natural Science Foundation of China, Science and Technology Commission of Shanghai Municipality