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

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.