On the recovery of two function-valued coefficients in the Helmholtz equation for inverse scattering problems via neural networks On the recovery of two function-valued coefficients in the Helmholtz

• Published in: Advances in computational mathematics Vol. 51; no. 1
• Main Author: Zhou, Zehui
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2025
• Subjects: Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Visualization; Approximation; Two function-valued coefficients; Inverse scattering problem; Neural network; Generalization
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-025-10225-z

Recently, deep neural networks (DNNs) have become powerful tools for solving inverse scattering problems. However, the approximation and generalization rates of DNNs for solving these problems remain largely under-explored. In this work, we introduce two types of combined DNNs (uncompressed and comp...