2023/10/07 by Yue Luo, Luo, Yue, Xiangcheng Zheng +3 · 2 citations
Computer Science · Engineering · Physics and Astronomy · #37M05 #37N30 #65B99 #65L20 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Neural Networks and Applications #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2310.04656
openalex publication_date 2023/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The high-index saddle dynamics (HiSD) method [J. Yin, L. Zhang, and P. Zhang, \it SIAM J. Sci. Comput., 41 (2019), pp.A3576-A3595] serves as an efficient tool for computing index-k saddle points and constructing solution landscapes. Nevertheless, the conventional HiSD method often encounters slow convergence rates on ill-conditioned problems. To address this challenge, we propose an accelerated high-index saddle dynamics (A-HiSD) by incorporating the heavy ball method. We prove the linear stability theory of the continuous A-HiSD, and subsequently estimate the local convergence rate for the discrete A-HiSD. Our analysis demonstrates that the A-HiSD method exhibits a faster convergence rate compared to the conventional HiSD method, especially when dealing with ill-conditioned problems. We also perform various numerical experiments including the loss function of neural network to substantiate the effectiveness and acceleration of the A-HiSD method.