Neural Network-based High-index Saddle Dynamics Method for Searching Saddle Points and Solution Landscape
This work addresses a computational bottleneck for researchers in fields like chemistry and biology who need to find saddle points without explicit energy functions, though it is incremental as it builds on existing methods with enhancements.
The authors tackled the limitation of the high-index saddle dynamics method requiring explicit energy functions by proposing a neural network-based surrogate model, enabling its use when energy functions are unavailable or expensive, and demonstrated its effectiveness on systems like alanine dipeptide and bacterial ribosomal assembly intermediates.
The high-index saddle dynamics (HiSD) method is a powerful approach for computing saddle points and solution landscape. However, its practical applicability is constrained by the need for the explicit energy function expression. To overcome this challenge, we propose a neural network-based high-index saddle dynamics (NN-HiSD) method. It utilizes neural network-based surrogate model to approximates the energy function, allowing the use of the HiSD method in the cases where the energy function is either unavailable or computationally expensive. We further enhance the efficiency of the NN-HiSD method by incorporating momentum acceleration techniques, specifically Nesterov's acceleration and the heavy-ball method. We also provide a rigorous convergence analysis of the NN-HiSD method. We conduct numerical experiments on systems with and without explicit energy functions, specifically including the alanine dipeptide model and bacterial ribosomal assembly intermediates for the latter, demonstrating the effectiveness and reliability of the proposed method.