用神经网络替代能量函数，高效搜索复杂系统中的鞍点。
Neural Network-based High-index Saddle Dynamics Method for Searching Saddle Points and Solution Landscape
- 用神经网络逼近能量函数，让鞍点搜索无需显式能量表达式。
- 在阿兰尼二肽和核糖体组装中间体上验证，计算精度与传统方法相当。
- 结合动量加速技术，提升收敛速度，适合高维复杂系统研究者使用。
高指标鞍点动力学（HiSD）方法是计算鞍点与解空间的强大工具，但其实际应用受限于必须有显式的能量函数表达式。为克服这一挑战，本文提出基于神经网络的高指标鞍点动力学（NN-HiSD）方法，利用神经网络构建能量函数的代理模型，使HiSD方法可应用于能量函数不可得或计算成本过高的场景。通过引入动量加速技术，包括Nesterov加速和重球法，进一步提升了算法效率。本文还提供了对NN-HiSD方法的严格收敛性分析。在具有与不具有显式能量函数的系统上进行了数值实验，包括阿兰尼二肽模型和细菌核糖体组装中间体，结果表明该方法有效且可靠。
原文摘要 · Abstract (English)
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.
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