# Neural Network-based High-index Saddle Dynamics Method for Searching Saddle Points and Solution Landscape

arXiv: https://arxiv.org/abs/2411.16200 · HTML: https://mlsanity.com/paper/2411.16200/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 48 references that are in the map.
- First posted on arXiv 25 Nov 2024.

## Builds on (most cited first, 5 of 5)

- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [Accelerated Gradient Descent Escapes Saddle Points Faster than Gradient Descent](https://mlsanity.com/paper/1711.10456/) (2017)
- [Escaping Saddles with Stochastic Gradients](https://mlsanity.com/paper/1803.05999/) (2018)
- [Semi-flat minima and saddle points by embedding neural networks to overparameterization](https://mlsanity.com/paper/1906.04868/) (2019)
- [Active Learning for Saddle Point Calculation](https://mlsanity.com/paper/2108.04698/) (2021)

## Abstract (arXiv)

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.