论文标题
一个无模型的收缩二聚体鞍座动力学，用于查找马鞍点和解决方案景观
A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape
论文作者
论文摘要
我们提出了一种无模型的缩小二聚体鞍座动力学，用于查找任何索引鞍点并构建解决方案景观，其中标准鞍形动力学中的力是由Gassian过程学习训练的替代模型代替的。通过这种方式，不再需要模型的确切形式，以便只能基于对力的某些观察结果来实现鞍座动力学。这种数据驱动的方法不仅避免了可能很困难或不准确的建模过程，而且还大大减少了可能昂贵或耗时的力量的查询数量。因此，我们开发了一种顺序学习的鞍动力学算法来执行一系列局部鞍动力学，其中训练样本的查询以及在线和潜在轨迹周围进行替代力的更新或重新训练，以提高替代模型的准确性，并提高每个采样的值。进行数值实验以证明所提出算法的有效性和效率。
We propose a model-free shrinking-dimer saddle dynamics for finding any-index saddle points and constructing the solution landscapes, in which the force in the standard saddle dynamics is replaced by a surrogate model trained by the Gassian process learning. By this means, the exact form of the model is no longer necessary such that the saddle dynamics could be implemented based only on some observations of the force. This data-driven approach not only avoids the modeling procedure that could be difficult or inaccurate, but also significantly reduces the number of queries of the force that may be expensive or time-consuming. We accordingly develop a sequential learning saddle dynamics algorithm to perform a sequence of local saddle dynamics, in which the queries of the training samples and the update or retraining of the surrogate force are performed online and around the latent trajectory in order to improve the accuracy of the surrogate model and the value of each sampling. Numerical experiments are performed to demonstrate the effectiveness and efficiency of the proposed algorithm.
