A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape
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Publication:6072373
DOI10.1007/S13160-023-00604-8zbMATH Open1529.37047arXiv2212.14328OpenAlexW4384663525MaRDI QIDQ6072373
Author name not available (Why is that?)
Publication date: 13 October 2023
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/2212.14328
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