A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape

We propose a model-free shrinking-dimer saddle dynamics for finding any-index points and constructing the solution landscapes, in which force standard is replaced by surrogate model trained Gassian process learning. By this means, exact form of no longer necessary such that could be implemented based only on some observations force. This data-driven approach not avoids modeling procedure difficult or inaccurate, but also significantly reduces number queries may expensive time-consuming. accordingly develop sequential learning algorithm to perform sequence local dynamics, training samples update retraining are performed online around latent trajectory order improve accuracy value each sampling. Numerical experiments demonstrate effectiveness efficiency proposed algorithm.