Probabilistic Error Estimate for Numerical Discretization of High-Index Saddle Dynamics with Inaccurate Models
Year: 2024
Author: Lei Zhang, Pingwen Zhang, Xiangcheng Zheng
Annals of Applied Mathematics, Vol. 40 (2024), Iss. 1 : pp. 1–20
Abstract
We prove probabilistic error estimates for high-index saddle dynamics with or without constraints to account for the inaccurate values of the model, which could be encountered in various scenarios such as model uncertainties or surrogate model algorithms via machine learning methods. The main contribution lies in incorporating the probabilistic error bound of the model values with the conventional error estimate methods for high-index saddle dynamics. The derived results generalize the error analysis of deterministic saddle dynamics and characterize the affect of the inaccuracy of the model on the convergence rate.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2023-0030
Annals of Applied Mathematics, Vol. 40 (2024), Iss. 1 : pp. 1–20
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Saddle point saddle dynamics solution landscape Gaussian process probabilistic error estimate.