伊人直播

Probabilistic error estimate for numerical discretization of high-index saddle dynamics with inaccurate models

摘要

We prove probabilistic error estimates for high-index saddle dynam ics 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 contribu tion 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 a ect of the inaccuracy of the model on the convergence rate.

出版物
Zhang L., Zhang P., Zheng X. (2023). Probabilistic error estimate for numerical discretization of high-index saddle dynamics with inaccurate models. In Annals of Applied Mathematics, 40.