Probabilistic Error Estimate for Numerical Discretization of High-Index Saddle Dynamics with Inaccurate Models  

作　　者：Lei Zhang Pingwen Zhang Xiangcheng Zheng 

机构地区：[1]Beijing International Center for Mathematical Research,Center for Machine Learning Research,Center for Quantitative Biology,Peking University,Beijing 100871,China [2]School of Mathematics and Statistics,Wuhan University,Wuhan,Hubei 430072,China [3]School of Mathematical Sciences,Laboratory of Mathematics and Applied Mathematics,Peking University,Beijing 100871,China [4]School of Mathematics,Shandong University,Jinan,Shandong 250100,China

出　　处：《Annals of Applied Mathematics》2024年第1期1-20,共20页应用数学年刊（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.12225102,T2321001,12288101 and 12301555);the National Key R&D Program of China(Nos.2021YFF1200500 and 2023YFA1008903);the Taishan Scholars Program of Shandong Province(No.tsqn202306083).

摘　　要：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.

关 键 词：Saddle point saddle dynamics solution landscape Gaussian process prob-abilistic error estimate 

分 类 号：O212.1[理学—概率论与数理统计]