TY - JOUR
T1 - Probabilistic Error Estimate for Numerical Discretization of High-Index Saddle Dynamics with Inaccurate Models
AU - Zhang , Lei
AU - Zhang , Pingwen
AU - Zheng , Xiangcheng
JO - Annals of Applied Mathematics
VL - 1
SP - 1
EP - 20
PY - 2024
DA - 2024/02
SN - 40
DO - http://doi.org/10.4208/aam.OA-2023-0030
UR - https://global-sci.org/intro/article_detail/aam/22925.html
KW - Saddle point, saddle dynamics, solution landscape, Gaussian process, probabilistic error estimate.
AB - <p style="text-align: justify;">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.</p>