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

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.

Author Details

Lei Zhang

Pingwen Zhang

Xiangcheng Zheng