Volume 40, Issue 1
Probabilistic Error Estimate for Numerical Discretization of High-Index Saddle Dynamics with Inaccurate Models

Lei Zhang, Pingwen Zhang & Xiangcheng Zheng

Ann. Appl. Math., 40 (2024), pp. 1-20.

Published online: 2024-02

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  • 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.

  • AMS Subject Headings

37M05, 65L20, 60G15

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COPYRIGHT: © Global Science Press

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@Article{AAM-40-1, author = {Zhang , LeiZhang , Pingwen and Zheng , Xiangcheng}, title = {Probabilistic Error Estimate for Numerical Discretization of High-Index Saddle Dynamics with Inaccurate Models}, journal = {Annals of Applied Mathematics}, year = {2024}, volume = {40}, number = {1}, pages = {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.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2023-0030}, url = {http://global-sci.org/intro/article_detail/aam/22925.html} }
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 -

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.

Zhang , LeiZhang , Pingwen and Zheng , Xiangcheng. (2024). Probabilistic Error Estimate for Numerical Discretization of High-Index Saddle Dynamics with Inaccurate Models. Annals of Applied Mathematics. 40 (1). 1-20. doi:10.4208/aam.OA-2023-0030
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