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

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.