  Memory effects emerge as a fundamental consequence of dimensionality
reduction when low-dimensional observables are used to describe the dynamics of
complex many-body systems. In the context of molecular dynamics (MD) data
analysis, accounting for memory effects using the framework of the generalized
Langevin equation (GLE) has proven efficient, accurate and insightful,
particularly when working with high-resolution time series data. However, in
experimental systems, high-resolution data is often unavailable, raising
questions about the impact of the data resolution on the estimated GLE
parameters. This study demonstrates that direct memory extraction remains
accurate when the discretization time is below the memory time. To obtain
memory functions reliably even when the discretization time exceeds the memory
time, we introduce a Gaussian Process Optimization (GPO) scheme. This scheme
minimizes the deviation of discretized two-point correlation functions between
MD and GLE simulations and is able to estimate accurate memory kernels as long
as the discretization time stays below the longest time scale in the data,
typically the barrier crossing time.
