
they represent conservative Hamiltonian systems, while the surrogate models established from **data** are usually not. The lack of symplecticity can result in artificial damping or excitation in long-term transformations. The established surrogate models should not be used for the DA computation. However, while constructing data-driven chaos indicators, surrogate models were only used to characterize the sensitivity of transformations to their initial conditions. Even if the transformations are not perfectly symplectic, it does not affect such applications. Due to the lack of a real physics model, this chaos indicator cannot replace the diffusion rate obtained with the FMA, which measures the regularity of resonant motions of a nonlinear dynamical system. Using this indicator as the optimization objective might not be as competitive as the direct tracking-based optimization if not taking the computation cost into account. This method
