A nonlocal adaptive discrete empirical interpolation method combined with modified hp-refinement for order reduction of molecular dynamics systems

Model order reduction is an emerging technique to tackle the computational complexities of molecular dynamics (MD) simulations. Different strategies are required to adequately obtain the reduced solutions of different classes of molecular dynamics systems. In this work, a proper orthogonal decomposition (POD) is combined with the discrete empirical interpolation method (DEIM) to study atomic systems. Due to the limitations of the DEIM in capturing the nonlocal response of the nonlinear force field of MD systems, a nonlocal adaptive discrete empirical interpolation method (ADEIM) is proposed. Furthermore, a modified hp-refinement algorithm is introduced to extend the application of the PODDEIM approach to order reduction of multi-dimensional MD systems. In the DEIM, the distance between atoms and hence the reduced internal force vector is estimated based on a local interpolation of the state variables. The internal forces of a multi-dimensional MD system depend on the distance between the atoms, represented in space by more than one coordinate. Therefore, the ADEIM approach seeks to obtain a nonlocal interpolation of the state variables to accurately predict the distance between the interpolated atoms and hence the reduced force vector. Simulation of MD systems with frequently changing neighbour atoms leads to change in the system dynamics, which further leads to change of properties of the snapshots. Therefore, the temporal domain is adaptively subdivided into smaller sub-domains using the adopted hp-refinement procedure. The reduced system parameters are effectively derived over the sub-domains. Considering the computational cost, a modified hp-refinement algorithm is developed in this study, which is further coupled with the POD-ADEIM approach to obtain the reduced-order solution of the MD systems. The results of the proposed approach demonstrate the efficiency and accuracy of the reduced solutions.