Force-field coefficient optimization of coarse-grained molecular dynamics models with a small computational budget

Abstract

Coarse-grained models in molecular dynamics are low-fidelity models developed to study the properties and behavior of materials. These force-field models are popular due to their simpler implementation and significant computational benefit of their use as compared to complex high-fidelity atomistic models. On the other hand, these advantages often come at the expense of accuracy. One effective way to resolve this issue is tuning their corresponding force-field coefficients such that the estimation error of atomistic properties is minimal with respect to high-fidelity reference data. However, acquisition/computation of these data is often costly, and in most practical cases in materials sciences only a small experimental/computational budget is available to obtain high-fidelity reference data. In this work, a multi-fidelity surrogate modeling strategy for resolving the trade-off between accuracy of a full of set of quantities of interest for an atomistic system and computational expenses is proposed. The proposed procedure takes advantage of the multi-fidelity upper error bound calculated using low-fidelity data by (i) employing an efficient point selection mechanism in the design space and obtaining a set of coarse-grained models, (ii) building stochastic collocation models corresponding to each selected low-fidelity model and obtaining the optimal small group of physical input parameter sets at which a high-fidelity model is evaluated, (iii) constructing a non-intrusive spectral polynomial-based surrogate based on the error of the low-fidelity emulators corresponding to the selected coarse-grained models, and (iv) optimizing force-field coefficients using the resultant surrogate with the objective of error minimization. Moreover, in the context of using a multi-fidelity framework and in order to construct a more accurate emulator, an approach for optimal kernel function selection is implemented in this work. Also, for the purpose of obtaining a set of optimal force-field coefficients using the constructed surrogate model, we used a heuristic population-based optimization approach. For the proof of concept, we applied the proposed approach for the force-field coefficient optimization of the coarse-grained monatomic water (mW) model based on the data obtained from the high-fidelity TIP4P/2005 water model simulations. The outcome of this study is an optimal coarse-grained monatomic water model that along with the TIP4P/2005 water model, provides an accurate emulator for exploration of the properties of water in the designated pressure-temperature input parameter space. Furthermore, this approach provides a more accurate way of sampling important points in the pressure-temperature plane. Finally, the cross-validation results indicate that a certain combination of quantities of interest can produce a more accurate multi-fidelity emulator for the TIP4P/2005 water model.