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.

中文翻译：

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计算预算小的粗粒分子动力学模型的力场系数优化

摘要 分子动力学中的粗粒度模型是为研究材料的性质和行为而开发的低保真模型。与复杂的高保真原子模型相比，这些力场模型因其更简单的实现和显着的计算优势而广受欢迎。另一方面，这些优势往往以牺牲准确性为代价。解决此问题的一种有效方法是调整其相应的力场系数，以使原子特性的估计误差相对于高保真参考数据最小。然而，这些数据的获取/计算通常是昂贵的，并且在材料科学的大多数实际案例中，只有很少的实验/计算预算可用于获得高保真参考数据。在这项工作中，提出了一种多保真代理建模策略，用于解决原子系统的全套感兴趣数量的准确性与计算费用之间的权衡。所提出的程序利用了使用低保真数据计算的多保真误差上限，方法是 (i) 在设计空间中采用有效的点选择机制并获得一组粗粒度模型，(ii) 构建随机搭配模型对应于每个选定的低保真模型并获得评估高保真模型的最佳物理输入参数组，（iii）基于低保真度模型的误差构建基于非侵入式频谱多项式的代理与所选粗粒度模型相对应的保真模拟器，(iv) 以误差最小化为目标，使用合成代理优化力场系数。此外，在使用多保真框架的背景下，为了构建更准确的仿真器，本文实施了一种优化核函数选择的方法。此外，为了使用构建的替代模型获得一组最佳力场系数，我们使用了一种基于群体的启发式优化方法。为了验证概念，我们基于从高保真 TIP4P/2005 水模型模拟获得的数据，将所提出的方法应用于粗粒度单原子水 (mW) 模型的力场系数优化。这项研究的结果是一个最佳的粗粒度单原子水模型，连同 TIP4P/2005 水模型，提供了一个精确的模拟器，用于在指定的压力-温度输入参数空间中探索水的特性。此外，这种方法提供了一种在压力-温度平面中对重要点进行采样的更准确方法。最后，交叉验证结果表明，特定的感兴趣量组合可以为 TIP4P/2005 水模型生成更准确的多保真仿真器。