Molecular dynamics (MD) simulations give access to equilibrium structures and dynamic properties given an ergodic sampling and an accurate force-field. The force-field parameters are calibrated to reproduce properties measured by experiments or simulations. The main contribution of this paper is an approximate Bayesian framework for the calibration and uncertainty quantification of the force-field parameters, without assuming parameter uncertainty to be Gaussian. To this aim, since the likelihood function of the MD simulation models is intractable in the absence of Gaussianity assumption, we use a likelihood-free inference scheme known as approximate Bayesian computation (ABC) and propose an adaptive population Monte Carlo ABC algorithm, which is illustrated to converge faster and scales better than the previously used ABCsubsim algorithm for the calibration of the force-field of a helium system. The second contribution is the adaptation of ABC algorithms for High Performance Computing to MD simulations within the Python ecosystem ABCpy. This adaptation includes a novel use of a dynamic allocation scheme for Message Passing Interface (MPI). We illustrate the performance of the developed methodology to learn posterior distribution and Bayesian estimates of Lennard-Jones force-field parameters of helium and the TIP4P system of water implemented for both simulated and experimental datasets collected using neutron and X-ray diffraction. For simulated data, the Bayesian estimate is in close agreement with the true parameter value used to generate the dataset. For experimental as well as for simulated data, the Bayesian posterior distribution shows a strong correlation pattern between the force-field parameters. Providing an estimate of the entire posterior distribution, our methodology also allows us to perform the uncertainty quantification of model prediction. This research opens up the possibility to rigorously calibrate force-fields from available experimental datasets of any structural and dynamic property.

中文翻译：

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根据实验数据对力场进行贝叶斯校准：TIP4P水

通过遍历采样和精确的力场，分子动力学（MD）模拟可以访问平衡结构和动力学特性。校准力场参数以重现通过实验或模拟测得的特性。本文的主要贡献是一个近似的贝叶斯框架，用于力场参数的校准和不确定性量化，而没有将参数不确定性假定为高斯。为此，由于在没有高斯假设的情况下，MD仿真模型的似然函数很难处理，因此我们使用了称为似然贝叶斯计算（ABC）的无似然推理方案，并提出了一种自适应总体蒙特卡洛ABC算法，与以前使用的用于校准氦气系统力场的ABCsubsim算法相比，该算法收敛速度更快，缩放效果更好。第二个贡献是将适用于高性能计算的ABC算法改编为Python生态系统ABCpy。这种改编包括将动态分配方案用于消息传递接口（MPI）的新颖用法。我们说明了开发的方法的性能，以学习后验分布和氦的Lennard-Jones力场参数的后验分布和贝叶斯估计以及针对模拟和实验数据集实施的水的TIP4P系统使用中子和X射线衍射收集。对于模拟数据，贝叶斯估计与用于生成数据集的真实参数值非常一致。对于实验数据和模拟数据，贝叶斯后验分布在力场参数之间显示出很强的相关性。通过提供整个后验分布的估计，我们的方法还使我们能够执行模型预测的不确定性量化。这项研究开辟了从任何具有结构和动力学特性的可用实验数据集中严格校准力场的可能性。