Effective forces derived from experimental or in silico molecular dynamics time traces are critical in developing reduced and computationally efficient descriptions of otherwise complex dynamical problems. This helps motivate why it is important to develop methods to efficiently learn effective forces from time series data. A number of methods already exist to do this when data are plentiful but otherwise fail for sparse datasets or datasets where some regions of phase space are undersampled. In addition, any method developed to learn effective forces from time series data should be minimally a priori committal as to the shape of the effective force profile, exploit every data point without reducing data quality through any form of binning or pre-processing, and provide full credible intervals (error bars) about the prediction for the entirety of the effective force curve. Here, we propose a generalization of the Gaussian process, a key tool in Bayesian nonparametric inference and machine learning, which meets all of the above criteria in learning effective forces for the first time.

中文翻译：

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使用高斯过程推断朗之万动力学的有效力


来自实验或计算机分子动力学时间轨迹的有效力对于开发对其他复杂动力学问题的简化且计算有效的描述至关重要。这有助于激发为什么开发从时间序列数据中有效学习有效力的方法很重要。当数据充足时，已经存在许多方法可以做到这一点，但对于稀疏数据集或相空间某些区域采样不足的数据集则失败。此外，为从时间序列数据中学习有效力而开发的任何方法都应至少先验地确定有效力分布的形状，利用每个数据点而不通过任何形式的分箱或预处理降低数据质量，并提供关于整个有效力曲线预测的完整可信区间（误差线）。在这里，我们提出了高斯过程的推广，这是贝叶斯非参数推理和机器学习的关键工具，它首次满足了学习有效力的所有上述标准。