Machine learned force fields typically require manual construction of training sets consisting of thousands of first principles calculations, which can result in low training efficiency and unpredictable errors when applied to structures not represented in the training set of the model. This severely limits the practical application of these models in systems with dynamics governed by important rare events, such as chemical reactions and diffusion. We present an adaptive Bayesian inference method for automating the training of interpretable, low-dimensional, and multi-element interatomic force fields using structures drawn on the fly from molecular dynamics simulations. Within an active learning framework, the internal uncertainty of a Gaussian process regression model is used to decide whether to accept the model prediction or to perform a first principles calculation to augment the training set of the model. The method is applied to a range of single- and multi-element systems and shown to achieve a favorable balance of accuracy and computational efficiency, while requiring a minimal amount of ab initio training data. We provide a fully open-source implementation of our method, as well as a procedure to map trained models to computationally efficient tabulated force fields.

机器学习的力场通常需要手动构建包含数千个第一性原理计算的训练集，当将其应用于未在模型的训练集中表示的结构时，这可能导致训练效率低下和不可预测的错误。这严重限制了这些模型在动力学受重要稀有事件（例如化学反应和扩散）支配的系统中的实际应用。我们提出了一种自适应贝叶斯推理方法，该方法使用从分子动力学模拟中动态绘制的结构来自动训练可解释的，低维的和多元素的原子间力场。在积极的学习框架内，高斯过程回归模型的内部不确定性用于确定是否接受模型预测或执行第一性原理计算以增强模型的训练集。该方法应用于一系列的单元素和多元素系统，并显示出在准确性和计算效率之间取得良好的平衡，同时需要最少的从头开始训练数据。我们提供了我们方法的完全开源实现，以及将训练后的模型映射到计算有效的制表力场的过程。