A central object in the computational studies of rare events is the committor function. Though costly to compute, the committor function encodes complete mechanistic information of the processes involving rare events, including reaction rates and transition-state ensembles. Under the framework of transition path theory (TPT), recent work [1] proposes an algorithm where a feedback loop couples a neural network that models the committor function with importance sampling, mainly umbrella sampling, which collects data needed for adaptive training. In this work, we show additional modifications are needed to improve the accuracy of the algorithm. The first modification adds elements of supervised learning, which allows the neural network to improve its prediction by fitting to sample-mean estimates of committor values obtained from short molecular dynamics trajectories. The second modification replaces the committor-based umbrella sampling with the finite-temperature string (FTS) method, which enables homogeneous sampling in regions where transition pathways are located. We test our modifications on low-dimensional systems with non-convex potential energy where reference solutions can be found via analytical or the finite element methods, and show how combining supervised learning and the FTS method yields accurate computation of committor functions and reaction rates. We also provide an error analysis for algorithms that use the FTS method, using which reaction rates can be accurately estimated during training with a small number of samples.
翻译:在对稀有事件的计算研究中,一个核心物体是承诺函数。虽然计算成本昂贵,但承诺函数编码了稀有事件过程的完整机械信息,包括反应率和转型状态集合。在过渡路径理论(TPT)的框架内,最近的工作[1]提出了一种算法,即反馈环状结合一个神经网络,以重要取样来模拟承诺函数,主要是伞式取样,以收集适应性培训所需的数据。在这项工作中,我们需要显示更多的修改,以提高算法的准确性。第一次修改增加了受监督学习的元素,使神经网络能够通过适应对从短期分子动态轨迹学中获得的承诺值的样本-平均估计来改进预测。第二次修改用有限温度绳(FTS)方法取代基于承诺的伞式取样,在过渡路径所在区域进行同质抽样。我们测试了对低度系统所作的修改,通过分析或定数元素方法可以找到参考解决方案,从而使得神经网络能够改进它的预测,从而使神经网络能够与从短分子动态动态轨迹轨迹中获得的样本和精确性分析方法相结合。我们还可以使用受监督的精确的算算算法,从而在进行精确的精确分析时,从而进行精确地算算算法和精确分析。