可观测量的机器学习：原子-硅藻碰撞产物态分布的反应物
Machine Learning for Observables: Reactant to Product State Distributions for Atom-Diatom Collisions
摘要：
提出并定量测试了基于机器学习的模型，用于根据原子与硅藻碰撞的反应物条件分布预测产物状态分布。该模型是基于功能，内核和网格为基础的表示的反应物和产物的状态分布。虽然这三种方法都能从显式准经典轨迹模拟中预测最终状态分布，R $^2$ > 0.998，但基于网格的方法表现最好。虽然基于函数的方法被发现是在计算性能的两倍以上，基于内核和网格的方法是首选的预测精度，实用性和通用性。基于功能的方法也缺乏一套通用的模型功能。应用基于网格的方法，非平衡，多温度的初始状态分布，一种常见的情况下，在高超音速流的能量分布。这些模型在直接模拟蒙特卡罗和计算流体动力学模拟中的作用也进行了讨论。
英文摘要：
Machine learning-based models to predict product state distributions from a distribution of reactant conditions for atom-diatom collisions are presented and quantitatively tested. The models are based on function-, kernel- and grid-based representations of the reactant and product state distributions. While all three methods predict final state distributions from explicit quasi-classical trajectory simulations with R$^2$ > 0.998, the grid-based approach performs best. Although a function-based approach is found to be more than two times better in computational performance, the kernel- and grid-based approaches are preferred in terms of prediction accuracy, practicability and generality. The function-based approach also suffers from lacking a general set of model functions. Applications of the grid-based approach to nonequilibrium, multi-temperature initial state distributions are presented, a situation common to energy distributions in hypersonic flows. The role of such models in Direct Simulation Monte Carlo and computational fluid dynamics simulations is also discussed.
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