The principle of least action is the cornerstone of classical mechanics, theory of relativity, quantum mechanics, and thermodynamics. Here, we describe how a neural network (NN) learns to find the trajectory for a Lennard-Jones (LJ) system that maintains balance in minimizing the Onsager–Machlup (OM) action and maintaining the energy conservation. The phase-space trajectory thus calculated is in excellent agreement with the corresponding results from the “ground-truth” molecular dynamics (MD) simulation. Furthermore, we show that the NN can easily find structural transformation pathways for LJ clusters, for example, the basin-hopping transformation of an LJ₃₈ from an incomplete Mackay icosahedron to a truncated face-centered cubic octahedron. Unlike MD, the NN computes atomic trajectories over the entire temporal domain in one fell swoop, and the NN time step is a factor of 20 larger than the MD time step. The NN approach to OM action is quite general and can be adapted to model morphometrics in a variety of applications.

中文翻译：

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最小作用原理的神经网络

最小作用原理是经典力学、相对论、量子力学和热力学的基石。在这里，我们描述了神经网络 (NN) 如何学习找到 Lennard-Jones (LJ) 系统的轨迹，该系统在最小化 Onsager-Machlup (OM) 作用和保持能量守恒方面保持平衡。由此计算的相空间轨迹与“真实”分子动力学（MD）模拟的相应结果非常一致。此外，我们表明，NN 可以轻松找到 LJ 星团的结构转换路径，例如 LJ _{38的盆地跳跃转换}从不完整的麦凯二十面体到截断面心立方八面体。与 MD 不同，NN 一举计算整个时间域上的原子轨迹，并且 NN 时间步长比 MD 时间步长大 20 倍。OM 动作的 NN 方法非常通用，可以适应各种应用中的形态计量学建模。