用神经网络替代复杂自由能计算中的解析雅可比，提升精度与适用性。
Neural Network Surrogates for Free Energy Computation of Complex Chemical Systems
- 用神经网络直接从原子坐标学习集体变量，自动求导获取雅可比
- 在MgCl2离子对系统中，对简单距离与复杂配位数变量均达高精度
- 雅可比误差近似正态分布，适合集成到高斯过程回归流程中
自由能重构方法如高斯过程回归（GPR）需要集体变量（CVs）的雅可比矩阵，而这一需求成为使用复杂或机器学习所得CVs的瓶颈。本文提出一种神经网络代理框架，直接从笛卡尔坐标学习CV，并利用自动微分提供雅可比，避免了显式解析表达式的依赖。在MgCl2离子对系统中，该方法对简单距离CV和复杂配位数CV均实现了高精度计算。此外，雅可比误差呈近似高斯分布，适用于现有GPR流程。该框架使基于梯度的自由能方法可纳入复杂及机器学习构建的CV，拓展了生物化学与材料模拟的应用范围。
原文摘要 · Abstract (English)
Free energy reconstruction methods such as Gaussian Process Regression (GPR) require Jacobians of the collective variables (CVs), a bottleneck that restricts the use of complex or machine-learned CVs. We introduce a neural network surrogate framework that learns CVs directly from Cartesian coordinates and uses automatic differentiation to provide Jacobians, bypassing analytical forms. On an MgCl2 ion-pairing system, our method achieved high accuracy for both a simple distance CV and a complex coordination-number CV. Moreover, Jacobian errors also followed a near-Gaussian distribution, making them suitable for GPR pipelines. This framework enables gradient-based free energy methods to incorporate complex and machine-learned CVs, broadening the scope of biochemistry and materials simulations.
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