Random feature neural network approximations of the potential in Hamiltonian systems yield approximations of molecular dynamics correlation observables that have the expected error $\mathcal{O}\big((K^{-1}+J^{-1/2})^{\frac{1}{2}}\big)$, for networks with $K$ nodes using $J$ data points, provided the Hessians of the potential and the observables are bounded. The loss function is based on the least squares error of the potential and regularizations, with the data points sampled from the Gibbs density. The proof uses an elementary new derivation of the generalization error for random feature networks that does not apply the Rademacher or related complexities.

翻译：哈密顿系统中势能的随机特征神经网络近似，对于具有$K$个节点并使用$J$个数据点的网络，在势能和观测量的Hessian矩阵有界的条件下，可得到分子动力学相关观测量的近似误差为$\mathcal{O}\big((K^{-1}+J^{-1/2})^{\frac{1}{2}}\big)$。损失函数基于势能的最小二乘误差及正则化项，数据点从吉布斯密度中采样。该证明采用了一种新的基本推导方法，用于分析随机特征网络的泛化误差，该方法未应用Rademacher复杂度或相关复杂性度量。