标题： 用于使用变分蒙特卡罗和神经网络估计\textit{n-p}系统的反散射势 显示英文标题

标题： Estimating Inverse Scattering Potentials for \textit{n-p} System Using Variational Monte Carlo \& Neural Networks

摘要： 具有Riccati类型的非线性微分方程，也称为变相方法或相函数方法，用于构建氘核的$^3S_1$和$^1S_0$状态的局部逆势。 这些势能通过调整Morse势参数，利用变分蒙特卡罗（VMC）和多层感知器（MLP）类型的神经网络（NN）进行了优化。 从VMC和NN获得的逆势显示几乎相同的参数。在VMC中，所有三个参数都被改变以获得相移，而在NN中，三维参数问题被转换为一维参数优化问题。 最近，GRANADA小组发表了一项对散射数据的全面部分波分析，其中包括从1950年到2013年的6713个\textit{np}相移数据点。 使用GRANADA的最终实验数据点，我们通过将均方误差（MSE）作为成本函数来最小化，获得了Morse势的参数。 各种量子函数，如相位$\delta(r)$，振幅$A(r)$和波函数$u(r)$，在能量$E_{\ell ab}=[1-350 MeV]$下描述到 5\textit{fm}对于$^3S_1$和$^1S_0$状态。 显示英文摘要

摘要： The Riccati-type nonlinear differential equation, also named the Variable Phase Approach or Phase Function Method, is used to construct local inverse potentials for the $^3S_1$ and $^1S_0$ states of the deuteron. These potentials have been optimized by adjusting Morse potential parameters using the Variational Monte Carlo (VMC) and Multilayer perceptron (MLP) type Neural Networks (NN). The inverse potentials obtained from VMC and NN show almost identical parameters. In VMC all three parameters are varied to obtain the phase shifts while in NN the 3D-parameter problem is converted to a 1D-parameter optimization problem. Recently, the GRANADA group published a comprehensive partial wave analysis of scattering data, which includes 6713 \textit{np} phase shift data points from 1950 to 2013. Using the final experimental data points from GRANADA, we obtained the parameters for the Morse potential by minimizing the mean square error (MSE) as the cost function. Various quantum functions, such as phase $\delta(r)$, amplitude $A(r)$, and wave function $u(r)$, are described up to 5\textit{fm} with energies $E_{\ell ab}=[1-350 MeV]$ for $^3S_1$ and $^1S_0$ state.