  The Riccati-type nonlinear differential equation, also known as 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. The
Morse potential has been optimized by adjusting 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 of the Morse potential are
varied to obtain the phase shifts, while in NN, the 3D-parameter optimization
problem is converted to a 1D-parameter optimization problem, thus reducing
optimization parameters, time, and computational cost.
  Recently, the GRANADA group published a comprehensive partial wave analysis
of scattering data, which includes 6713 \( np \) 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. The MSE using VMC (NN) is found to be 0.65
(2.5) for the \( ^1S_0 \) state and 0.16 (0.22) for the \( ^3S_1 \) state.
Various quantum functions, such as phase \( \delta(r) \), amplitude \( A(r) \),
and wave function \( u(r) \), are described up to 5 fm with energies \( E_{\ell
ab} = [1-350 \text{ MeV}] \).
