  We consider a hierarchy of nonlinear Schr\"{o}dinger equations (NLSEs) and
forecast the evolution of positon solutions using a deep learning approach
called Physics Informed Neural Networks (PINN). Notably, the PINN algorithm
accurately predicts positon solutions not only in the standard NLSE but also in
other higher order versions, including cubic, quartic and quintic NLSEs. The
PINN approach also effectively handles two coupled NLSEs and two coupled Hirota
equations. In addition to the above, we report exact second-order positon
solutions of the sextic NLSE and coupled generalized NLSE. These solutions are
not available in the existing literature and we construct them through
generalized Darboux transformation method. Further, we utilize PINNs to
forecast their behaviour as well. To validate PINN's accuracy, we compare the
predicted solutions with exact solutions obtained from analytical methods. The
results show high fidelity and low mean squared error in the predictions
generated by our PINN model.
