  A novel algorithm was recently presented to utilize emerging time dependent
probability density data to extract molecular potential energy surfaces. This
paper builds on the previous work and seeks to enhance the capabilities of the
extraction algorithm: An improved method of removing the generally ill-posed
nature of the inverse problem is introduced via an extended Tikhonov
regularization and methods for choosing the optimal regularization parameters
are discussed. Several ways to incorporate multiple data sets are investigated,
including the means to optimally combine data from many experiments exploring
different portions of the potential. Results are presented on the stability of
the inversion procedure, including the optimal combination scheme, under the
influence of data noise. The method is applied to the simulated inversion of a
double well system.
