We generated 81 sound feature vectors from a sparse sampling of the space of the four parameters. Each parameter was normalized to lie in a range of 0-1, then sampled at three points in the physical space, 0.33, 0.66, and 1.0. The 81 feature and parameter pairs were then used to acquire a forward model of the physical system. The forward model converged within 2000 iterations through the 81 training data pairs to a criteria of 0.05 mean square error.\
Next a direct inverse model was trained on the sound/parameter pairs. This technique was adopted to facilitate speeding up of the training process. A direct inverse modeling technique is generally undesirable for two reasons: The training set requires explicit knowledge of the parameters and the direct approximator is unable to resolve one-to-many mappings. (Such mappings are common in sound systems where multiple sets of parameters give rise to the same sound). We should emphasize that the direct modeling technique was adopted as a convenience to allow out models to converge faster. The direct model was trained to a local minima and the function parameters were saved to be use for the initial conditions of the distal inverse approximator.
Using the direct inverse model weights as initial conditions, the distal inverse model converged to a mean-squared performance error criteria of 0.001. This indicated that the estimator was able to partition the parameter space successfully. We believe that such a convergence criteria leads to results that are within the perceptual discriminability of humans but experiments must be conducted in order to verify this.