This thread aims at linking first principle to deeper understanding of neural network implementation.

First principle first, in both Unconventional and classic producing area, typical IP distribution is anything but a bell curve. For example,

http://aemstatic-ww2.azureedge.net/content/dam/ogfj/print-articles/volume-13/issue-12/1612OGFJng-z01.jpg.scale.LARGE.jpg

Recall geology fundamental, grain size distribution of sediments is also log normal. It suffices to reason that using bell curve (normality assumption, average as well as P10 and P90), can lead to overly optimistic projection of production forecast, net present value and return on investment.

What should we do with existing neural network?

If log normal were true, a better handle on the underlying distribution would have material impact on the implementation of the activation function that converts output from the hidden layer into meaningful estimate. Perhaps we implement an activation function that exhibits characteristics between sigmoid and rectified linear unit (ReLU).

Comments and thoughts from the community will make this post better and relevant.