Integrating Neural Net: Deriving the Normal Distribution CDF

1. Introduction

This article presents a method for training a neural network to derive the integral of a function. The technique works not only with analytically-solvable integrals but also with integrals that do not have a closed-form solution and are typically solved by numerical methods. An example is the normal distribution's cumulative density function (CDF). Equation 1 is this distribution's probability density function (PDF), and Equation 2 is its CDF, the integral of the PDF. Figure 1 is a plot of these functions. After being trained, the resulting network can serve as a stand-alone function generator that delivers points on the CDF curve given points from the domain of the distribution's PDF.