This mathematical technique is based on the natural neural network in the human brain.

In order to interpolate a function, we build a network with three levels (Inp, Hidden, Out) where the connections between them are weighed, like this:

At each arrow is associated a weight (w) and each ring is called a cell (like a neural).

If the inputs are x_i, the hidden level contains function g_j (x_i) and the output solution is also:

where K is a predefined function, such as the hyperbolic tangent or an exponential based function in order to obtain something similar to the binary behavior of the electrical brain signal (like a step function). The function is chosen to be able to handle mathematically (continuous, differentiable).

The weight functions (w_jk)are issued from an algorithm which minimizes (as the least squares method) the distance between the interpolation and the known values (design points). This is called the learning. The error is checked at each algorithm iteration with the design points which are not used for the learning. We need to separate learning design points and error checking design points.

The error decreases and then increases when the interpolation order is too high. The minimization algorithm is stopped when the error is the lowest.

This method uses a limited number of design points to build the approximation. It works better when the number of design points and the number of intermediate cells are high. And it can give interesting results with several parameters.