Dear scholars,

I was wondering if there are any scientific methods to train a neural network or ANFIS when one of the input variables is stochastic (random) and more importantly non-measurable?

Suppose we have two inputs: x1, and x2 and y as output. x1 is measurable and deterministic but x2 is a random input and it is not measurable at all.

Now we need a model (trained via neural networks, or ANFIS (adaptive-neuro fuzzy logic)).

Is this possible at all?

I can run the experiment for 5 cases of x1, each case for 10 times (10 times of experiment iteration represents the x2). Then I can find the average of such 10 iterations and represent the average value as the output for x1. This works but the problem is I'll have only 5 data-sets which is quite small for training a network. This is why I considered to take into account my 10 iterations (for each x1). If I could I'll have 50 data-set.