Model building with neural networks

Assume the existence of a collection of physical parameters and a collection of output variables which may depend on the physical parameters. An example in the training dataset consists of a vector with the actual measurement of the physical parameters, and another vector with the output values which were measured.

To my understanding, I can train a neural network such as a MLP to learn the mapping from the measured input parameters to the measured output values. If a model could be learned and assuming the learned relations are due to causality and not some unfortunate correlation, then for an arbitrary input vector the model could predict the vector of output values. Note that the relationship between input and output is not a 1:1 map, rather n:1. Different parameter choices may thus lead to the same output.

I want to go one step further and define an interval for each output value. I then want to know how I must set the ideal input parameter values to ensure that the output values are in the corresponding intervals, i.e. how to alter inputs for the output values to be within the ranges. I tried feeding the output values as input and trying to predict the physical parameters, but I have problems due to the ratio input/output. I have 130 physical parameters and only 10 output variables. How can I achieve this with a neural network?

• Could you clarify how the interval works? Are you wanting to force the output to be within a fixed range (and if so, is that for the training data, or when making a prediction)? Or are you wanting to predict or alter inputs that would produce an output within the range? From your last paragraph I think it's the latter, you want to run the network backwards . . . Is the relationship between input and output a one to one map? Commented Jul 24, 2017 at 15:49
• The relationship between input and output is not a 1:1 map, rather n:1. Different parameter choices may thus lead to the same output. I want to know how to alter inputs for the output values to be within the ranges. I tried feeding the output values as input and trying to predict the physical parameters (running backwards if I understand you correctly), but I have problems due to the ratio input/output. I have 130 physical parameters and only 10 output variables. Commented Jul 24, 2017 at 19:37
• Can you edit your question to clarify it, so that the question is self-contained and we don't have to read the comments to understand what you're asking? Thanks.
– D.W.
Commented Jul 24, 2017 at 22:46