Neural network construction where different outputs have different dependencies on the inputs

I want to construct a neural network for a system which is described by the image below. The arrows in the images shows the dependencies of the variables in the system (e.g., is dependent on ). I have two inputs and and outputs and , ,..., , . Three intermediate variables , and connect the inputs and outputs together, while the outputs , ,..., , have dependencies sequentially and is dependent on all the . How can I construct a neural network where the inputs are and and the outputs are and , ,..., , ?

[Ben]

The diagram suggests depends on and depend on (via ). Could you clarify how the simultaneous dependency should be handled?

One way might be a recurrent style network - all the variables are actually time series, and depends on , while depend on . You would hook up a neural network with the and as outputs and write code to feed the back into the network at the next time step.