I have a problem that seems relatively straightforward yet I am stuck on how to proceed. I have several time series of variables $P(t), Q(t), E(t)$ and I want to train an RNN to predict $Q(t)$ given the other two variables. This is a physical modeling problem - Q represents water flowing out from a watershed while P is rainfall and E is loss due to evaporation. Unfortunately, I have been unable to find resources or examples for doing something similar  (recursively predicting continuous variables with exogenous data - i.e. predicting given past observations and recently modeled observations) in Python with Keras, Lasagne or any related libraries. Are there any examples of this? It is a sort of time series forecasting with exogenous data, but in a neural net context.

Specifically, the problems that I have with using existing Python packages are:

1. Doing recursive prediction by using RNN predictions as the priming data for the next time step

2. Using exogenous data that will be observed for the predictive phase - i.e. we will have observations of E and P while making predictions of Q which will not be observed.

Any advice would be really appreciated. Thanks!