There is plenty of literature describing LSTMs in a lot of detail and how to use them for multi-variate or uni-variate forecasting problems. What I couldn't find though, is any papers or discussions describing time series forecasting where we have correlated forecast data.
An example is best to describe what I mean. Say I wanted to predict number of people at a beach for the next 24 hours and I want to predict this in hourly granularity. This quantity of people would clearly depend on the past quantity of people at the beach as well as the weather. Now I can make an LSTM architecture of some sort to predict these future quantities based upon what happened in the past quite easily. But what if I now have access to weather forecasts for the next 24 hours too? (and historical forecast data too).
The architecture I came up with looks like this:
So I train the left upper branch on forecast data, then train the right upper branch on out-turn data, then freeze their layers to and join them to form the final network in the picture and train that on both forecasts and out-turns. (when I say train, the output is always the forecast for the next 24 hours). This method does in fact have better performance than using forecasts or out-turns alone.
I guess my question is, has anyone seen any literature around on this topic and/ or knows a better way to solve these sort of multivariate time series forecasting problems and is my method okay or completely flawed?