I'll try to rephrase my problem in the context of video processing. Imagine that initial frame of video has some translational symmetry. The frame evolves according to an update rule.
I generate a time series for how an edge, say right up edge, of the frame evolves. I generate another time series for how a larger edge, including the smaller right up edge, evolves. Since there is translational symmetry, I should be able to find how the smaller edge is related to the larger edge. The final goal is to use the obtained correlation to extrapolate to larger edges. I want to find the correlation between these two multivariate time series using machine learning (ML) methods.
I want to know
1 - which one of ML methods can be used in general for this task?
2 - if I use neural networks, the input and output shapes would be
(values at time steps, number of variables). For the input it makes sense, but how can I define the output layer (for example, for LSTM in tensorflow)?