Predict a time series from another time series

I am trying to build a model that can generate a time series from another time series. The input time series corresponds to photometric data (light curve) which gathers an intensity of light through time, and the output corresponds to the spinning velocity of the objects (There are three DOF for pitch, yaw, and roll). For instance, from the following input sequence on the left, I would like to retrieve the three sequences on the right. (Even one of them would work). The problem is that as you can see there is not a clear correlation between the two. I have a bunch of input-output sequences, and I was wondering if there exists a data driven method for doing such a task. I have tried using LSTMs, and transformers. The problem is that the model learns the shape of the input and the output looks like the input, but mapped to the output values. I was wondering if there is another method which would allow to do this effectively. Thank you!