I have a problem where I know p features which are each scalar values and the output of 1 set of those features is a time history. Is there a specific neural network (NN) type architecture that can handle this?
From my searching, a 1D convolutional NN can do the opposite of what I need where it goes from time history to scalar prediction. A recurrent NN can go from time history to time history so in theory I could just replicate my scalar features to be constant in time. However, that seems very inefficient and I'm not sure how well the model would learn with constant inputs.
I've also considered breaking the time history output into m principal components (PCs) using functional PCA (FPCA). Then I could fit either m different regular NNs to each PC or fit a single regular NN to all the PCs simultaneously. In the first case, I'd have to fit multiple networks, which seems less than ideal. In both cases, I'd have to represent my data using PCs, which means I'm only using a finite approximation to the data and not the actual data. However, in the absence of any other existing architectures, the second approach with a single NN and FPCA seems the most promising so far.
If it matters, typical values for the size I'm working with are: number of features p=5-20, number of data points n=5000-25000, and when I've done FPCA before m=3-7 to capture >99% of the variance. Each time series output can be very general and does not necessarily follow a continuous function (e.g. linear, polynomial, etc.).