How to handle variable number of time series?

[tueboesen]

I am trying to predict energy consumption for individual households. So in some sense it is very similar to some of the datasets that your foundational model has been trained on.
Currently I have about n_h =300 households, but the number is growing as I progressively get data from more and more households. The task is to predict the energy consumption for the next 36 hours.
Note that when a new household is added I basically have no historical data on it, but I am still expected to be able to start predicting its energy consumption (basically zero-shot), and of course do a progressively better and better job over time.

Train a model which takes each household as a different channel

So essentially this would be a model where the input is batch_size*(n_h+n_extra)*512
Where n_extra is a few extra channels containing useful information like :
time_of_day R [0 24)
day_of_week N {0, 1, 2, 3, 4 ,5 ,6}
week_of_year N [0, 51]
is_holiday N {0, 1}

There are two problems with this approach, the main one being that the input_mask is for all channels, but in this case I would need an input_mask for each individual channel.
Secondly, once a new household is added I have to add another channel to the input and basically retrain the model. This might work for low number of households, but I suspect this approach will eventually break down, or at the very least have to be somehow split up as the number of households grows to 1000, 10000, ect.

Train a model which only takes a single household energy consumption

So this model would take input of size batch_size*(1+n_extra+1)*512
where I add the same extra dimensions as before, but now I also somehow want to add the household ID, so essentially some way for the neural network to disinguish which household it is currently getting data from. Ideally this information should probably be embedded such that households that have similar energy consumption patterns eventually have similar embeddings. Though I don't think anything like that is possible with the current version of moment?

Which approach to choose?

I'm hoping someone has done something similar or have some insight on what would likely be the best approach to take to get the desired predictions.