A Suitable Machine Learning Technique to Learn Y=f(X,t)

I have a blackbox model that accepts an input vector X (variables) and gives three outputs Ys but as a function of time Y1(t), Y2(t) and Y3(t). In the outputs "t" is the discrete time with a known number of time steps. The model is a simulator that predicts the output quantities as a function of time. Therefore Y1(t1), Y1(t2),... are not independent. Y1(t), Y2(t) and Y3(t) can also have some relationships but for now we can ignore that.

I have several instances (samples) of X with their corresponding outputs. Which machine learning technique can handle this learning process to relate X with Y(t) ?

I am a bit confused because I have always seen the machine learning algorithm to relate X with one output Y which is not time dependent. On the other hand the time series prediction methods only look at Y=f(t) and not the X (i.e. the input is t and the output is Y)

Any suggestion to a specific method is highly appreciated

Answer 1

[Ameer Hamza]

Yes, common neural networks are not well-suited for time-series data. Although you can use them by defining multiple inputs (say n), where each corresponding to a time step value t(n), t(n-1), t(n-2), ..., t(1), but that is not a commonly used way.

For time-dependent series, mainly we use LSTM networks:

https://en.wikipedia.org/wiki/Long_short-term_memory

https://colah.github.io/posts/2015-08-Understanding-LSTMs/

See MATLAB examples here:

https://www.mathworks.com/help/deeplearning/ug/long-short-term-memory-networks.html

https://www.mathworks.com/help/deeplearning/ug/classify-sequence-data-using-lstm-networks.html

You can also see the Recurrent Neural networks which are a general form of LTSM.

https://www.mathworks.com/help/deeplearning/ref/layrecnet.html