Say I have a model $M$ that takes in a parameter vector $\beta$, and produces a (numerical) time series. This could be a complicated model (e.g. a bespoke enzyme reaction model), or something simple like a VAR(1) (e.g. $x_{t}=\beta_0+\beta_1 x_{t-1}+\varepsilon_t$). I can run this model multiple times with the same parameter vector, and get a different time series each run.

(Even for the same parameter vector, the output may be different each run, as is the case when you simulate a VAR(1) with known variance $\sigma^2_\varepsilon$)

How can I design/implement a neural network that acts as a surrogate to my model - i.e. when given a parameter set $\beta$, it produces plausible time series sequences?



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