AD of UDEs - how to set it up?

If the intention is to use the model for prediction, for instance for MPC, then certainly yes. There’s an ongoing discussion in this thread regarding different approaches to optimizing multi-step prediction performance rather than single-step performance.

In that tutorial in particular, we are interested in learning an unknown function, and since we have access to the ground truth of the unknown function the main comparison made is against this.

The summary of that discussion is that you typically want to perform filtering, and at each point in time start a multi-step prediction from the current filter estimate. Unless the prediction horizon you care about is super long (such that the information gained from using measurements up until the current time point does not matter for most of the prediction), using a multi-step prediction rather than pure simulation tend to be favorable.

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