# Observability and sensitivity in learning dynamical systems

Parameter identifiability in dynamical models

November 9, 2020 — November 9, 2020

In linear systems theory the term *observability* is used to discuss whether we can in fact identify a parameter or a latent state, which I will conflate for the current purposes.

Sometimes learning a *parameter* as such is a red herring; we in fact wish to learn an object which function of parameters, such as a transfer function, and many different parameter combinations will approximate the object similarly well. If we know that the actual object of interest *is*, we might hope to integrate out the nuisance parameters and detect sensitivity to this object itself; but maybe we do not even know that. Then what do we do?

Very closely related, perhaps identical uncertainty quantification.

## 1 Dynamical systems

How precisely can I learn a given parameter of a dynamical system from observation? In ODE theory a useful concept is *sensitivity analysis*, which tells us how much gradient information our observations give us about a parameter. This comes in *local* (at my current estimate) and *global* (for all parameter ranges) flavours

## 2 Incoming

## 3 References

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