General State Space Examples
This is a placeholder for future support for general nonlinear state-space problems. The basic implementation is a relatively simple variation on the linear version, where you call back into AD for the f,g,h calls in the rrule definition. Because of the mixture of AD calls and rules, it may make sense to wait for Enzyme.jl to be ready.
A future feature, if anyone is interested in writing it, is full support for
\[u_{n+1} = f(u_n,p,t_n) + g(u_n,p,t_n) w_{n+1}\]
for some functions $f$ and $g$, where $w_{n+1}$ are IID random shocks to the evolution equation. The $p$ is a vector of potentially differentiable parameters.
In addition, there is an optional observation equation
\[z_n = h(u_n, p, t_n) + v_n\]
This could involve both the simulation and the calculation of the joint likelihood conditional on the noise, as in the other examples.