Update note on sensitivity analysis for hybrid DEs

[frankschae]

#612 .

Use BacksolveAdjoint if
the event terminates the time evolution and several states are saved.

That one is very technical...I'm not sure if we want that in here. If you terminate the integration but save the time points, the ts range in InterpolatingAdjoint and QuadratureAdjoint will (likely) be wrong. This is like using a saveat which doesn't fit to the time span...Thus a wrong gradient ..

the continuous adjoint sensitivities do not support multiple events per time point.

Just a bookkeeping issue.. This can be solved but not done yet (at least no tests).

[ChrisRackauckas]

That one is very technical...I'm not sure if we want that in here. If you terminate the integration but save the time points, the ts range in InterpolatingAdjoint and QuadratureAdjoint will (likely) be wrong. This is like using a saveat which doesn't fit to the time span...Thus a wrong gradient ..

Oh interesting. Is this because of the save at the terminating point?

[frankschae]

It happens here:
https://github.com/SciML/DiffEqSensitivity.jl/blob/a6fff921278bf8f14b9f2a3bc451245a72f963bc/src/concrete_solve.jl#L128

Without events, the issue is that when you choose a saveat which doesn't match the time span, you'll loose the endtime:

julia> collect(0.:2.3:10.)
5-element Vector{Float64}:
 0.0
 2.3
 4.6
 6.9
 9.2

Regarding terminating events. Suppose you had tspan=(0,10) with saveat=1.0 (which works) but then you terminate earlier. The range still goes until 10 (because it checks in prob). This results in loss function gradients that are off, i.e., applied at the wrong times.

[ChrisRackauckas]

ahh, thanks. Yeah that is worth handling.

[ChrisRackauckas]

Is there an issue on this?

[frankschae]

No, it doesn't have an issue yet. I only mentioned it briefly in SciML/SciMLSensitivity.jl#474 .

[ChrisRackauckas]

Alright, please document it. It doesn't sound too hard to fix though.