Need new ways to specify parameters for adjoint sensitivity analysis

[huanglangwen]

I think it is better to pass in f_p, g_p and g_u explicitly for adjoint sensitivity analysis instead of relying on the parameter p in f(du,u,p,t) and dg(out,u,p,t). Because p can be used for other purposes like caching and storing configurations which are not for differentiation.

[ChrisRackauckas]

I think we definitely want to make it so that people can just use the same function. However, there does need to be a nicer way to mix non-parameters with parameters. Maybe an array type.

[huanglangwen]

But someone may prefer their own f_p g_p and g_u compared to AD-generated one for reasons like analytical solutions, foreign language calls, etc. For the non-parameters, perhaps we need a new optional argument for f?

[ChrisRackauckas]

Which function is missing? You don't need to rely on AD?

[huanglangwen]

For example, f_p is needed when doing back-integration in adjoint sensitivity. I can't find anyplace to specify them.

[ChrisRackauckas]

http://docs.juliadiffeq.org/latest/features/performance_overloads.html#ODEFunction-1

[huanglangwen]

Oh, I didn't notice that. How about g_u and g_p because adjoint_sensitivities only got dg?

[ChrisRackauckas]

For discrete adjoints we only need dg. For continuous adjoints we only need g and dg.

[huanglangwen]

Sorry, I can't get your point. How does the adjoint sensitivity equation go to your conclusion that only dg and g are needed?

[ChrisRackauckas]

dg=g_u. For everything but continuous adjoints where g is dependent on p, this is sufficient. We could use a PR to add g_p to the integrand for continuous adjoints, right now that's just not supported.

[huanglangwen]

Thank you.