Second order derivatives

[tomix1024]

Hi there,

I was just wondering, if it is possible to compute second order derivatives using drjit?
E.g. if I have two variables a and b and compute some function f(a,b), I can simply compute df(a,b)/da for example using dr.forward_to.
But what if I now want to compute the derivative wrt. b of the resulting gradient value (df(a,b)/(da*db))?

Here is a simple example of what I want to do:

import mitsuba as mi
import drjit as dr

mi.set_variant('cuda_ad_rgb')

a = mi.Float(3)
b = mi.Float(2)

# compute dab/da
dr.set_grad_enabled(a, True)
dr.set_grad(a, mi.Float(1))
ab = a*b
dr.forward_to(ab)
dab_da = dr.grad(ab)
print(f'{dab_da=}')


# TODO compute [dab/da]/db
dr.set_grad_enabled(b, True)
dr.backward_from(dab_da)
ddab_da_db = dr.grad(b)
print(f'{ddab_da_db=}')

Regards,
Tom

[njroussel]

Hi @tomix1024

Drjit doesn't currently support second order derivatives. The few places where we need them we typically the first derivative "manually" and let the autodiff handle the second one.