IMO this is pretty cool because it allows to transparantly calculate
higher order derivatives. for example this enables to implement the
linearization stage of higher-order non-linear solvers without much
additional effort compared to just evaluating the function in
question. (essentially, such higher order non-linear solvers are based
on truncating the Taylor series not after the first term -- like for the
Newton scheme -- but later. That said, they require to solve linear
systems of equations which involve tensors of orders greater than 2,
so they are not really practical as far as I can see.)
A more practical motivation for this is to allow the constraint
solvers to be used in "nested mode", i.e., linearizing the system of
equations they need to solve using automatic differentiation, but
allowing the value objects which are passed to the constraint solvers
be function evaluations themselves. (E.g. the result of a flash
calculation can also include the derivatives with regard to the
primary variables of the flow model. Note that the individual
constraint solvers need to some patches to make this work.)
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