Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic Runge-Kutta schemes for adjoint equations, automatic
  differentiation, optimal control and more   It is well known that symplectic Runge-Kutta and Partitioned Runge-Kutta
methods exactly preserve {\em quadratic} first integrals (invariants of motion)
of the system being integrated. While this property is often seen as a mere
curiosity (it does not hold for arbitrary first integrals), it plays an
important role in the computation of numerical sensitivities, optimal control
theory and Lagrangian mechanics, as described in this paper, which, together
with some new material, presents in a unified way a number of results now
scattered or implicit in the literature. Some widely used procedures, such as
the direct method in optimal control theory and the computation of
sensitivities via reverse accumulation imply "hidden" integrations with
symplectic Partitioned Runge-Kutta schemes.

26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics