… their own adjoints. • We illustrate how combinatory differentiation and combinatory adjoint
… More speculatively, we believe our combinatory setting is useful for a differential and adjoint …

… of differential equations with respect to changes in the initial conditions leads to the introduction
of an adjoint … Of course, the idea of an adjoint problem is not restricted to differential …

… We describe computational aspects of automatic differentiation applied … of the cost gradient
wrt a set of controls via the adjoint technique. The … The combination of four related elements: …

… an adjoint formulation for the flowfield. For a single design variable, the use of a direct mode
of differentiation to obtain the derivative of a … In combination with an adjoint procedure for the …

… and compiler, and the performance characteristics that result from this combination. … for
differentiation via the J function and pullbacks, and uses these to build a system for differentiation …

… ) adjoints in the reverse mode, and derivative accumulation … The differentiation of these
units in combination with an inho… structure is still a real challenge for automatic differentiation. …

… of adjoint variables, and the combination of the adjoint … be approximated by finite differences,
which needs at least n … the adjoint model has two advantages over finite differences: …

… Adjoint methods quantify the error in a particular output functional that results from residual
errors in approximating the solution to the partial differential … or in combination to obtain highly …

… from a combination of manually and automatically derived discrete adjoint algorithms and
nu… calculated using the adjoint model to those calculated using the finite difference method, …

… differentiation. Thus efficient methods for CASA necessarily mix a reverse-mode AD into the
generated adjoint … This combination is what we define as forward-mode DSAAD, and this …