The advent of high-speed computers and sophisticated software tools has made the
computation of derivatives for functions defined by evaluation programs both easier and …

In its basic form, the reverse mode of computational differentiation yields the gradient of a
scalar-valued function at a cost that is a small multiple of the computational work needed to …

Automatic, or algorithmic, differentiation addresses the need for the accurate and efficient
calculation of derivative values in scientific computing. To this end procedural programs for …

Combinatorial techniques have become essential tools across the landscape of
computational science, and some of the combinatorial ideas undergirding these tools are …

We show that the problem of accumulating Jacobian matrices by using a minimal number of
floating-point operations is NP-complete by reduction from Ensemble Computation. The …

In this paper we present a discrete adjoint approach for the optimization of unsteady,
turbulent flows. While discrete adjoint methods usually rely on the use of the reverse mode …

We reexamine the work of Stumm and Walther on multistage algorithms for adjoint
computation. We provide an optimal algorithm for this problem when there are two levels of …

Deep learning training memory needs can prevent the user from considering large models
and large batch sizes. In this work, we propose to use techniques from memory-aware …

The adjoint code of a nonlinear computer model calculates gradients along a trajectory that
has to be known at integration time. When the storage of the whole trajectory requires too …

Runs of numerical computer programs can be visualized as directed acyclic graphs (DAGs).
We consider the problem of restoring the intermediate values computed by such a program …