By H. Cabannes, M. Holt, V. V. Rusanov
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Extra info for 6th Int'l Conference on Numerical Methods in Fluid Dynamics
It is trivial to design toy problems that illustrate this effect impressively. An example can be found in the appendix. The computation of the partial derivative of y with respect to x as arguments of the top-level routine f0 in adjoint mode requires the reversal of a call tree (a simple chain in this case) of depth five. The leaf routine f5 is computationally much more expensive than the others. 6 seconds whereas additional result checkpointing as in Fig. 25 seconds. These results were obtained on a state-of-the-art Intel PC.
To ensure the correctness of the AD transformed code, particularly for safety critical applications, we propose using the proof-carrying code paradigm: an AD tool must provide a machine checkable certificate for an AD generated code, which can be checked in polynomial time in the size of the certificate by an AD user using a simple and easy to validate program. Using a WHILE-language, we show how such proofs can be constructed. In particular, we show that certain code transformations and static analyses used in AD can be certified using the well-established Hoare logic for program verification.
In this paper we show that a generalization of this problem that allows for subsets of subroutine arguments and/or results to be taped is NP-complete. Hence, we believe that the likelihood of an efficient exact solution of this problem is low. Heuristics for finding good reversal schemes are currently being developed in collaboration with colleagues at INRIA, France, and at Argonne National Laboratory, USA. e. sizeof(argchp3 ) ≤ 1, and that sizeof(argchp2 ) ≤ 2. provided that sizeof(argchp2 ) + sizeof(reschp3 ) ≤ 2 and sizeof(argchp3 ) + sizeof(reschp3 ) ≤ 2, where sizeof(reschpi ) denotes the size of a result checkpoint of subroutine i (in memory units).
6th Int'l Conference on Numerical Methods in Fluid Dynamics by H. Cabannes, M. Holt, V. V. Rusanov