By Christian H. Bischof, H. Martin Bücker, Paul Hovland, Uwe Naumann, Jean Utke
This assortment covers advances in automated differentiation idea and perform. machine scientists and mathematicians will find out about fresh advancements in automated differentiation conception in addition to mechanisms for the development of sturdy and strong automated differentiation instruments. Computational scientists and engineers will enjoy the dialogue of varied functions, which supply perception into powerful recommendations for utilizing automated differentiation for inverse difficulties and layout optimization.
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Extra resources for Advances in Automatic Differentiation (Lecture Notes in Computational Science and Engineering)
Given this semi-automatic usage of AD, can we trust AD for safety-critical applications? Although the chain rule of calculus and the analyses used in AD are proved correct, the correctness of the AD generated code is tricky to establish. First, AD may locally replace some part B of the input code by B that is not observationally equivalent to B even though both are semantically equivalent in that particular context. Second, the input code may not be piecewise differentiable in contrast to the AD assumption.
Q, operating on a global memory space p ∈ Rµ . The fi are assumed to encapsulate the ϕi from (1). Hence, the local tapes are empty since the single output is computed without evaluation of intermediate values directly from the inputs of fi . Any given instance of DAGR can thus be mapped uniquely to an instance of RC and vice versa. A solution for DAGR can be obtained by solving the corresponding RC problem. Therefore RC must be at least as hard as DAGR. A given solution to RC is trivially verified in polynomial time by counting the number of flops performed.
Our theoretical approach needs be implemented using an AD tool and a theorem prover for at least the WHILE-language considered in this work. We need also to find a logical formalism in which to express a certificate so that its checking is tractable. Examples of such formalisms are investigated in [5, 12]. References 1. : Compilers: principles, techniques, and tools, Second edn. Addison-Wesley Publishing Company, Boston, USA (2006) 2. : Certification of directional derivatives computed by automatic differentiation.