By H. Martin Bücker, George Corliss, Paul Hovland, Uwe Naumann, Boyana Norris
This assortment covers the cutting-edge in computerized differentiation idea and perform. Practitioners and scholars will know about advances in computerized differentiation ideas and methods for the implementation of sturdy and strong instruments. Computational scientists and engineers will enjoy the dialogue of purposes, which offer perception into potent innovations for utilizing automated differentiation for layout optimization, sensitivity research, and uncertainty quantification.
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Additional info for Automatic Differentiation: Applications, Theory, and Implementations (Lecture Notes in Computational Science and Engineering)
It is known from work of Charney , Kerner , and Moore  that, by adding more dependent variables if necessary, the vector functions f may be restricted to polynomials (even polynomials of degrees at most 2). We are grateful to Alexander Gofen for suggesting this inquiry and for many helpful discussions and suggestions. 36 Harley Flanders In this article we explore the question of whether a function with a removable singularity at t0 may actually be the solution function of an ODE with polynomial or rational right side, so its Taylor approximations can be computed by AD.
The dual subroutine inputs the entire set of F Y variables, but it implements a single reverse calculation aimed at a single scalar quantity of interest further downstream. Only about 12 people have fully implemented structures like Fig. 7 so far, because it requires us to keep track of three main scalar quantities of interest, the specific error measure used in training the Critic, the error measure used in training the Model, and the estimate of J itself as used to train the Action network.
Algorithms for functions represented by Fourier-type series can be used to obtain the coefficients of the series expansions, much like what has already been done for Taylor series. In other words, the transformation of an FNA can be accomplished once the appropriate transformations of arithmetic operations and intrinsic functions involved are known. As initially realized by Wengert , this is indeed the key to the method. Backwards Differentiation in AD and Neural Nets: Past Links and New Opportunities Paul J.
Automatic Differentiation: Applications, Theory, and Implementations (Lecture Notes in Computational Science and Engineering) by H. Martin Bücker, George Corliss, Paul Hovland, Uwe Naumann, Boyana Norris