Automatic Differentiation: Applications, Theory, and by H. Martin Bücker, George Corliss, Paul Hovland, Uwe Naumann,

By H. Martin Bücker, George Corliss, Paul Hovland, Uwe Naumann, Boyana Norris

This assortment covers the state-of-the-art in automated differentiation thought and perform. Practitioners and scholars will know about advances in automated differentiation ideas and methods for the implementation of strong and strong instruments. Computational scientists and engineers will enjoy the dialogue of functions, which offer perception into potent techniques for utilizing computerized differentiation for layout optimization, sensitivity research, and uncertainty quantification.

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Extra resources for Automatic Differentiation: Applications, Theory, and Implementations (Lecture Notes in Computational Science and Engineering)

Example text

I have seen enough confusion about partial derivatives in the study of complex systems, all across social sciences and basic science and engineering, that I believe it would save a lot of time in the end to be clear about these distinctions from the first. The three basic concepts are: 1) the algebraic partial derivative, whose value (as an algebraic expression) depends on the explicit algebraic expression for the quantity being differentiated; 2) the field or functional partial derivative, whose value is well-defined only for a specific set of coordinate variables or input vector; and 3) the ordered derivative, which represents the total change in a later quantity which results when the value of an earlier quantity is changed, in an ordered system.

One reason is that the proven and powerful tools in AD today mainly focus on differentiating C or Fortran programs, but good economists only rarely write their models in C or in Fortran. They generally use packages such as Troll or TSP or SPSS or SAS, which make it easy to perform statistical analysis on their models. Engineering students tend to use MatLab. Many engineers are willing to try out very complex designs requiring fast derivatives, when using neural networks but not when using other kinds of nonlinear models, simply because backpropagation for neural networks is available “off the shelf” with no work required on their part.

Thus the function of the brain as a whole system is to learn to compute the actions which best serve the interests of the organism over time. The standard neuroanatomy textbook by Nauta [404] stresses that we cannot really say which parts of the brain are involved in computing actions, since all parts of the brain feed into that computation. The brain has many interesting capabilities for memory and pattern recognition, but these are all subsystems or even emergent dynamics within the larger system.

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