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About 6,015 papers for “Automatic differentiation”

Automatic Differentiation

Nikhil Ketkar · Apress eBooks · 2017

In the chapter on Stochastic Gradient Descent, we treated the computation of gradients of the loss function as a black box.

Cited by 73

Automatic Differentiation

Hans J. Skaug · Wiley StatsRef: Statistics Reference Online · 2014

Abstract Automatic differentiation (AD) is a technique for numerical differentiation of computer algorithms.

Cited by 5

Stochastic automatic differentiation: automatic differentiation for Monte-Carlo simulations

Christian Fries · Quantitative Finance · 2019

In this paper we re-formulate the automatic differentiation (and in particular, the backward automatic differentiation, also known as adjoint automatic differentiation, AAD) for random variables. While this is just a formal re-interpretation it allows one to investigate the algorithms in the presence of stochastic operators like expectation, conditional expectation or indicator functions.We then specify the algorithms to efficiently incorporate non-pathwise operators (like conditional expectation operators). Under a comparably mild assumption it is possible to retain the simplicity of the backward automatic differentiation algorithm in the presence of conditional expectation operators. This simplifies important applications like - in mathematical finance - the application of backward automatic differentiation to the valuation of Bermudan options or calculation of xVA's.We give the proof for a generalized version of the result. We then discuss in detail how the framework allows dramatic reduction of the memory requirements and improves the performance of a tapeless implementation of automatic differentiation (while the implementation brings advantages similar to ‘vector AAD’ (sometimes called tape compression) for free, it allows improvements beyond this. We present the implementation aspects and show how concepts from object-functional programing, like immutable objects and lazy evaluation enable additional reductions of the memory requirements.

Cited by 16

Automatic differentiation bibliography

George F. Corliss · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1992

This is a bibliography of work related to automatic differentiation. Automatic differentiation is a technique for the fast, accurate propagation of derivative values using the chain rule. It is neither symbolic nor numeric. Automatic differentiation is a fundamental tool for scientific computation, with applications in optimization, nonlinear equations, nonlinear least squares approximation, stiff ordinary differential equation, partial differential equations, continuation methods, and sensitivity analysis. This report is an updated version of the bibliography which originally appeared in Automatic Differentiation of Algorithms: Theory, Implementation, and Application.

Cited by 4Open access

Automatic Differentiation Package

OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2016

Sacado is an automatic differentiation package for C++ codes using operator overloading and C++ templating. Sacado provide forward, reverse, and Taylor polynomial automatic differentiation classes and utilities for incorporating these classes into C++ codes. Users can compute derivatives of computations arising in engineering and scientific applications, including nonlinear equation solving, time integration, sensitivity analysis, stability analysis, optimization and uncertainity quantification.

Cited by 0Open access

Automatic differentiation bibliography

George F. Corliss · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1992

This is a bibliography of work related to automatic differentiation. Automatic differentiation is a technique for the fast, accurate propagation of derivative values using the chain rule. It is neither symbolic nor numeric. Automatic differentiation is a fundamental tool for scientific computation, with applications in optimization, nonlinear equations, nonlinear least squares approximation, stiff ordinary differential equation, partial differential equations, continuation methods, and sensitivity analysis. This report is an updated version of the bibliography which originally appeared in Automatic Differentiation of Algorithms: Theory, Implementation, and Application.

Cited by 9Open access

On Automatic Differentiation

Andreas Griewank · 1989

In comparison to symbolic differentiation and numerical differencing, the chain rule based technique of automatic differentiation is shown to evaluate partial derivatives accurately and cheaply. In particular it is demonstrated that the reverse mode of automatic differentiation yields any gradient vector at no more than five times the cost of evaluating the underlying scalar function. After developing the basic mathematics we describe several software implementations and briefly discuss the ramifications for optimization.

Cited by 0

Semi-Automatic Differentiation

Thomas F. Coleman, Fadil Santosa, Arun Verma · Birkhäuser Boston eBooks · 1998

We demonstrate how the structure that arises in inverse and optimal design problems can be used to aid in the efficient application of automatic differentiation ideas. We discuss the program structure of generic inverse problems and then illustrate, with two examples (one example involves the heat equation, the other involves wave propagation) how structure can be used in combination with automatic differentiation. Finally, we report numerical results and describe the ADMIT-2 software package which enables efficient derivative computation of structured problems.

Cited by 7

Implementing automatic differentiation efficiently

David Juedes, Andreas Griewank · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1990

The automatic differentiation of computer arithmetic has been investigated since before 1960. Most of this effort has been centered on the forward mode of derivative evaluation. Speelpenning, Iri and Kubota, and Horwedel et al. have all implemented the more efficient reverse mode of evaluating derivatives in their respective Fortran precompilers. The reverse mode requires information about a computation to be stored in order that derivatives may be calculated after the function evaluation has been completed. This additional storage cost may be prohibitive. The goals of our research have been to implement an automatic differentiation package that gracefully handles the storage issue and to generate a parallel implementation of derivative evaluation in the reverse mode. This paper discusses results of both research efforts, specifically those involving the ADOL-C package. 10 refs., 4 figs.

Cited by 5Open access