Related papers: Tangent: Automatic differentiation using source-co…
Automatic differentiation (AD) is an essential primitive for machine learning programming systems. Tangent is a new library that performs AD using source code transformation (SCT) in Python. It takes numeric functions written in a syntactic…
Automatic differentiation (AD) is a technique for computing the derivative of a function represented by a program. This technique is considered as the de-facto standard for computing the differentiation in many machine learning and…
Derivative computation is a key component of optimization, sensitivity analysis, uncertainty quantification, and nonlinear solvers. Automatic differentiation (AD) is a powerful technique for evaluating such derivatives, and in recent years,…
In mathematics and computer algebra, automatic differentiation (AD) is a set of techniques to evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how…
Automatic differentiation (AD) is a set of techniques that systematically applies the chain rule to compute the gradients of functions without requiring human intervention. Although the fundamentals of this technology were established…
Automatic differentiation (AD) is an ensemble of techniques that allow to evaluate accurate numerical derivatives of a mathematical function expressed in a computer programming language. In this paper we use AD for stating and solving solid…
Algorithmic Differentiation (AD) can be used to automate the generation of derivatives in arbitrary software projects. This will generate maintainable derivatives, that are always consistent with the computation of the software. If a domain…
The Rust programming language is an attractive choice for robotics and related fields, offering highly efficient and memory-safe code. However, a key limitation preventing its broader adoption in these domains is the lack of high-quality,…
This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to…
Automatic Differentiation (AD) is instrumental for science and industry. It is a tool to evaluate the derivative of a function specified through a computer program. The range of AD application domain spans from Machine Learning to Robotics…
Algorithmic differentiation (AD) allows exact computation of derivatives given only an implementation of an objective function. Although many AD tools are available, a proper and efficient implementation of AD methods is not…
Optimizing the expected values of probabilistic processes is a central problem in computer science and its applications, arising in fields ranging from artificial intelligence to operations research to statistical computing. Unfortunately,…
Algorithmic differentiation (AD) is a set of techniques that provide partial derivatives of computer-implemented functions. Such a function can be supplied to state-of-the-art AD tools via its source code, or via an intermediate…
We introduce Combinatory Homomorphic Automatic Differentiation (CHAD), a principled, pure, provably correct define-then-run method for performing forward- and reverse-mode automatic differentiation (AD) on programming languages with…
We give a gentle introduction to using various software tools for automatic differentiation (AD). Ready-to-use examples are discussed, and links to further information are presented. Our target audience includes all those who are looking…
Automatic Differentiation (AD) is a powerful tool that allows calculating derivatives of implemented algorithms with respect to all of their parameters up to machine precision, without the need to explicitly add any additional functions.…
Automatic differentiation is involved for long in applied mathematics as an alternative to finite difference to improve the accuracy of numerical computation of derivatives. Each time a numerical minimization is involved, automatic…
In scientific computation, it is often necessary to calculate higher-order derivatives of a function. Currently, two primary methods for higher-order automatic differentiation exist: symbolic differentiation and algorithmic automatic…
This study explores matrix-free tangent evaluations in finite-strain elasticity with the use of automatically-generated code for the quadrature-point level calculations. The code generation is done via automatic differentiation (AD) with…
We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher-order language with algebraic data types and we characterise it as the unique structure-preserving macro given a…