Related papers: Algorithmic differentiation for domain specific la…

We propose extensions to Fortran which integrate forward and reverse Automatic Differentiation (AD) directly into the programming model. Irrespective of implementation technology, embedding AD constructs directly into the language extends…

A C++ library for sensitivity analysis of optimisation problems involving ordinary differential equations (ODEs) enabled by automatic differentiation (AD) and SIMD (Single Instruction, Multiple data) vectorization is presented. The discrete…

Forward Automatic Differentiation (AD) is a technique for augmenting programs to compute derivatives. The essence of Forward AD is to attach perturbations to each number, and propagate these through the computation. When derivatives are…

Parameter identification for mechanistic Ordinary Differential Equation (ODE) models underpins prediction and control in several applications, yet remains a manual and labor-intensive process: datasets are noisy and partial, models can be…

As we reach the limit of Moore's Law, researchers are exploring different paradigms to achieve unprecedented performance. Approximate Computing (AC), which relies on the ability of applications to tolerate some error in the results to…

Recent work has shown that forward- and reverse- mode automatic differentiation (AD) over the reals is almost always correct in a mathematically precise sense. However, actual programs work with machine-representable numbers (e.g.,…

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…

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…

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…

This paper presents reverse-mode algorithmic differentiation (AD) based on source code transformation, in particular of the Static Single Assignment (SSA) form used by modern compilers. The approach can support control flow, nesting,…

Automatic differentiation (AD) is conventionally understood as a family of distinct algorithms, rooted in two "modes" -- forward and reverse -- which are typically presented (and implemented) separately. Can there be only one? Following up…

Objective. Algorithmic differentiation (AD) can be a useful technique to numerically optimize design and algorithmic parameters by, and quantify uncertainties in, computer simulations. However, the effectiveness of AD depends on how…

This paper presents a new functionality of the Automatic Differentiation (AD) tool Tapenade. Tapenade generates adjoint codes which are widely used for optimization or inverse problems. Unfortunately, for large applications the adjoint code…

No single Automatic Differentiation (AD) system is the optimal choice for all problems. This means informed selection of an AD system and combinations can be a problem-specific variable that can greatly impact performance. In the Julia…

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…

We present the new software OpDiLib, a universal add-on for classical operator overloading AD tools that enables the automatic differentiation (AD) of OpenMP parallelized code. With it, we establish support for OpenMP features in a reverse…

Anomaly detection (AD) is essential in areas such as fraud detection, network monitoring, and scientific research. However, the diversity of data modalities and the increasing number of specialized AD libraries pose challenges for…

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…

In practice, machine learning methods commonly require anomaly detection (AD) to filter inputs or detect distributional shifts. Typically, this is implemented by running a separate AD model alongside the primary model. However, this…

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…