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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.…

Chemical Physics · Physics 2020-06-23 Teresa Tamayo-Mendoza , Christoph Kreisbeck , Roland Lindh , Alán Aspuru-Guzik

Automatic differentiation---the mechanical transformation of numeric computer programs to calculate derivatives efficiently and accurately---dates to the origin of the computer age. Reverse mode automatic differentiation both antedates and…

Machine Learning · Computer Science 2014-04-30 Atilim Gunes Baydin , Barak A. Pearlmutter

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…

Programming Languages · Computer Science 2022-12-07 Alexey Radul , Adam Paszke , Roy Frostig , Matthew Johnson , Dougal Maclaurin

Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…

Programming Languages · Computer Science 2020-02-04 Martin Abadi , Gordon D. Plotkin

In this paper we introduce DiffSharp, an automatic differentiation (AD) library designed with machine learning in mind. AD is a family of techniques that evaluate derivatives at machine precision with only a small constant factor of…

Mathematical Software · Computer Science 2015-11-30 Atilim Gunes Baydin , Barak A. Pearlmutter , Jeffrey Mark Siskind

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…

Computational Physics · Physics 2025-06-03 He Zhang

Automatic differentiation (AD) in reverse mode (RAD) is a central component of deep learning and other uses of large-scale optimization. Commonly used RAD algorithms such as backpropagation, however, are complex and stateful, hindering deep…

Programming Languages · Computer Science 2018-10-03 Conal Elliott

Algorithmic differentiation (AD) has become increasingly capable and straightforward to use. However, AD is inefficient when applied directly to solvers, a feature of most engineering analyses. We can leverage implicit differentiation to…

Optimization and Control · Mathematics 2023-06-28 Andrew Ning , Taylor McDonnell

Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic…

Computational Finance · Quantitative Finance 2011-07-12 Cristian Homescu

Differentiable programming allows for derivatives of functions implemented via computer code to be calculated automatically. These derivatives are calculated using automatic differentiation (AD). This thesis explores two applications of…

Plasma Physics · Physics 2024-10-16 Nick McGreivy

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…

Computational Engineering, Finance, and Science · Computer Science 2025-09-16 Saakaar Bhatnagar

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…

Numerical Analysis · Mathematics 2025-06-03 Julian Andrej , Tzanio Kolev , Boyan Lazarov

This paper presents a novel optimization for differentiable programming named coarsening optimization. It offers a systematic way to synergize symbolic differentiation and algorithmic differentiation (AD). Through it, the granularity of the…

A large class of non-smooth practical optimization problems can be written as minimization of a sum of smooth and partly smooth functions. We examine such structured problems which also depend on a parameter vector and study the problem of…

Optimization and Control · Mathematics 2024-10-28 Sheheryar Mehmood , Peter Ochs

Automatic differentiation (AD) is an important family of algorithms which enables derivative based optimization. We show that AD can be simply implemented with effects and handlers by doing so in the Frank language. By considering how our…

Programming Languages · Computer Science 2021-01-21 Jesse Sigal

Derivatives of computer graphics, image processing, and deep learning algorithms have tremendous use in guiding parameter space searches, or solving inverse problems. As the algorithms become more sophisticated, we no longer only need to…

Graphics · Computer Science 2019-08-30 Tzu-Mao Li

We apply program verification technology to the problem of specifying and verifying automatic differentiation (AD) algorithms. We focus on define-by-run, a style of AD where the program that must be differentiated is executed and monitored…

Logic in Computer Science · Computer Science 2024-02-14 Paulo Emílio de Vilhena , François Pottier

We discuss the role of automatic differentiation tools in optimization software. We emphasize issues that are important to large-scale optimization and that have proved useful in the installation of nonlinear solvers in the NEOS Server. Our…

Mathematical Software · Computer Science 2007-05-23 Jorge J. Moré

Differentiable programming is a fresh programming paradigm which composes parameterized algorithmic components and trains them using automatic differentiation (AD). The concept emerges from deep learning but is not only limited to training…

Strongly Correlated Electrons · Physics 2019-09-11 Hai-Jun Liao , Jin-Guo Liu , Lei Wang , Tao Xiang

Simulation-based optimization using agent-based models is typically carried out under the assumption that the gradient describing the sensitivity of the simulation output to the input cannot be evaluated directly. To still apply…

Machine Learning · Computer Science 2021-03-24 Philipp Andelfinger