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We develop nested automatic differentiation (AD) algorithms for exact inference and learning in integer latent variable models. Recently, Winner, Sujono, and Sheldon showed how to reduce marginalization in a class of integer latent variable…

Machine Learning · Statistics 2018-06-11 Daniel Sheldon , Kevin Winner , Debora Sujono

Automated code generation allows for a separation between the development of a model, expressed via a domain specific language, and lower level implementation details. Algorithmic differentiation can be applied symbolically at the level of…

Programming Languages · Computer Science 2024-09-27 James R. Maddison

Determining physical properties inside an object without access to direct measurements of target regions can be formulated as a specific type of \textit{inverse problem}. One of such problems is applied in \textit{Electrical Impedance…

Numerical Analysis · Mathematics 2023-01-30 Ivan Pombo , Luis Sarmento

Automatic differentiation (AD) has driven recent advances in machine learning, including deep neural networks and Hamiltonian Markov Chain Monte Carlo methods. Partially observed nonlinear stochastic dynamical systems have proved resistant…

Methodology · Statistics 2024-07-04 Kevin Tan , Giles Hooker , Edward L. Ionides

The successes of deep learning, variational inference, and many other fields have been aided by specialized implementations of reverse-mode automatic differentiation (AD) to compute gradients of mega-dimensional objectives. The AD…

Machine Learning · Computer Science 2021-03-16 Deniz Oktay , Nick McGreivy , Joshua Aduol , Alex Beatson , Ryan P. Adams

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

Most nonlinear partial differential equation (PDE) solvers require the Jacobian matrix associated to the differential operator. In PETSc, this is typically achieved by either an analytic derivation or numerical approximation method such as…

Mathematical Software · Computer Science 2019-09-09 J. G. Wallwork , P. Hovland , H. Zhang , O. Marin

In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of finite element models. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques.…

Mathematical Software · Computer Science 2013-10-17 Patrick E. Farrell , David A. Ham , Simon F. Funke , Marie E. Rognes

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

A computational fluid dynamics code is differentiated using algorithmic differentiation (AD) in both tangent and adjoint modes. The two novelties of the present approach are 1) the adjoint code is obtained by letting the AD tool Tapenade…

Computational Physics · Physics 2020-07-10 J. I. Cardesa , L. Hascoët , C. Airiau

Probabilistic modeling is iterative. A scientist posits a simple model, fits it to her data, refines it according to her analysis, and repeats. However, fitting complex models to large data is a bottleneck in this process. Deriving…

Machine Learning · Statistics 2016-03-03 Alp Kucukelbir , Dustin Tran , Rajesh Ranganath , Andrew Gelman , David M. Blei

Automatic differentiation (AD) is a range of algorithms to compute the numeric value of a function's (partial) derivative, where the function is typically given as a computer program or abstract syntax tree. AD has become immensely popular…

Programming Languages · Computer Science 2023-05-16 Tom Schrijvers , Birthe van den Berg , Fabrizio Riguzzi

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

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…

Mathematical Software · Computer Science 2018-07-27 Filip Šrajer , Zuzana Kukelova , Andrew Fitzgibbon

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

Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…

High Energy Physics - Phenomenology · Physics 2010-05-28 Mathias Wagner , Andrea Walther , Bernd-Jochen Schaefer

Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded…

Machine Learning · Computer Science 2023-01-10 Gaurav Arya , Moritz Schauer , Frank Schäfer , Chris Rackauckas

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…

Programming Languages · Computer Science 2026-05-07 Mathieu Huot , Sam Staton , Matthijs Vákár

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…

Mathematical Software · Computer Science 2018-03-13 Max Sagebaum , Nicolas R. Gauger

Implicit time integration schemes are widely used in computational fluid dynamics numerical codes to speed-up computations. Indeed, implicit schemes usually allow for less stringent time-step stability constraints than their explicit…

Computational Physics · Physics 2019-10-23 François Fraysse , Richard Saurel