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Numerical calculations carrying along derivatives
algebra, automatic differentiation (auto-differentiation, autodiff, or AD), also called algorithmic differentiation, computational differentiation, and differentiation
Automatic_differentiation
Probabilistic programming language for Bayesian inference
automatic differentiation to calculate gradients of the model, which is required by HMC, NUTS, L-BFGS, BFGS, and variational inference. The automatic
Stan_(software)
and open source symbolic framework for automatic differentiation and optimal control. Automatic differentiation JModelica.org "Optimization in Engineering
CasADi
In applied mathematics, Hessian automatic differentiation are techniques based on automatic differentiation (AD) that calculate the second derivative
Hessian automatic differentiation
Hessian_automatic_differentiation
Real numbers adjoined with a nil-squaring element
isomorphic to the complex plane. One application of dual numbers is automatic differentiation. Any polynomial P ( x ) = p 0 + p 1 x + p 2 x 2 + ⋯ + p n x n
Dual_number
Technique to solve partial differential equations
can be computed using automatic differentiation (AD), which is assessed to be superior to numerical or symbolic differentiation. A general nonlinear partial
Physics-informed neural networks
Physics-informed_neural_networks
Programming paradigm
Differentiable programming is a programming paradigm in which a numeric computer program can be differentiated throughout via automatic differentiation
Differentiable_programming
Tabular comparison of deep learning software
Andreyevich Radul; Jeffrey Mark Siskind (20 February 2015). "Automatic differentiation in machine learning: a survey". arXiv:1502.05767 [cs.LG]. "Microsoft/caffe"
Comparison of deep learning software
Comparison_of_deep_learning_software
Automatic differentiation and array software library
Adept is a combined automatic differentiation and array software library for the C++ programming language. The automatic differentiation capability facilitates
Adept_(C++_library)
Machine-learning framework
It is described as bringing together a modified version of the automatic differentiation system autograd and OpenXLA's XLA (Accelerated Linear Algebra)
JAX_(software)
Optimization algorithm for artificial neural networks
Some other names for the technique include "reverse mode of automatic differentiation" or "reverse accumulation". Backpropagation computes the gradient
Backpropagation
dynamics (differential equations) model, the automatic differentiation arithmetic includes differentiation of the integration algorithm of the simulation
PROSE_modeling_language
Deep learning library
type, similarly to NumPy. Training is facilitated by a reversed automatic differentiation system, Autograd, that constructs a directed acyclic graph of
PyTorch
Machine learning software library
the most significant being TensorFlow eager, which changed the automatic differentiation scheme from the static computational graph to the "Define-by-Run"
TensorFlow
Mathematical function whose derivative exists
\to \mathbb {C} } , that is complex-differentiable at a point x = a {\textstyle x=a} is automatically differentiable at that point, when viewed as a function
Differentiable_function
Finnish mathematician and computer scientist
introduced the reverse mode of automatic differentiation (AD), in order to efficiently compute the derivative of a differentiable composite function that can
Seppo_Linnainmaa
S2CID 122357351. Griewank, Andreas (2012). "Who Invented the Reverse Mode of Differentiation?". Documenta Mathematica, Extra Volume ISMP. Documenta Mathematica
Timeline_of_machine_learning
Algebraic modeling language
Library (ASL), which allows reading nl files and provides the automatic differentiation, is open-source. It is used in many solvers to implement AMPL
AMPL
Formula in calculus
because the two functions being composed are of different types. Automatic differentiation – Numerical calculations carrying along derivatives − a computational
Chain_rule
Non-linear statistical modeling software suite
non-profit ADMB Foundation. The "AD" in AD Model Builder refers to the automatic differentiation capabilities that come from the AUTODIF Library, a C++ language
ADMB
Sampling algorithm
mid-2010s the developers of Stan implemented HMC in combination with automatic differentiation. Suppose the target distribution to sample is f ( x ) {\displaystyle
Hamiltonian_Monte_Carlo
Open-source machine-learning software library
convolutional networks. It is also capable of differentiable programming through its source-to-source automatic differentiation package, Zygote.jl. Julia is a popular
Flux (machine-learning framework)
Flux_(machine-learning_framework)
Class of artificial neural network
Such networks are typically also trained by the reverse mode of automatic differentiation. They can process distributed representations of structure, such
Recurrent_neural_network
Technique and research method within computational imaging
Chris (2020-03-27). "Three dimensions, two microscopes, one code: Automatic differentiation for x-ray nanotomography beyond the depth of focus limit". Science
Differentiable_imaging
Use of numerical analysis to estimate derivatives of functions
function. Unlike analytical differentiation, which provides exact expressions for derivatives, numerical differentiation relies on the function's values
Numerical_differentiation
interpreted by tomSym it is possible to use either automatic differentiation or numerical differentiation. In the following example a simple problem is solved
TomSym
toolkit JAX — machine learning library for numerical computing and automatic differentiation H2O — machine learning and predictive analytics platform Infer
Lists of open-source artificial intelligence software
Lists_of_open-source_artificial_intelligence_software
external tools such as the AWA toolbox and the Taylor model toolbox) Automatic differentiation Numerical integration Fast Fourier transform Rigorously compute
INTLAB
infinity. automatic differentiation In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation or computational
Glossary_of_calculus
Type of programming language
optimization routines through libraries such as SciPy, where automatic differentiation and specialized algorithms are available, albeit not as an intrinsic
Scientific programming language
Scientific_programming_language
Interface Supervised learning Unsupervised learning Deep learning Automatic differentiation Has pretrained models Actively developed Apache Mahout Apache
Comparison of machine learning software
Comparison_of_machine_learning_software
British-Canadian computer scientist (born 1947)
backpropagation, it was not the first to suggest the approach. Reverse-mode automatic differentiation, of which backpropagation is a special case, was proposed by Seppo
Geoffrey_Hinton
Reinforcement learning algorithms
This is a common source of error in implementations that use automatic differentiation, and requires "stopping the gradient" at that point. Similarly
Actor-critic_algorithm
Mathematical algorithm
method which uses a provided Jacobian and another computing with automatic differentiation. """ gaussnewton(r, J, β₀, maxiter, tol) Perform Gauss–Newton
Gauss–Newton_algorithm
C++ template metaprogramming technique
Library, and xtensor. Expression templates can also accelerate C++ automatic differentiation implementations, as demonstrated in the Adept library. Outside
Expression_templates
Type of algorithm
solving time dependent adjoint equations, as well as reverse mode automatic differentiation. D. K. Pradhan and N. H. Vaidya, "Roll-forward checkpointing scheme:
Checkpointing_scheme
for sparse matrices in MATLAB and SciPy. Adept is a combined automatic differentiation and array library. Advanced Simulation Library is free and open
List_of_numerical_libraries
Process of finding the optimal set of variables for a machine learning algorithm
hyperparameters consists in differentiating the steps of an iterative optimization algorithm using automatic differentiation. A more recent work along this
Hyperparameter_optimization
Specialized notation for multivariable calculus
and Matrix Differentiation (notes on matrix differentiation, in the context of Econometrics), Heino Bohn Nielsen. A note on differentiating matrices (notes
Matrix_calculus
License Description ADMB BSD nonlinear optimization framework using automatic differentiation. ASCEND GPL mathematical modelling chemical process modelling
List_of_optimization_software
German mathematician
algorithmic differentiation (Society for Industrial and Applied Mathematics, 2008) on the theoretical foundation of Algorithmic Differentiation. "DNB, Katalog
Andrea_Walther
Model in finance
Another possibility is to resort to automatic differentiation. For example, the tangent mode of algorithmic differentiation may be applied using dual numbers
Heston_model
Topics referred to by the same term
used in the fields of computer vision and image analysis Hessian automatic differentiation Hessian equations, partial differential equations (PDEs) based
Hessian
Software library of numerical-analysis algorithms
Fortran,Python, MATLAB, Java, and .NET. A separate library supports Automatic differentiation (AD). The main supported systems are currently Windows, Linux
NAG_Numerical_Library
developed in several fields, most directly as the reverse mode of automatic differentiation published by Seppo Linnainmaa (1970). It was applied to neural
History of artificial intelligence
History_of_artificial_intelligence
American mathematician (1925–2013)
workshop on automatic differentiation, held in Breckenridge, Colorado. Flanders' chapter in the Proceedings is titled "Automatic differentiation of composite
Harley_Flanders
Academic journal
also covers linear programming, computational complexity theory, automatic differentiation, approximations and error analysis, parametric programming, sensitivity
Computational Optimization and Applications
Computational_Optimization_and_Applications
Optimization algorithm
and L-BFGS-B algorithm. Stan implements L-BFGS together with automatic differentiation as an option to solve maximum likelihood estimation and maximum
Limited-memory_BFGS
group at SRI. 1970 Seppo Linnainmaa publishes the reverse mode of automatic differentiation. This method became later known as backpropagation, and is heavily
Timeline of artificial intelligence
Timeline_of_artificial_intelligence
Optimization software library
2nd derivative (Hessian) information if provided (usually via automatic differentiation routines in modeling environments such as AMPL). If no Hessians
IPOPT
Topics referred to by the same term
Category:Duality (mathematics) Dual number, a number system used in automatic differentiation Dual (grammatical number), a grammatical category used in some
Dual
Topics referred to by the same term
facility Analog-to-digital converter, a type of electronic circuit Automatic differentiation, a set of computer programming techniques to speedily compute
AD_(disambiguation)
High-level computer programming conceptualization
Prolog. Differentiable programming structures programs so that they can be differentiated throughout, usually via automatic differentiation. Literate
Programming_paradigm
Concept in machine learning
tensors in higher dimensions. The unified data architecture and automatic differentiation of tensors has enabled higher-level designs of machine learning
Tensor_(machine_learning)
Effect of variables' uncertainties on the uncertainty of a function based on them
{\sigma _{I}}{I}}\right)^{2}}}.} Accuracy and precision Automatic differentiation Bienaymé's identity Delta method Dilution of precision (navigation)
Propagation_of_uncertainty
Manifold upon which it is possible to perform calculus
directional differentiation adapted to the case of differentiable manifolds ultimately captures the intuitive features of directional differentiation in an
Differentiable_manifold
suite for non-linear statistical modeling based on C++ which uses automatic differentiation. AMPL is a mathematical modeling language for describing and solving
List of numerical-analysis software
List_of_numerical-analysis_software
suite for non-linear statistical modeling based on C++ which uses automatic differentiation Chronux – for neurobiological time series data DAP – free replacement
List_of_statistical_software
models in script format automatic differentiation: Yes Yes Yes Forward-mode for Jacobian computation, symbolic differentiation capabilities multiphysics:
List of finite element software packages
List_of_finite_element_software_packages
Partitioning and load balancing of distributed data structures. Automatic differentiation Discretizing partial differential equations. Trilinos supports
Trilinos
Computer algebra system
A template class for quaternions Derive: A template class for automatic differentiation Vector: A template class for vectors (see vector space) Matrix:
SymbolicC++
Machine learning software library
MindSpore adopts a source-to-source (S2S) automatic differentiation approach, allowing Python code to be automatically transformed into optimized computational
MindSpore
Semi-automatic pistol
case of Colt-produced models) is a single-action, recoil-operated, semi-automatic pistol chambered primarily for the .45 ACP cartridge. The M1911 pistol
M1911_pistol
Optimization method
function (among other options). Stan implements BFGS together with automatic differentiation as an option to solve maximum likelihood estimation and maximum
Broyden–Fletcher–Goldfarb–Shanno algorithm
Broyden–Fletcher–Goldfarb–Shanno_algorithm
Topics referred to by the same term
multiphysics simulation software AMPL Solver Library, an open-source automatic differentiation library Apache Software License, an open-source license for software
ASL_(disambiguation)
Mathematical optimization software
Optimal control with PROPT using Gauss and Chebyshev collocation. Automatic differentiation with MAD Interface to AMPL TOMLAB supports solvers like CPLEX
TOMLAB
Political essay by Václav Havel
by an individual "living in truth" in their daily life they automatically differentiate themselves from the officially mandated culture prescribed by
The_Power_of_the_Powerless
Statistical model used in machine learning
flows. On a software platform equipped with linear algebra and automatic differentiation, R f ( x ) = | det ( T y ′ F x T x ) | {\displaystyle R_{f}(\mathbf
Flow-based_generative_model
Type of artificial neural network
include, in the training objective, the residual computed via automatic differentiation. Instead, encode-process-decode architectures (e.g. CORAL), built
Neural_field
Hydraulic fluid used in vehicles with automatic transmissions
green to differentiate it from motor oil and other fluids in the vehicle. This fluid is designed to meet the unique demands of an automatic transmission
Automatic_transmission_fluid
American mathematician
STG is modified by chemical and electrical inputs. Employing automatic differentiation, Guckenheimer has constructed a new family of algorithms that
John_Guckenheimer
Extremely small quantity in calculus; thing so small that there is no way to measure it
uniquely determined real numbers. One application of dual numbers is automatic differentiation. This application can be generalized to polynomials in n variables
Infinitesimal
Intelligence of machines
Gradient calculation in computational graphs, backpropagation, automatic differentiation: Russell & Norvig (2021, sect. 21.2), Luger & Stubblefield (2004
Artificial_intelligence
Numerical programming library for the OCaml programming language
a core functionality, Owl provides the algorithmic differentiation (or automatic differentiation) and dynamic computation graph modules. The highest
Owl_Scientific_Computing
Imaging technique
expressed as a differentiable computational graph and optimized end-to-end with gradient-based techniques. Implemented in automatic differentiation frameworks
Digital_holography
Julia software and development tools
solving Symbolics.jl — symbolic computing library ForwardDiff.jl — automatic differentiation package Optim.jl — mathematical optimization package Roots.jl
List of Julia software and tools
List_of_Julia_software_and_tools
Topics referred to by the same term
Autodiff may refer to: Automatic differentiation, a set of techniques to numerically evaluate the derivative of a function specified by a computer program
Autodiff
Fundamental construction of differential calculus
Mathematical operation in calculus Logarithmic differentiation – Method of mathematical differentiation Non-classical analysis – Branch of mathematicsPages
Generalizations of the derivative
Generalizations_of_the_derivative
Topics referred to by the same term
Optimal Jacobian Accumulation, an NP-complete problem related to automatic differentiation Oja (disambiguation) This disambiguation page lists articles associated
OJA_(disambiguation)
American-born computer scientist
rendering engine using Automatic differentiation. This provided a framework for posing a forward synthesis problem and automatically obtaining an optimization
Michael_J._Black
Modelling language for algebraic equations
second derivatives of continuous functions to the solvers through automatic differentiation and in sparse matrix form. Julia, MATLAB, Python are mathematical
APMonitor
Species of butterfly
Pieris bryoniae, the dark-veined white or mountain green-veined white, is a Palearctic butterfly of the family Pieridae. It has variously been considered
Pieris_bryoniae
Names of (7,3,1) Dan Kalman 2003 Doubly Recursive Multivariate Automatic Differentiation Mark McKinzie and Curtis Tuckey 2002 Higher Trigonometry, Hyperreal
Carl_B._Allendoerfer_Award
Radio telescope array
"Computationally Efficient Design of an LNA Input Matching Network Using Automatic Differentiation". IEEE Journal of Microwaves. 5 (4): 972–982. Bibcode:2025IJMic
Deep_Synoptic_Array
Graph coloring in which all 2-chromatic subgraphs are acyclic
"Efficient Computation of Sparse Hessians Using Coloring and Automatic Differentiation", INFORMS Journal on Computing, 21 (2): 209–223, doi:10.1287/ijoc
Acyclic_coloring
Differentiated service is a design pattern for business services and software, in which the service varies automatically according to the identity of the
Differentiated_service
Species of orchid
Jumellea fragrans, also known as faham, is a species of orchid in the genus Jumellea. It is native to the islands of Mauritius and Réunion. It grows as
Jumellea_fragrans
Species of epiphytic orchid
Phalaenopsis marriottiana is a species of orchid native to Southeast China and Myanmar. The specific epithet marriottiana honours William Henry Smith-Marriott
Phalaenopsis_marriottiana
Tracking system using transceivers on ships
The automatic identification system (AIS) is an automatic tracking system that uses transponders on ships and is used by vessel traffic services (VTS)
Automatic identification system
Automatic_identification_system
Award
was awarded to Chris Bischof and Alan Carle for ADIFOR 2.0, an automatic differentiation tool for Fortran 77 programs. The code is available for educational
J. H. Wilkinson Prize for Numerical Software
J._H._Wilkinson_Prize_for_Numerical_Software
Class of mathematical root-finding algorithm
functions the derivative evaluation using the Taylor arithmetic of automatic differentiation requires the equivalent of (d + 1)(d + 2)/2 function evaluations
Householder's_method
Generalization of the concept of directional derivative
redirect targets Differentiable vector-valued functions from Euclidean space – Differentiable function in functional analysis Differentiation in Fréchet spaces
Gateaux_derivative
be fitted using gradient and Hessian information easily with Automatic_differentiation, arbitrary distance metrics can be provided for conditioning set
Vecchia_approximation
Technique for designing controllers
Active disturbance rejection control (or ADRC, also known as automatic disturbance rejection control) is a model-free control technique used for designing
Active disturbance rejection control
Active_disturbance_rejection_control
Software libraries
extensible monitoring solution for Java applications Nabla Provides automatic differentiation classes that can generate derivative of any function implemented
Apache_Commons
Method for bounding the errors of numerical computations
Engineering Computing). Affine arithmetic INTLAB (Interval Laboratory) Automatic differentiation Multigrid method Monte-Carlo simulation Interval finite element
Interval_arithmetic
Specialist field of computer science
as convergent and asymptotic series Computing derivatives by Automatic differentiation (AD) Finite element method for solving PDEs High order difference
Computational_science
French award
Retrieved 2025-12-03. "Aladin Lite documentation". Retrieved 2025-12-03. "DifferentiationInterface.jl documentation". Retrieved 2025-12-03. "Pharo". Retrieved
Open Science Award for Open Source Research Software
Open_Science_Award_for_Open_Source_Research_Software
Software application of the concept of reversible computing
David; Utke, Jean (1996). "Algorithm 755: Adolc: a package for the automatic differentiation of algorithms written in c/c++". ACM Transactions on Mathematical
Reverse_computation
AI research laboratory
was announced with the aim of developing an algorithm that can automatically differentiate between healthy and cancerous tissues in head and neck areas
Google_DeepMind
AUTOMATIC DIFFERENTIATION
AUTOMATIC DIFFERENTIATION
Girl/Female
Arabic, Muslim
Aromatic Sweet Basil
Girl/Female
Arabic, Muslim
Aromatic; Rare Moon
Boy/Male
Muslim/Islamic
Aromatic
Boy/Male
Muslim
Aromatic
Girl/Female
Afghan, Arabic, Australian
Aromatic; Sweet Basil
Girl/Female
Latin
Fortuna.
Girl/Female
Muslim/Islamic
Aromatic
Girl/Female
Arabic, Muslim
Aromatic; Sweet Basil
Girl/Female
Arabic, Muslim
Aromatic
Girl/Female
Muslim
Flower, Kind of aromatic plant
Girl/Female
Indian
Flower, Kind of aromatic plant
Girl/Female
Arabic, French, Muslim
Aromatic
Girl/Female
Arabic, Australian, Muslim
Kind of Aromatic Plant
Girl/Female
Muslim
Aromatic
Girl/Female
Muslim/Islamic
Aromatic
Girl/Female
Muslim
Aromatic, A narrator of Hadith
Girl/Female
Muslim
Flower, Kind of aromatic plant
Boy/Male
Indian
Aromatic
Girl/Female
Indian
Aromatic, A narrator of Hadith
Boy/Male
Arabic, Muslim
Fragrant; Aromatic
AUTOMATIC DIFFERENTIATION
AUTOMATIC DIFFERENTIATION
Biblical
cluster of figs
Girl/Female
Bengali, Hindu, Indian, Kannada
Little Heart
Boy/Male
Gujarati, Hawaiian, Hebrew, Hindu, Indian, Kannada, Marathi, Telugu
Deer; Sky; Wolf
Male
Hindi/Indian
(अà¤à¤¯) Hindi name ABHAY means "brave; fearless."
Surname or Lastname
English
English : occupational name for a gatherer or seller of woad, from an agent derivative of Middle English wade ‘woad’ (Old English wÄd). This plant produces a blue dye, which was widely used in the Middle Ages.
Girl/Female
Arabic, Danish
Shield of Allah
Boy/Male
Muslim
Religion, Faith, Belief
Female
Irish
Variant spelling of Irish Gaelic Eithne, AITHNEA means "kernel."
Boy/Male
Gaelic Welsh
Great.
Female
Hebrew
(×§Ö·×¨Ö°× Ö´×™) Hebrew unisex name KARNI means "my horn," a symbol of strength. Also spelled Carni.
AUTOMATIC DIFFERENTIATION
AUTOMATIC DIFFERENTIATION
AUTOMATIC DIFFERENTIATION
AUTOMATIC DIFFERENTIATION
AUTOMATIC DIFFERENTIATION
n.
An apparatus for automatic ignition.
a.
Not voluntary; not depending on the will; mechanical; as, automatic movements or functions.
a.
Automatic.
n.
A medicine for diseases of the mouth.
a.
Aromatic.
n.
The state or quality of being automatic; the power of self-moving; automatic, mechanical, or involuntary action. (Metaph.) A theory as to the activity of matter.
pl.
of Automaton
a.
Alt. of Axiomatical
adv.
In an automatic manner.
v. i.
Any thing or being regarded as having the power of spontaneous motion or action.
a.
Alt. of Automatical
pl.
of Automaton
n.
A person affected with asthma.
a.
Pertaining to, or produced by, an automaton; of the nature of an automaton; self-acting or self-regulating under fixed conditions; -- esp. applied to machinery or devices in which certain things formerly or usually done by hand are done by the machine or device itself; as, the automatic feed of a lathe; automatic gas lighting; an automatic engine or switch; an automatic mouse.
a.
Having an inherent power of action or motion.
a.
Alt. of Autocratical
v. i.
A self-moving machine, or one which has its motive power within itself; -- applied chiefly to machines which appear to imitate spontaneously the motions of living beings, such as men, birds, etc.
a.
Alt. of Autoptical
a.
Of or pertaining to a stoma; of the nature of a stoma.
a.
Alt. of Asthmatical