Search Results for "automatic differentiation"
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Showing 77 open source projects for "automatic differentiation"
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ImplicitDifferentiation.jl
Automatic differentiation of implicit functions
ImplicitDifferentiation.jl is a package for automatic differentiation of functions defined implicitly, i.e., forward mappings. Those for which automatic differentiation fails. Reasons can vary depending on your backend, but the most common include calls to external solvers, mutating operations or type restrictions. Those for which automatic differentiation is very slow. A common example is iterative procedures like fixed point equations or optimization algorithms. -
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ForwardDiff.jl
Forward Mode Automatic Differentiation for Julia
ForwardDiff implements methods to take derivatives, gradients, Jacobians, Hessians, and higher-order derivatives of native Julia functions (or any callable object, really) using forward mode automatic differentiation (AD). While performance can vary depending on the functions you evaluate, the algorithms implemented by ForwardDiff generally outperform non-AD algorithms (such as finite-differencing) in both speed and accuracy. Functions like f which map a vector to a scalar are the best case for reverse-mode automatic differentiation, but ForwardDiff may still be a good choice if x is not too large, as it is much simpler. ... -
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ReverseDiff
Reverse Mode Automatic Differentiation for Julia
ReverseDiff is a fast and compile-able tape-based reverse mode automatic differentiation (AD) that implements methods to take gradients, Jacobians, Hessians, and higher-order derivatives of native Julia functions (or any callable object, really). While performance can vary depending on the functions you evaluate, the algorithms implemented by ReverseDiff generally outperform non-AD algorithms in both speed and accuracy. -
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Enzyme.jl
Julia bindings for the Enzyme automatic differentiator
This is a package containing the Julia bindings for Enzyme. This is very much a work in progress and bug reports/discussion is greatly appreciated. Enzyme is a plugin that performs automatic differentiation (AD) of statically analyzable LLVM. It is highly-efficient and its ability perform AD on optimized code allows Enzyme to meet or exceed the performance of state-of-the-art AD tools. -
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VoronoiFVM.jl
Solution of nonlinear multiphysics partial differential equations
Solver for coupled nonlinear partial differential equations (elliptic-parabolic conservation laws) based on the Voronoi finite volume method. It uses automatic differentiation via ForwardDiff.jl and DiffResults.jl to evaluate user functions along with their jacobians and calculate derivatives of solutions with respect to their parameters. -
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StructuralEquationModels.jl
A fast and flexible Structural Equation Modelling Framework
...We provide fast objective functions, gradients, and for some cases hessians as well as approximations thereof. As a user, you can easily define custom loss functions. For those, you can decide to provide analytical gradients or use finite difference approximation / automatic differentiation. You can choose to mix loss functions natively found in this package and those you provide. In such cases, you optimize over a sum of different objectives (e.g. ML + Ridge). This strategy also applies to gradients, where you may supply analytic gradients or opt for automatic differentiation or mixed analytical and automatic differentiation. ... -
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Taichi
Productive, portable, and performant GPU programming in Python
...It uses JIT compilation (via LLVM and its runtime TiRT) to offload compute-heavy code to CPUs, GPUs, mobile devices, and embedded systems. With built-in support for sparse data structures (SNode), automatic differentiation, AOT deployment, and compatibility with CUDA, Vulkan, Metal, and OpenGL ES, it empowers disciplines like simulation, graphics, AI, and robotics -
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Agent Executor (AX)
Google's open source distributed agent runtime
...It is designed for situations where a model needs to predict choices from a finite set of alternatives, such as ranking, recommendation, preference modeling, or decision behavior analysis. The project provides JAX-based tools for defining and training choice models with automatic differentiation. It focuses on flexible model construction rather than a single fixed estimator, making it useful for researchers who want to experiment with different utility functions and optimization setups. ax is especially relevant for machine learning and econometrics workflows that need scalable, differentiable approaches to choice modeling. ... -
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ggml
Tensor library for machine learning
ggml is an open-source tensor library designed for efficient machine learning computation with a focus on running models locally and with minimal dependencies. Written primarily in C and C++, the library provides low-level tensor operations and automatic differentiation that allow developers to implement machine learning algorithms and neural networks efficiently. The project emphasizes portability and performance, enabling machine learning inference across a wide range of hardware environments including CPUs and specialized accelerators. It is widely used as a foundational component in projects that run large language models locally, including tools that perform inference for transformer-based models. ... -
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Yao
Extensible, Efficient Quantum Algorithm Design for Humans
An intermediate representation to construct and manipulate your quantum circuit and let you make own abstractions on the quantum circuit in native Julia. Yao supports both forward-mode (faithful gradient) and reverse-mode automatic differentiation with its builtin engine optimized specifically for quantum circuits. Top performance for quantum circuit simulations. Its CUDA backend and batched quantum register support can make typical quantum circuits even faster. Yao is designed to be extensible. Its hierarchical architecture allows you to extend the framework to support and share your new algorithm and hardware. -
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ChainRulesCore
AD-backend agnostic system defining custom forward and reverse rules
...The ChainRulesCore package provides a light-weight dependency for defining sensitivities for functions in your packages, without you needing to depend on ChainRules itself. This will allow your package to be used with ChainRules.jl, which aims to provide a variety of common utilities that can be used by downstream automatic differentiation (AD) tools to define and execute forward-, reverse-, and mixed-mode primitives. -
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DynamicHMC
Implementation of robust dynamic Hamiltonian Monte Carlo methods
...In contrast to frameworks that utilize a directed acyclic graph to build a posterior for a Bayesian model from small components, this package requires that you code a log-density function of the posterior in Julia. Derivatives can be provided manually, or using automatic differentiation. Consequently, this package requires that the user is comfortable with the basics of the theory of Bayesian inference, to the extent of coding a (log) posterior density in Julia. This approach allows the use of standard tools like profiling and benchmarking to optimize its performance. -
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ChainRules.jl
Forward and reverse mode automatic differentiation primitives
The ChainRules package provides a variety of common utilities that can be used by downstream automatic differentiation (AD) tools to define and execute forward-, reverse--, and mixed-mode primitives. The core logic of ChainRules is implemented in ChainRulesCore.jl. To add ChainRules support to your package, by defining new rules or frules, you only need to depend on the very light-weight package ChainRulesCore.jl. This repository contains ChainRules.jl, which is what people actually use directly. ... -
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Diffrax
Numerical differential equation solvers in JAX
...The project provides tools for solving ordinary differential equations, stochastic differential equations, controlled differential equations, and related systems in a way that fits naturally into modern machine learning and differentiable programming workflows. Because it is written to work closely with JAX, it supports just-in-time compilation, automatic differentiation, vectorization, and accelerator-backed execution on hardware such as GPUs and TPUs. This makes it especially appealing for researchers who need equation solvers that can be embedded inside trainable models or simulation-heavy learning systems. -
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micrograd
A tiny scalar-valued autograd engine and a neural net library
micrograd is a tiny, educational automatic differentiation engine focused on scalar values, built to show how backpropagation works end to end with minimal code. It constructs a dynamic computation graph as you perform math operations and then computes gradients by walking that graph backward, making it an approachable “from scratch” autograd reference. On top of the core autograd “Value” concept, the project includes a small neural network library that lets you define and train simple models with a PyTorch-like feel, including multilayer perceptrons. ... -
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TensorFlow Quantum
Open-source Python framework for hybrid quantum-classical ml learning
...TensorFlow Quantum integrates with the Cirq quantum computing framework to define and manipulate quantum circuits, while leveraging TensorFlow’s infrastructure for optimization, automatic differentiation, and large-scale computation. The library also supports high-performance simulation of quantum circuits, enabling researchers to test and evaluate quantum models even without direct access to quantum hardware. -
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PyTorch
Open source machine learning framework
PyTorch is a Python package that offers Tensor computation (like NumPy) with strong GPU acceleration and deep neural networks built on tape-based autograd system. This project allows for fast, flexible experimentation and efficient production. PyTorch consists of torch (Tensor library), torch.autograd (tape-based automatic differentiation library), torch.jit (a compilation stack [TorchScript]), torch.nn (neural networks library), torch.multiprocessing (Python multiprocessing), and torch.utils (DataLoader and other utility functions). PyTorch can be used as a replacement for Numpy, or as a deep learning research platform that provides optimum flexibility and speed. -
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JAX
Composable transformations of Python+NumPy programs
...But JAX also lets you just-in-time compile your own Python functions into XLA-optimized kernels using a one-function API, jit. Compilation and automatic differentiation can be composed arbitrarily, so you can express sophisticated algorithms and get maximal performance without leaving Python. -
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NNlib.jl
Neural Network primitives with multiple backends
This package provides a library of functions useful for neural networks, such as softmax, sigmoid, batched multiplication, convolutions and pooling. Many of these are used by Flux.jl, which loads this package, but they may be used independently. -
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CasADi
CasADi is a symbolic framework for numeric optimization
CasADi is a symbolic framework for numeric optimization implementing automatic differentiation in forward and reverse modes on sparse matrix-valued computational graphs. It supports self-contained C-code generation and interfaces state-of-the-art codes such as SUNDIALS, IPOPT, etc. It can be used in C++, Python, or Matlab/Octave. CasADi's backbone is a symbolic framework implementing forward and reverse modes of AD on expression graphs to construct gradients, large-and-sparse Jacobians, and Hessians. ... -
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PETSc.jl
Julia wrappers for the PETSc library
This package provides a low level interface for PETSc and allows combining julia features (such as automatic differentiation) with the PETSc infrastructure and nonlinear solvers. -
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NonlinearSolve.jl
High-performance and differentiation-enabled nonlinear solvers
...The package includes its own high-performance nonlinear solvers which include the ability to swap out to fast direct and iterative linear solvers, along with the ability to use sparse automatic differentiation for Jacobian construction and Jacobian-vector products. NonlinearSolve.jl interfaces with other packages of the Julia ecosystem to make it easy to test alternative solver packages and pass small types to control algorithm swapping. It also interfaces with the ModelingToolkit.jl world of symbolic modeling to allow for automatically generating high-performance code. -
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DiffEqFlux.jl
Pre-built implicit layer architectures with O(1) backprop, GPUs
DiffEqFlux.jl is a Julia library that combines differential equations with neural networks, enabling the creation of neural differential equations (neural ODEs), universal differential equations, and physics-informed learning models. It serves as a bridge between the DifferentialEquations.jl and Flux.jl libraries, allowing for end-to-end differentiable simulations and model training in scientific machine learning. DiffEqFlux.jl is widely used for modeling dynamical systems with learnable... -
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Tequila
A High-Level Abstraction Framework for Quantum Algorithms
Tequila is an abstraction framework for (variational) quantum algorithms. It operates on abstract data structures allowing the formulation, combination, automatic differentiation and optimization of generalized objectives. Tequila can execute the underlying quantum expectation values on state-of-the-art simulators as well as on real quantum devices. -
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CoordinateTransformations.jl
A fresh approach to coordinate transformations
...Transformations can be easily applied, inverted, composed, and differentiated (both with respect to the input coordinates and with respect to transformation parameters such as rotation angle). Transformations are designed to be light-weight and efficient enough for, e.g., real-time graphical applications, while support for both explicit and automatic differentiation makes it easy to perform optimization and therefore ideal for computer vision applications such as SLAM (simultaneous localization and mapping).
