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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.

AD-backend agnostic system defining custom forward and reverse mode rules. This is the light weight core to allow you to define rules for your functions in your packages, without depending on any particular AD system. The ChainRulesCore package provides a light-weight dependency for defining sensitivities for functions in your packages, without you needing to depend on ChainRules itself.

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. ...

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.

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. ...

...It enables rapid prototyping and experimentation with minimal syntax overhead by providing a uniform interface to >25 optimization libraries, hence 100+ optimization solvers encompassing almost all classes of optimization algorithms such as global, mixed-integer, non-convex, second-order local, constrained, etc. It allows you to choose an Automatic Differentiation (AD) backend by simply passing an argument to indicate the package to use and automatically generates the efficient derivatives of the objective and constraints while giving you the flexibility to switch between different AD engines as per your problem. Additionally, Optimization.jl takes care of passing problem-specific information to solvers that can leverage it such as the sparsity pattern of the hessian or constraint jacobian and the expression graph.

...EAGO is a deterministic global optimizer designed to address a wide variety of optimization problems, emphasizing nonlinear programs (NLPs), by propagating McCormick relaxations along the factorable structure of each expression in the NLP. Most operators supported by modern automatic differentiation (AD) packages (e.g., +, sin, cosh) are supported by EAGO and a number of utilities for sanitizing native Julia code and generating relaxations on a wide variety of user-defined functions have been included. Currently, EAGO supports problems that have a priori variable bounds defined and have differentiable constraints.

GraphQL is a data query language for APIs and a runtime for fulfilling those queries with your existing data developed by Facebook in 2012 and launched on the internet in 2015. It is an alternative to REST and ad-hoc web service architectures.

...It also seems that it might be better to gradually transition to defining the adjoints directly using ChainRules. A Ray Tracer written completely in Julia. This allows us to leverage the AD capabilities provided by Zygote to differentiate through the Ray Tracer.