JuliaDiff/ForwardDiff.jl

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1004 stars · 160 forks observed · 2026-09-03

What it is AI-extracted, prompt v1, taxonomy v1, 2026-08-30, confidence not recorded

ForwardDiff.jl is a Julia library implementing forward mode automatic differentiation for computing derivatives, gradients, Jacobians, Hessians, and higher-order derivatives of native Julia functions. It uses dual numbers to deliver exact derivatives that generally outperform finite-differencing in both speed and accuracy.

Use cases

• compute gradients of Julia functions for optimization
• calculate Jacobians of vector-valued functions
• compute Hessians for second-order optimization
• take derivatives of scalar functions exactly
• replace finite-difference approximations with exact AD
• differentiate arbitrary callable objects in Julia

When to choose

• you need exact derivatives of Julia code without manual derivation
• your functions map scalars to vectors or have moderate input dimensionality
• you want faster and more accurate results than finite differencing
• you are doing scientific computing or optimization in Julia

When to avoid

• your function has very large input dimensions where reverse-mode AD is more efficient
• you are not working in the Julia language
• your code uses operations that AD cannot differentiate through

Facets

library · maturity stable

math machine-learning data-science jvm-scripting julia automatic-differentiation forward-mode-ad calculus dual-numbers gradients jacobians hessians scientific-computing optimization algorithms

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markdown · JSON · MCP: product_card(name="JuliaDiff/ForwardDiff.jl")