Catalyst
Catalyst: a Python JIT compiler for auto-differentiable hybrid quantum programs - Published in JOSS (2024)
TaylorSeries.jl
TaylorSeries.jl: Taylor expansions in one and several variables in Julia - Published in JOSS (2019)
torchquad
torchquad: Numerical Integration in Arbitrary Dimensions with PyTorch - Published in JOSS (2021)
Krang
Krang: Kerr Raytracer for Analytic Null Geodesics - Published in JOSS (2024)
tensorcircuit
Tensor network based quantum software framework for the NISQ era
tensorcircuit-ng
The next-gen tensor network based quantum software framework: superseding the original TensorCircuit
pyerrors
Error propagation and statistical analysis for Monte Carlo simulations in lattice QCD and statistical mechanics using autograd.
pinocchio
A fast and flexible implementation of Rigid Body Dynamics algorithms and their analytical derivatives
torchopt
TorchOpt is an efficient library for differentiable optimization built upon PyTorch.
aesara
Aesara is a Python library for defining, optimizing, and efficiently evaluating mathematical expressions involving multi-dimensional arrays.
tensors.jl
Efficient computations with symmetric and non-symmetric tensors with support for automatic differentiation.
https://github.com/sciml/surrogates.jl
Surrogate modeling and optimization for scientific machine learning (SciML)
https://github.com/ami-iit/jaxsim
A differentiable physics engine and multibody dynamics library for control and robot learning.
differentiationinterface.jl
An interface to various automatic differentiation backends in Julia.
RadonKA
A simple yet sufficiently fast (attenuated) Radon and backproject implementation using KernelAbstractions.jl. Runs on CPU, CUDA, ...
yaeos
Thermodynamic Equations of State, Fortran library with both automatic and anallytical derivation capabilities
pennylane
PennyLane is a cross-platform Python library for quantum computing, quantum machine learning, and quantum chemistry. Built by researchers, for research.
hypermat
Hyperelastic formulations using an algorithmic differentiation with hyper-dual numbers in Python.
https://github.com/SciML/Optimization.jl
Mathematical Optimization in Julia. Local, global, gradient-based and derivative-free. Linear, Quadratic, Convex, Mixed-Integer, and Nonlinear Optimization in one simple, fast, and differentiable interface.
MITgcm
M.I.T General Circulation Model master code and documentation repository
Integrals
A common interface for quadrature and numerical integration for the SciML scientific machine learning organization
xcfun
XCFun: A library of exchange-correlation functionals with arbitrary-order derivatives
MultiScaleArrays
A framework for developing multi-scale arrays for use in scientific machine learning (SciML) simulations
PreallocationTools
Tools for building non-allocating pre-cached functions in Julia, allowing for GC-free usage of automatic differentiation in complex codes
Grassmann
⟨Grassmann-Clifford-Hodge⟩ multilinear differential geometric algebra
ott-jax
Optimal transport tools implemented with the JAX framework, to solve large scale matching problems of any flavor.
https://github.com/simple-robotics/pycppad
Python bindings for CppAD and CppADCodeGen using Boost.Python
https://github.com/ami-iit/adam
adam implements a collection of algorithms for calculating rigid-body dynamics in Jax, CasADi, PyTorch, and Numpy.
NBodySimulator
A differentiable simulator for scientific machine learning (SciML) with N-body problems, including astrophysical and molecular dynamics
mrst
Official GitHub repository for MRST - the MATLAB Reservoir Simulation Toolbox
diffeqdevmaterials
Various developer materials, like PDFs, notes, derivations, etc. for differential equations and scientific machine learning (SciML)
https://github.com/thoughtworksinc/deeplearning.scala
A simple library for creating complex neural networks
https://github.com/kul-optec/abstractoperators.jl
Abstract operators for large scale optimization in Julia
swiftt
SoftWare for Intrusive Function's Taylor-series Truncation (swiftt), a Pure Python library implementing the Taylor Differential Algebra
varipeps_python
variPEPS -- Versatile tensor network library for variational ground state simulations in two spatial dimensions
sparsematrixcolorings.jl
Coloring algorithms for sparse Jacobian and Hessian matrices
differentiableexpectations.jl
A Julia package for differentiating through expectations with Monte-Carlo estimates
ExaModels
An algebraic modeling and automatic differentiation tool in Julia Language, specialized for SIMD abstraction of nonlinear programs.
control-neuralode
Neural ODEs as Feedback Policies for Nonlinear Optimal Control (IFAC 2023) https://doi.org/10.1016/j.ifacol.2023.10.1248
physics.net.mathematics
Mathematics.NET is a C# class library that provides tools for solving advanced mathematical problems.
seismic-inversion
Seismic inversion using a neural network regulariser implemented as an ExternalOperator in Firedrake
pyrddlgym-jax
JAX compilation of RDDL description files, and a differentiable planner in JAX.
Tesseract Core
Tesseract Core: Universal, autodiff-native software components for Simulation Intelligence - Published in JOSS (2025)
physics.net
Physics.NET is a C# class libary that provides tools for solving physics problems.
differentiablefrankwolfe.jl
Differentiable wrapper for FrankWolfe.jl convex optimization routines
https://github.com/byuflowlab/implicitad.jl
Automates steady and unsteady adjoints (general solvers and ODEs respectively). Forward and reverse mode algorithmic differentiation around implicit functions (not propagating AD through), as well as custom rules to allow for mixed-mode AD or calling external (non-AD compatible) functions within an AD chain.
https://github.com/blegat/lsinc1113
Course material for the course LSINC1113 at UCLouvain
memoized_coduals
Shows that it is possible to implement reverse mode autodiff using a variation on the dual numbers called the codual numbers
PathSim - A System Simulation Framework
PathSim - A System Simulation Framework - Published in JOSS (2025)