Repository for automatic differentiation backend types

Importers for the BaseModelica standard into the Julia ModelingToolkit ecosystem

Boundary value problem (BVP) solvers for scientific machine learning (SciML)

A thin wrapper over Bridge.jl for the SciML scientific machine learning common interface, enabling new methods for neural stochastic differential equations (neural SDEs)

Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.

CellMLToolkit.jl is a Julia library that connects CellML models to the Scientific Julia ecosystem.

A common solve function for scientific machine learning (SciML) and beyond

Fixing the world one invalidator at a time.

Interface to DASKR, a differential algebraic system solver for the SciML scientific machine learning ecosystem

Solves stiff differential algebraic equations (DAE) using variable stepsize backwards finite difference formula (BDF) in the SciML scientific machine learning organization

Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization

A library of data interpolation and smoothing functions

A deprecated way of handling discrete data in continuous equations

Implicit Layer Machine Learning via Deep Equilibrium Networks, O(1) backpropagation with accelerated convergence.

Delay differential equation (DDE) solvers in Julia for the SciML scientific machine learning ecosystem. Covers neutral and retarded delay differential equations, and differential-algebraic equations.

Wrappers for calling the R deSolve differential equation solvers from Julia for scientific machine learning (SciML)

The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems

Extension functionality which uses Stan.jl, DynamicHMC.jl, and Turing.jl to estimate the parameters to differential equations and perform Bayesian probabilistic scientific machine learning

Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.

A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solvers

Developer documentation for the SciML scientific machine learning ecosystem's differential equation solvers

Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)

Documentation for the DiffEq differential equations and scientific machine learning (SciML) ecosystem

Differential equation problem specifications and scientific machine learning for common financial models

Pre-built implicit layer architectures with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods

GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem

Build and simulate jump equations like Gillespie simulations and jump diffusions with constant and state-dependent rates and mix with differential equations and scientific machine learning (SciML)

Monte Carlo simulation routines for high-performance parallelization of differential equation solvers and scientific machine learning

A library of noise processes for stochastic systems like stochastic differential equations (SDEs) and other systems that are present in scientific machine learning (SciML)

Linear operators for discretizations of differential equations and scientific machine learning (SciML)

Easy scientific machine learning (SciML) parameter estimation with pre-built loss functions

Library for common tools for solving PDEs with finite difference methods (FDM), finite volume methods (FVM), finite element methods (FEM), and psuedospectral methods in a way that integrates with the SciML Scientific Mechine Learning ecosystem

A library for building differential equations arising from physical problems for physics-informed and scientific machine learning (SciML)

A library of premade problems for examples and testing differential equation solvers and other SciML scientific machine learning tools

A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.

Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.

Fast uncertainty quantification for scientific machine learning (SciML) and differential equations

Solving difference equations with DifferenceEquations.jl and the SciML ecosystem.

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.

High dimensional numbers and reductions recipes for data visualization of scientific machine learning (SciML)