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.

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A SciML symbolic-numeric compiler tool for investigating functions in order to perform optimizations

Implementation of the finite volume method in 1D.

Solver for two-dimensional conservation equations using the finite volume method in Julia.

Finite State Projection algorithms for chemical reaction networks

Faster `findfirst(==(val), dense_vector)`.

A scientific machine learning (SciML) wrapper for the FEniCS Finite Element library in the Julia programming language

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Fast and differentiable implementations of matrix exponentials, Krylov exponential matrix-vector multiplications ("expmv"), KIOPS, ExpoKit functions, and more. All your exponential needs in SciML form.

Julia-based implementation of ellipsis array indexing notation `..`

High level functions for analyzing the output of simulations

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

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.

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

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

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

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.

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

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

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

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

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

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

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

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)

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

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

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

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

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

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

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

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

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

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

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

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.

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

A deprecated way of handling discrete data in continuous equations