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.

Award winning software library for nonlinear dynamics and nonlinear timeseries analysis

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

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.

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

Arrays with arbitrarily nested named components.

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

StateSpaceModels.jl is a Julia package for time-series analysis using state-space models.

Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem

Julia interface to Sundials, including a nonlinear solver (KINSOL), ODE's (CVODE and ARKODE), and DAE's (IDA) in a SciML scientific machine learning enabled manner

Computing reachable states of dynamical systems in Julia

Automatic Finite Difference PDE solving with Julia SciML

Solve non-linear HJB equations.

Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

Fast and automatic structural identifiability software for ODE systems

Assorted basic Ordinary Differential Equation solvers for scientific machine learning (SciML). Deprecated: Use DifferentialEquations.jl instead.

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

Solve Fractional Differential Equations using high performance numerical methods

A simple domain-specific language (DSL) for defining differential equations for use in scientific machine learning (SciML) and other applications

Flexible filtering and smoothing in Julia

A Julia package for Deep Backwards Stochastic Differential Equation (Deep BSDE) and Feynman-Kac methods to solve high-dimensional PDEs without the curse of dimensionality

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

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

A package for performing Singular Spectrum Analysis (SSA) and time-series decomposition

Julia package for solving singular integral equations

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

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.

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

Geometric Numerical Integration in Julia

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

No need to train, he's a smooth operator

A Julia package for solving Riemann–Hilbert problems

Integrals of arbitrary powers of R over flat triangles

HP Finite elements in Julia

Spectral element code implemented in Julia

Moving collocation method to solve one dimensional partial differential equations