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.

Bayesian inference with probabilistic programming.

Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

Solve and estimate Dynamic Stochastic General Equilibrium models (including the New York Fed DSGE)

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

Award winning software library for nonlinear dynamics and nonlinear timeseries analysis

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

Grid-based approximation of partial differential equations in Julia

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

Library for the numerical simulation of closed as well as open quantum systems.

Trixi.jl: Adaptive high-order numerical simulations of conservation laws in Julia

A Control Systems Toolbox for Julia

Probabilistic programming via source rewriting

"Distributions" that might not add to one.

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 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.

Modeling and simulation of multidomain engineering systems

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

Implementation of robust dynamic Hamiltonian Monte Carlo methods (NUTS) in Julia.

Robust, modular and efficient implementation of advanced Hamiltonian Monte Carlo algorithms

Tools for the exploration of chaos and nonlinear dynamics

Implementations of the models from the Statistical Rethinking book with Turing.jl

Causal, Higher-Order, Probabilistic Programming

Automatic Finite Difference PDE solving with Julia SciML

System Identification toolbox, compatible with ControlSystems.jl

A differentiable simulator for scientific machine learning (SciML) with N-body problems, including astrophysical and molecular dynamics

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

Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

Causal.jl - A modeling and simulation framework adopting causal modeling approach.

State estimation, smoothing and parameter estimation using Kalman and particle filters.

Equation-based modeling and simulations in Julia

Package for dynamical modeling of power grids

Parallel distributed-memory version of Gridap

Core functions for the Julia (2nd) edition of the text Fundamentals of Numerical Computation, by Driscoll and Braun.

A framework for simulating viscous incompressible flows about arbitrary body shapes.

A Julia library of summation-by-parts (SBP) operators used in finite difference, Fourier pseudospectral, continuous Galerkin, and discontinuous Galerkin methods to get provably stable semidiscretizations, paying special attention to boundary conditions.

A Julia rewrite of Dynare: solving, simulating and estimating DSGE models.

FMI.jl is a free-to-use software library for the Julia programming language which integrates FMI (fmi-standard.org): load or create, parameterize, differentiate and simulate FMUs seamlessly inside the Julia programming language!