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.

An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and automated transformations of differential equations

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.

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

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

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

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

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

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

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

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

High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.

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

Tools for the exploration of chaos and nonlinear dynamics

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

Automatic Finite Difference PDE solving with Julia SciML

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)

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)

System Identification toolbox, compatible with ControlSystems.jl

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

ODE integration using Taylor's method, and more, in Julia

Universal modeling and simulation of fluid mechanics upon machine learning. From the Boltzmann equation, heading towards multiscale and multiphysics flows.

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

SymbolicNumericIntegration.jl: Symbolic-Numerics for Solving Integrals

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