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.

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

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

LinearSolve.jl: High-Performance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.

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

Solution of nonlinear multiphysics partial differential equation systems using the Voronoi finite volume method

Tools for the exploration of chaos and nonlinear dynamics

A package for binary and continuous, single and multi-material, truss and continuum, 2D and 3D topology optimization on unstructured meshes using automatic differentiation in Julia.

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

Automatic Finite Difference PDE solving with Julia SciML

Interior-point solver in pure Julia

Predictive Uncertainty Quantification through Conformal Prediction for Machine Learning models trained in MLJ.

System Identification toolbox, compatible with ControlSystems.jl

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

Algorithms from circuit theory to predict connectivity in heterogeneous landscapes

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

Automatic differentiation of implicit functions

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

Algebraic Multigrid in Julia

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.