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

Julia Animations and Visualizations

Macro(s) for vectorizing loops.

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

Fast and simple fluid simulator in Julia

Julia package for function approximation

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

Julia Implementation of Transformer models

A Control Systems Toolbox for Julia

An extensible framework for geospatial data science and geostatistical modeling fully written in Julia

Compiles Julia code to a standalone library (experimental)

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.

Density-functional toolkit

Probabilistic programming via source rewriting

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

A Julia package for fitting (statistical) mixed-effects models

"Distributions" that might not add to one.

Julia package with selected functions in the R package `rethinking`. Used in the SR2... projects.

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

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)

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

Propagation of distributions by Monte-Carlo sampling: Real number types with uncertainty represented by samples.

Julia package for automated Bayesian inference on a factor graph with reactive message passing

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.

The cheapest threads you can find!

The cheapest threads you can find!