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

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

Universal neural differential equations with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods

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

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

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

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

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

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

Modeling and simulation of multidomain engineering systems

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.

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

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

Automatic Finite Difference PDE solving with Julia SciML

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

Equation-based modeling and simulations in Julia

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

Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

SymbolicNumericIntegration.jl: Symbolic-Numerics for Solving Integrals

Package for dynamical modeling of power grids

Rigorous floating-point calculations with interval arithmetic in Julia

A standard library of components to model the world and beyond

A julia package for representing and manipulating model semantics

OrbitalTrajectories.jl is a modern orbital trajectory design, optimisation, and analysis library for Julia, providing methods and tools for designing spacecraft orbits and transfers via high-performance simulations of astrodynamical models.

High level functions for analyzing the output of simulations

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

Modeling and Simulation of 3D systems

A framework for developing multi-scale arrays for use in scientific machine learning (SciML) simulations

Fast and automatic structural identifiability software for ODE systems

A simple tool for simulating trapped ion systems

Calculate rigorously the feasible region for a set of real-valued inequalities with Julia

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

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!

Atomic graph models for molecules and crystals in Julia

The amazing Reaction Mechanism Simulator for simulating large chemical kinetic mechanisms

Generalized mean-field equations in open quantum systems

CellMLToolkit.jl is a Julia library that connects CellML models to the Scientific Julia ecosystem.

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