Equation-based modeling and simulations in Julia

Assorted basic Ordinary Differential Equation solvers for scientific machine learning (SciML). Deprecated: Use DifferentialEquations.jl instead.

Package for dynamical modeling of power grids

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

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

A helper tool for visualizing and editing a ModelingToolkit.jl system connections

A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solvers

Rigorous floating-point calculations with interval arithmetic in Julia

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!

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.

Solve Fractional Differential Equations using high performance numerical methods

ClimaAtmos.jl is a library for building atmospheric circulation models that is designed from the outset to leverage data assimilation and machine learning tools. We welcome contributions!

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

A julia package for representing and manipulating model semantics

Modeling and Simulation of 3D systems

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

The amazing Reaction Mechanism Simulator for simulating large chemical kinetic mechanisms

Julia toolkit for open quantum system simulation.

A Julia package for Deep Backwards Stochastic Differential Equation (Deep BSDE) and Feynman-Kac methods to solve high-dimensional PDEs without the curse of dimensionality

Simulation and visualization of articulated rigid body systems in Julia

A simple tool for simulating trapped ion systems

Generalized mean-field equations in open quantum systems

Global glacier model using Universal Differential Equations for climate-glacier interactions

High-performance simulations of the Porous Electrode Theory for Li-ion batteries

Fast uncertainty quantification for scientific machine learning (SciML) and differential equations

Fast uncertainty quantification for scientific machine learning (SciML) and differential equations

An open-source framework written in Julia for global integrated assessment models.

An open source model predictive control package for Julia.

A library of noise processes for stochastic systems like stochastic differential equations (SDEs) and other systems that are present in scientific machine learning (SciML)

Fast and simple nonlinear solvers for the SciML common interface. Newton, Broyden, Bisection, Falsi, and more rootfinders on a standard interface.

Rigorous function approximation using Taylor models in Julia

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Atomic graph models for molecules and crystals in Julia

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

Easy scientific machine learning (SciML) parameter estimation with pre-built loss functions

Choo-choo

Delay differential equation (DDE) solvers in Julia for the SciML scientific machine learning ecosystem. Covers neutral and retarded delay differential equations, and differential-algebraic equations.

FMIFlux.jl is a free-to-use software library for the Julia programming language, which offers the ability to place FMUs (fmi-standard.org) everywhere inside of your ML topologies and still keep the resulting model trainable with a standard (or custom) FluxML training process.

Robust and optimal design and analysis of linear control systems