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

Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with 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 library of data interpolation and smoothing functions

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

Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

SymbolicNumericIntegration.jl: Symbolic-Numerics for Solving Integrals

A standard library of components to model the world and beyond

Equation-based modeling and simulations in Julia

Exploratory analysis of Bayesian models with Julia

Package for dynamical modeling of power grids

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

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

The amazing Reaction Mechanism Simulator for simulating large chemical kinetic mechanisms

Generalized mean-field equations in open quantum systems

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

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

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

Choo-choo

Efficient, Accurate, and Streamlined Training of Physics-Informed Neural Networks

Finds relationships between the parameters of a mathematical model

Tools to generate and study moment equations for any chemical reaction network using various moment closure approximations

A full end-to-end modular software suite for radiative transfer and related atmospheric analysis

Methods for computational information geometry

Common functions in actuarial and financial routines

SBML differential equation and chemical reaction model (Gillespie simulations) for Julia's SciML ModelingToolkit

High Quality Geophysical Analysis provides a general purpose Bayesian and deterministic inversion framework for various geophysical methods and spatially distributed / timeseries data

An interface for accelerated simulation of high-dimensional collisionless and electrostatic plasmas.

High-level model-order reduction to automate the acceleration of large-scale simulations

Create parameter estimation problems for ODE models

Composable contracts, models, and functions that allow for modeling of both simple and complex financial instruments

A library of systems of partial differential equations, as defined with ModelingToolkit.jl in Julia

A component library based on ModelingToolkit

ParameterEstimation.jl is a Julia package for estimating parameters and initial conditions of ODE models given measurement data.

Julia Catalyst.jl importers for various reaction network file formats like BioNetGen and stoichiometry matrices