Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components

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

A 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

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

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

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

Modeling and simulation of multidomain engineering systems

Local, global, and beyond optimization for scientific machine learning (SciML)

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

Linear operators for discretizations of differential equations and scientific machine learning (SciML)

Turing version of StatisticalRethinking models.

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

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

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

Rigorous floating-point calculations with interval arithmetic in Julia

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

Probabilistic ODE Solvers via Bayesian Filtering and Smoothing

Probabilistic ODE Solvers via Bayesian Filtering and Smoothing

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

Universal modeling and simulation of fluid dynamics upon machine learning

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.

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Generalized mean-field equations in open quantum systems

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

A library of premade problems for examples and testing differential equation solvers and other SciML scientific machine learning tools

Model and simulate physical systems (electrical, mechanical, thermo-fluild, ...)

A suite of tools for solving Nonlinear Schrodinger equations via higher-order algorithms and Darboux transformations.

Finds relationships between the parameters of a mathematical model

Simulation of simple controls problems in Julia

Pure Julia Implementation of Geometrically Exact Beam Theory

Julia MathML parser

Julia toolbox for underwater acoustic modeling

Common interface bindings for the MATLAB ODE solvers via MATLAB.jl for the SciML Scientific Machine Learning ecosystem

Develop tools for ensemble Kalman filter

Lightweight module of neural differential equations in Kinetic.jl

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Building dynamical systems compositionally

Methods for computational information geometry