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Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equat…
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 a…
Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
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
Mathematical Optimization in Julia. Local, global, gradient-based and derivative-free. Linear, Quadratic, Convex, Mixed-Integer, and Nonlinear Optimization in one simple, fast, and differentiable i…
Grid-based approximation of partial differential equations in Julia
High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learni…
Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.
Special mathematical functions in Julia
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…
The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
The JuliaFEM software library is a framework that allows for the distributed processing of large Finite Element Models across clusters of computers using simple programming models. It is designed t…
Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem
Julia interface to Sundials, including a nonlinear solver (KINSOL), ODE's (CVODE and ARKODE), and DAE's (IDA) in a SciML scientific machine learning enabled manner
A package for binary and continuous, single and multi-material, truss and continuum, 2D and 3D topology optimization on unstructured meshes using automatic differentiation in Julia.
Automatic Finite Difference PDE solving with Julia SciML
A development environment for robust and global optimization
Build and simulate jump equations like Gillespie simulations and jump diffusions with constant and state-dependent rates and mix with differential equations and scientific machine learning (SciML)
This is a Julia package of nonlinear solvers. These codes are used in my book, Solving Nonlinear Equations with Iterative Methods: Solvers and Examples in Julia.
A standard library of components to model the world and beyond
Sparse, General Linear Algebra for Graphs!
Global documentation for the Julia SciML Scientific Machine Learning Organization
Gmsh.jl contains API for Gmsh: a three-dimensional finite element mesh generator. With the help of Gmsh.jl, it is possible add parametric model construction and/or automatic mesh generation to a FE…
Boundary value problem (BVP) solvers for scientific machine learning (SciML)
RHEOS - Open Source Rheology data analysis software
