SciML

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential...

Parallel Computing and Scientific Machine Learning (SciML): Methods and Applications (MIT 18.337J/6.338J)

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...

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...

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

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine...

Solving differential equations in Python using DifferentialEquations.jl and 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.

Black-box optimization for Julia

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

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...

Surrogate modeling and optimization for scientific machine learning (SciML)

Arrays with arbitrarily nested named components.

The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems

Evolutionary & genetic algorithms for Julia

Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R

Documentation for the DiffEq differential equations and scientific machine learning (SciML) ecosystem

GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem

High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.

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

LinearSolve.jl: High-Performance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.

DeepONets, (Fourier) Neural Operators, Physics-Informed Neural Operators, and more in Julia

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

A library of data interpolation and smoothing functions

A common interface for quadrature and numerical integration for the SciML scientific machine learning organization

A style guide for stylish Julia developers

Tools for easily handling objects like arrays of arrays and deeper nestings in scientific machine learning (SciML) and other applications

Reservoir computing utilities for scientific machine learning (SciML)

Julia interface to Sundials, including a nonlinear solver (KINSOL), ODEs (CVODE and ARKODE), and DAEs (IDA)

Automatic Finite Difference PDE solving with Julia SciML

The Base interface of the SciML ecosystem

A standard library of components to model the world and beyond

High-Performance Scientific Modeling with Julia and SciML

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)

Solving differential equations in R using DifferentialEquations.jl and the SciML Scientific Machine Learning ecosystem

A differentiable simulator for scientific machine learning (SciML) with N-body problems, including astrophysical and molecular dynamics

Contributor's Guide on Collaborative Practices for Community Packages

Fast and automatic structural identifiability software for ODE systems

SymbolicNumericIntegration.jl: Symbolic-Numerics for Solving Integrals

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

Tools for building non-allocating pre-cached functions in Julia, allowing for GC-free usage of automatic differentiation in complex codes

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

Arrays which also have a label for each element for easy scientific machine learning (SciML)

Lightweight and easy generation of quasi-Monte Carlo sequences with a ton of different methods on one API for easy parameter exploration in scientific machine learning (SciML)

A Julia package to construct orthogonal polynomials, their quadrature rules, and use it with polynomial chaos expansions.

Functions generated at runtime without world-age issues or overhead

Fast and differentiable implementations of matrix exponentials, Krylov exponential matrix-vector multiplications ("expmv"), KIOPS, ExpoKit functions, and more. All your exponential needs in SciML...

A scientific machine learning (SciML) wrapper for the FEniCS Finite Element library in the Julia programming language

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Least squares and curve fitting in Julia with speed and robustness

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

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

Julia-based implementation of ellipsis array indexing notation `..`

Global documentation for the Julia SciML Scientific Machine Learning Organization

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

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

Automatic optimization and parallelization for Scientific Machine Learning (SciML)

The SciML Scientific Machine Learning Software Organization Website

Repository for automatic differentiation backend types

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

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

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

Robust, Fast, and Parallel Global Sensitivity Analysis (GSA) in Julia

Static types useful for dispatch and generated functions.

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

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

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.

Boundary value problem (BVP) solvers for scientific machine learning (SciML)

Implicit Layer Machine Learning via Deep Equilibrium Networks, O(1) backpropagation with accelerated convergence.

Automatic detection of sparsity in pure Julia functions for sparsity-enabled scientific machine learning (SciML)

SciMLOperators.jl: Matrix-Free Operators for the SciML Scientific Machine Learning Common Interface in Julia

Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)

Solver for two-dimensional conservation equations using the finite volume method in Julia.

This package contains a macro for converting expressions to use muladd calls and fused-multiply-add (FMA) operations for high-performance in the SciML scientific machine learning ecosystem

Finds relationships between the parameters of a mathematical model

A course on composable system modeling, differential-algebraic equations, acausal modeling, compilers for simulation, and building digital twins of real-world devices

A library for building differential equations arising from physical problems for physics-informed and scientific machine learning (SciML)

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