SciML/SciMLBook

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SciML/SciMLBook

SciML

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

Parallel Computing and Scientific Machine Learning (SciML): Methods and Applications

This book is a compilation of lecture notes from the MIT Course 18.337J/6.338J: Parallel Computing and Scientific Machine Learning. Links to the old notes https://mitmath.github.io/18337 will redirect here.

This repository is meant to be a live document, updating to continuously add the latest details on methods from the field of scientific machine learning and the latest techniques for high-performance computing.

To view this book, go to book.sciml.ai.

Editing the SciML Book

This is a Franklin.jl site. Much of the material originated from Julia Markdown Documents (*.jmd). Each of these documents are Weave.jl-ed with a custom template, and the resulting HTML is inserted into a corresponding markdown file. Updating the files in _weave will automatically update the webpages.

The theme is adapted from Tufte CSS.

DifferentialEquations.jl

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.

ModelingToolkit.jl

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

NeuralPDE.jl

Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

DiffEqFlux.jl

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

SciMLTutorials.jl

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

Optimization.jl

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 interface.

OrdinaryDiffEq.jl

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

diffeqpy

Solving differential equations in Python using DifferentialEquations.jl and the SciML Scientific Machine Learning organization

Catalyst.jl

Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.

DataDrivenDiffEq.jl

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

SciMLSensitivity.jl

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, SDEs, DDEs, DAEs, etc.

Surrogates.jl

Surrogate modeling and optimization for scientific machine learning (SciML)

SciMLBenchmarks.jl

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

DiffEqOperators.jl

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

DiffEqGPU.jl

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

FluxNeuralOperators.jl

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

DiffEqDocs.jl

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

DiffEqBase.jl

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

LinearSolve.jl

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.

Integrals.jl

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

NonlinearSolve.jl

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

DataInterpolations.jl

A library of data interpolation and smoothing functions

SciMLStyle

A style guide for stylish Julia developers

StochasticDiffEq.jl

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

ReservoirComputing.jl

Reservoir computing utilities for scientific machine learning (SciML)

Sundials.jl

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

RecursiveArrayTools.jl

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

MethodOfLines.jl

Automatic Finite Difference PDE solving with Julia SciML

diffeqr

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

JumpProcesses.jl

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)

SciMLBase.jl

The Base interface of the SciML ecosystem

NBodySimulator.jl

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

ColPrac

Contributor's Guide on Collaborative Practices for Community Packages

DiffEqBayes.jl

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

LabelledArrays.jl

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

PolyChaos.jl

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

SymbolicNumericIntegration.jl

SymbolicNumericIntegration.jl: Symbolic-Numerics for Solving Integrals

ModelingToolkitStandardLibrary.jl

A standard library of components to model the world and beyond

PreallocationTools.jl

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

StructuralIdentifiability.jl

Fast and automatic structural identifiability software for ODE systems

ODE.jl

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

QuasiMonteCarlo.jl

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)

RuntimeGeneratedFunctions.jl

Functions generated at runtime without world-age issues or overhead

FEniCS.jl

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

DiffEqCallbacks.jl

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

ExponentialUtilities.jl

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

EllipsisNotation.jl

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

EasyModelAnalysis.jl

High level functions for analyzing the output of simulations

AutoOptimize.jl

Automatic optimization and parallelization for Scientific Machine Learning (SciML)

ParameterizedFunctions.jl

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

HighDimPDE.jl

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

SciMLExpectations.jl

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

MultiScaleArrays.jl

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

SimpleNonlinearSolve.jl

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

DiffEqNoiseProcess.jl

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

CellMLToolkit.jl

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

SciMLDocs

Global documentation for the Julia SciML Scientific Machine Learning Organization

SparsityDetection.jl

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

DelayDiffEq.jl

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.

DiffEqProblemLibrary.jl

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

sciml.ai

The SciML Scientific Machine Learning Software Organization Website

DiffEqParamEstim.jl

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

Static.jl

Static types useful for dispatch and generated functions.

GlobalSensitivity.jl

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

DeepEquilibriumNetworks.jl

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

MinimallyDisruptiveCurves.jl

Finds relationships between the parameters of a mathematical model

DiffEqPhysics.jl

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

OperatorLearning.jl

No need to train, he's a smooth operator

MuladdMacro.jl

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

DiffEqDevTools.jl

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

BoundaryValueDiffEq.jl

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

SciMLOperators.jl

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

SBMLToolkit.jl

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

HelicopterSciML.jl

Helicopter Scientific Machine Learning (SciML) Challenge Problem

ADTypes.jl

Repository for automatic differentiation backend types

RootedTrees.jl

A collection of functionality around rooted trees to generate order conditions for Runge-Kutta methods in Julia for differential equations and scientific machine learning (SciML)

SciMLWorkshop.jl

Workshop materials for training in scientific computing and scientific machine learning

AutoOffload.jl

Automatic GPU, TPU, FPGA, Xeon Phi, Multithreaded, Distributed, etc. offloading for scientific machine learning (SciML) and differential equations

ModelOrderReduction.jl

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

ModelingToolkitCourse

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

DifferenceEquations.jl

Solving difference equations with DifferenceEquations.jl and the SciML ecosystem.

DASSL.jl

Solves stiff differential algebraic equations (DAE) using variable stepsize backwards finite difference formula (BDF) in the SciML scientific machine learning organization

FiniteVolumeMethod.jl

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

SteadyStateDiffEq.jl

Solvers for steady states in scientific machine learning (SciML)

TruncatedStacktraces.jl

Simpler stacktraces for the Julia Programming Language

PDESystemLibrary.jl

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

DiffEqOnline

It's Angular2 business in the front, and a Julia party in the back! It's scientific machine learning (SciML) for the web

ReactionNetworkImporters.jl

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

StochasticDelayDiffEq.jl

Stochastic delay differential equations (SDDE) solvers for the SciML scientific machine learning ecosystem

DiffEqOnlineServer

Backend for DiffEqOnline, a webapp for scientific machine learning (SciML)

MathML.jl

Julia MathML parser

IRKGaussLegendre.jl

Implicit Runge-Kutta Gauss-Legendre 16th order (Julia)

Jupyter Notebook

SimpleDiffEq.jl

Simple differential equation solvers in native Julia for scientific machine learning (SciML)

DiffEqFinancial.jl

Differential equation problem specifications and scientific machine learning for common financial models

ModelingToolkitNeuralNets.jl

Symbolic-Numeric Universal Differential Equations for Automating Scientific Machine Learning (SciML)

SciPyDiffEq.jl

Wrappers for the SciPy differential equation solvers for the SciML Scientific Machine Learning organization

SciMLTutorialsOutput

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

OptimalControl.jl

A component of the SciML scientific machine learning ecosystem for optimal control

MATLABDiffEq.jl

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

IfElse.jl

Under some conditions you may need this function