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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>SciMLTutorials.jl: Tutorials for Scientific Machine Learning (SciML), Equation Solvers, and AI for Science · The SciML Tutorials</title><script data-outdated-warner src="assets/warner.js"></script><link rel="canonical" href="https://tutorials.sciml.ai/stable/"/><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script><link href="assets/favicon.ico" rel="icon" type="image/x-icon"/></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>The SciML Tutorials</a></span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>SciMLTutorials.jl: Tutorials for Scientific Machine Learning (SciML), Equation Solvers, and AI for Science</a><ul class="internal"><li><a class="tocitem" href="#Interactive-Notebooks"><span>Interactive Notebooks</span></a></li><li><a class="tocitem" href="#Video-Tutorial"><span>Video Tutorial</span></a></li><li><a class="tocitem" href="#Table-of-Contents"><span>Table of Contents</span></a></li><li><a class="tocitem" href="#Contributing"><span>Contributing</span></a></li></ul></li><li><span class="tocitem">DiffEqUncertainty</span><ul><li><a class="tocitem" href="DiffEqUncertainty/01-expectation_introduction/">An Intro to Expectations via DiffEqUncertainty.jl</a></li><li><a class="tocitem" href="DiffEqUncertainty/02-AD_and_optimization/">Optimization Under Uncertainty with DiffEqUncertainty.jl</a></li></ul></li><li><span class="tocitem">advanced</span><ul><li><a class="tocitem" href="advanced/01-beeler_reuter/">An Implicit/Explicit CUDA-Accelerated Solver for the 2D Beeler-Reuter Model</a></li><li><a class="tocitem" href="advanced/02-advanced_ODE_solving/">Solving Stiff Equations</a></li><li><a class="tocitem" href="advanced/03-kolmogorov_equations/">Kolmogorov Backward Equations</a></li><li><a class="tocitem" href="advanced/04-diffusion_implicit_heat_equation/">Solving the heat equation with diffusion-implicit time-stepping</a></li></ul></li><li><span class="tocitem">exercises</span><ul><li><a class="tocitem" href="exercises/01-workshop_exercises/">SciML Workshop Exercises</a></li><li><a class="tocitem" href="exercises/02-workshop_solutions/">SciML Workshop Exercise Solutions</a></li></ul></li><li><span class="tocitem">introduction</span><ul><li><a class="tocitem" href="introduction/01-ode_introduction/">An Intro to DifferentialEquations.jl</a></li><li><a class="tocitem" href="introduction/02-choosing_algs/">Choosing an ODE Algorithm</a></li><li><a class="tocitem" href="introduction/03-optimizing_diffeq_code/">Optimizing DiffEq Code</a></li><li><a class="tocitem" href="introduction/04-callbacks_and_events/">Callbacks and Events</a></li><li><a class="tocitem" href="introduction/05-formatting_plots/">Formatting Plots</a></li></ul></li><li><span class="tocitem">jumps</span><ul><li><a class="tocitem" href="jumps/spatial/">Ilin</a></li></ul></li><li><span class="tocitem">model_inference</span><ul><li><a class="tocitem" href="model_inference/01-pendulum_bayesian_inference/">Bayesian Inference on a Pendulum using DiffEqBayes.jl</a></li><li><a class="tocitem" href="model_inference/02-monte_carlo_parameter_estim/">Monte Carlo Parameter Estimation From Data</a></li></ul></li><li><span class="tocitem">models</span><ul><li><a class="tocitem" href="models/01-classical_physics/">Classical Physics Models</a></li><li><a class="tocitem" href="models/02-conditional_dosing/">Conditional Dosing Pharmacometric Example</a></li><li><a class="tocitem" href="models/03-diffeqbio_I_introduction/">DiffEqBiological Tutorial I: Introduction</a></li><li><a class="tocitem" href="models/04-diffeqbio_II_networkproperties/">DiffEqBiological Tutorial II: Network Properties API</a></li><li><a class="tocitem" href="models/04b-diffeqbio_III_steadystates/">DiffEqBiological Tutorial III: Steady-States and Bifurcations</a></li><li><a class="tocitem" href="models/05-kepler_problem/">Kepler Problem</a></li><li><a class="tocitem" href="models/07-outer_solar_system/">The Outer Solar System</a></li><li><a class="tocitem" href="models/08-spiking_neural_systems/">Spiking Neural Systems</a></li></ul></li><li><span class="tocitem">ode_extras</span><ul><li><a class="tocitem" href="ode_extras/01-ModelingToolkit/">ModelingToolkit.jl, An IR and Compiler for Scientific Models</a></li><li><a class="tocitem" href="ode_extras/02-feagin/">Feagin's Order 10, 12, and 14 Methods</a></li><li><a class="tocitem" href="ode_extras/03-ode_minmax/">Finding Maxima and Minima of DiffEq Solutions</a></li></ul></li><li><span class="tocitem">perturbation</span><ul><li><a class="tocitem" href="perturbation/01-perturbation_algebraic/">Mixed Symbolic/Numerical Methods for Perturbation Theory - Algebraic Equations</a></li><li><a class="tocitem" href="perturbation/02-perturbation_differential/">Mixed Symbolic/Numerical Methods for Perturbation Theory - Differential Equations</a></li></ul></li><li><span class="tocitem">type_handling</span><ul><li><a class="tocitem" href="type_handling/02-uncertainties/">Numbers with Uncertainties</a></li><li><a class="tocitem" href="type_handling/03-unitful/">Unit Checked Arithmetic via Unitful.jl</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>SciMLTutorials.jl: Tutorials for Scientific Machine Learning (SciML), Equation Solvers, and AI for Science</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>SciMLTutorials.jl: Tutorials for Scientific Machine Learning (SciML), Equation Solvers, and AI for Science</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/SciML/SciMLTutorialsOutput/blob/main/docs/src/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="SciMLTutorials.jl:-Tutorials-for-Scientific-Machine-Learning-and-Differential-Equations"><a class="docs-heading-anchor" href="#SciMLTutorials.jl:-Tutorials-for-Scientific-Machine-Learning-and-Differential-Equations">SciMLTutorials.jl: Tutorials for Scientific Machine Learning and Differential Equations</a><a id="SciMLTutorials.jl:-Tutorials-for-Scientific-Machine-Learning-and-Differential-Equations-1"></a><a class="docs-heading-anchor-permalink" href="#SciMLTutorials.jl:-Tutorials-for-Scientific-Machine-Learning-and-Differential-Equations" title="Permalink"></a></h1><p><a href="https://buildkite.com/julialang/scimltutorials-dot-jl"><img src="https://badge.buildkite.com/8a39c2e1b44511eb84bdcd9019663cad757ae2479abd340508.svg" alt="Build status"/></a></p><p><a href="https://gitter.im/JuliaDiffEq/Lobby?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge"><img src="https://badges.gitter.im/JuliaDiffEq/Lobby.svg" alt="Join the chat at https://gitter.im/JuliaDiffEq/Lobby"/></a></p><p>SciMLTutorials.jl holds PDFs, webpages, and interactive Jupyter notebooks showing how to utilize the software in the <a href="https://sciml.ai/">SciML Scientific Machine Learning ecosystem</a>. This set of tutorials was made to complement the <a href="https://sciml.ai/documentation/">documentation</a> and the <a href="http://devdocs.sciml.ai/latest/">devdocs</a> by providing practical examples of the concepts. For more details, please consult the docs.</p><h2 id="Interactive-Notebooks"><a class="docs-heading-anchor" href="#Interactive-Notebooks">Interactive Notebooks</a><a id="Interactive-Notebooks-1"></a><a class="docs-heading-anchor-permalink" href="#Interactive-Notebooks" title="Permalink"></a></h2><p>To run the tutorials interactively via Jupyter notebooks, install the package and open the tutorials like:</p><pre><code class="language-julia hljs">using Pkg
pkg"add https://github.com/SciML/SciMLTutorials.jl"
using SciMLTutorials
SciMLTutorials.open_notebooks()</code></pre><h2 id="Video-Tutorial"><a class="docs-heading-anchor" href="#Video-Tutorial">Video Tutorial</a><a id="Video-Tutorial-1"></a><a class="docs-heading-anchor-permalink" href="#Video-Tutorial" title="Permalink"></a></h2><p><a href="https://youtu.be/KPEqYtEd-zY"><img src="https://user-images.githubusercontent.com/1814174/36342812-bdfd0606-13b8-11e8-9eff-ff219de909e5.PNG" alt="Video Tutorial"/></a></p><h2 id="Table-of-Contents"><a class="docs-heading-anchor" href="#Table-of-Contents">Table of Contents</a><a id="Table-of-Contents-1"></a><a class="docs-heading-anchor-permalink" href="#Table-of-Contents" title="Permalink"></a></h2><ul><li>Introduction<ul><li><a href="http://tutorials.sciml.ai/html/introduction/01-ode_introduction.html">Introduction to DifferentialEquations.jl through ODEs</a></li><li><a href="http://tutorials.sciml.ai/html/introduction/02-choosing_algs.html">Detecting Stiffness and Choosing an ODE Algorithm</a></li><li><a href="http://tutorials.sciml.ai/html/introduction/03-optimizing_diffeq_code.html">Optimizing your DiffEq Code</a></li><li><a href="http://tutorials.sciml.ai/html/introduction/04-callbacks_and_events.html">Callbacks and Event Handling</a></li><li><a href="http://tutorials.sciml.ai/html/introduction/05-formatting_plots.html">Formatting Plots</a></li></ul></li><li>Exercise Sheets<ul><li><a href="http://tutorials.sciml.ai/html/exercises/01-workshop_exercises.html">DifferentialEquations.jl Workshop Exercises</a></li><li><a href="http://tutorials.sciml.ai/html/exercises/02-workshop_solutions.html">DifferentialEquations.jl Workshop Exercise Solutions</a></li></ul></li><li>Modeling Examples<ul><li><a href="http://tutorials.sciml.ai/html/models/01-classical_physics.html">Classical Physics Models</a></li><li><a href="http://tutorials.sciml.ai/html/models/02-conditional_dosing.html">Conditional Dosing Example</a></li><li><a href="http://tutorials.sciml.ai/html/models/03-diffeqbio_I_introduction.html">DiffEqBiological Tutorial I: Introduction</a></li><li><a href="http://tutorials.sciml.ai/html/models/04-diffeqbio_II_networkproperties.html">DiffEqBiological Tutorial II: Network Properties API</a></li><li><a href="http://tutorials.sciml.ai/html/models/04b-diffeqbio_III_steadystates.html">DiffEqBiological Tutorial III: Steady-States and Bifurcations</a></li><li><a href="http://tutorials.sciml.ai/html/jumps/spatial.html">Tutorial on using spatial SSAs in DiffEqJump</a></li><li><a href="http://tutorials.sciml.ai/html/models/05-kepler_problem.html">Kepler Problem Orbit</a></li><li><a href="http://tutorials.sciml.ai/html/models/08-spiking_neural_systems.html">Spiking Neural Systems</a></li></ul></li><li>Advanced ODE Features<ul><li><a href="http://tutorials.sciml.ai/html/ode_extras/01-feagin.html">Feagin's Order 10, 12, and 14 Methods</a></li><li><a href="http://tutorials.sciml.ai/html/ode_extras/02-ode_minmax.html">Finding Maxima and Minima of DiffEq Solutions</a></li></ul></li><li>Model Inference<ul><li><a href="http://tutorials.sciml.ai/html/model_inference/01-pendulum_bayesian_inference.html">Bayesian Inference of Pendulum Parameters</a></li><li><a href="http://tutorials.sciml.ai/html/model_inference/02-monte_carlo_parameter_estim.html">Monte Carlo Parameter Estimation from Data</a></li></ul></li><li>Type Handling<ul><li><a href="http://tutorials.sciml.ai/html/type_handling/01-number_types.html">Solving Equations with Julia-Defined Types</a></li><li><a href="http://tutorials.sciml.ai/html/type_handling/02-uncertainties.html">Numbers with Uncertainties</a></li><li><a href="http://tutorials.sciml.ai/html/type_handling/03-unitful.html">Unit Check Arithmetic via Unitful.jl</a></li></ul></li><li>DiffEqUncertainty<ul><li><a href="http://tutorials.sciml.ai/html/DiffEqUncertainty/01-expectation_introduction.html">An Intro to Expectations via DiffEqUncertainty.jl</a></li><li><a href="http://tutorials.sciml.ai/html/DiffEqUncertainty/02-AD_and_optimization.html">Optimization Under Uncertainty with DiffEqUncertainty.jl</a></li><li><a href="http://tutorials.sciml.ai/html/DiffEqUncertainty/03-GPU_Bayesian_Koopman.html">GPU-Accelerated Data-Driven Bayesian Uncertainty Quantification with Koopman Operators</a></li></ul></li><li>Advanced<ul><li><a href="http://tutorials.sciml.ai/html/advanced/01-beeler_reuter.html">A 2D Cardiac Electrophysiology Model (CUDA-accelerated PDE solver)</a></li><li><a href="http://tutorials.sciml.ai/html/advanced/02-advanced_ODE_solving.html">Solving Stiff Equations</a></li><li><a href="http://tutorials.sciml.ai/html/advanced/04-diffusion_implicit_heat_equation.html">Solving the heat equation with diffusion-implicit time-stepping</a></li><li><a href="http://tutorials.sciml.ai/html/advanced/03-kolmogorov_equations.html">Kolmogorov Backward Equations</a></li></ul></li><li>Perturbation Theory<ul><li><a href="http://tutorials.sciml.ai/html/perturbation/01-perturbation_algebraic.html">Mixed Symbolic/Numerical Methods for Perturbation Theory - Algebraic Equations</a></li><li><a href="http://tutorials.sciml.ai/html/perturbation/02-perturbation_differential.html">Mixed Symbolic/Numerical Methods for Perturbation Theory - Differential Equations</a></li></ul></li></ul><h2 id="Contributing"><a class="docs-heading-anchor" href="#Contributing">Contributing</a><a id="Contributing-1"></a><a class="docs-heading-anchor-permalink" href="#Contributing" title="Permalink"></a></h2><p>First of all, make sure that your current directory is <code>SciMLTutorials</code>. All of the files are generated from the Weave.jl files in the <code>tutorials</code> folder. To run the generation process, do for example:</p><pre><code class="language-julia hljs">using Pkg, SciMLTutorials
cd(joinpath(dirname(pathof(SciMLTutorials)), ".."))
Pkg.pkg"activate ."
Pkg.pkg"instantiate"
SciMLTutorials.weave_file("introduction","01-ode_introduction.jmd")</code></pre><p>To generate all of the notebooks, do:</p><pre><code class="language-julia hljs">SciMLTutorials.weave_all()</code></pre><p>If you add new tutorials which require new packages, simply updating your local environment will change the project and manifest files. When this occurs, the updated environment files should be included in the PR.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="DiffEqUncertainty/01-expectation_introduction/">An Intro to Expectations via DiffEqUncertainty.jl »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.22 on <span class="colophon-date" title="Saturday 13 August 2022 04:28">Saturday 13 August 2022</span>. Using Julia version 1.7.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>