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README.md

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-# SciMLWorkshop
+# SciMLWorkshop: Workshop Materials for Training in Scientific Computing and Scientific Machine Learning (SciML)
+
+These exercises teach common workflows which involve SciML's tools like
+DifferentialEquations.jl, ModelingToolkit.jl DiffEqFlux.jl, and the connections to parts
+like stochastic differential equations and Bayesian estimation.
+
+## Difficulty Levels
+
+The designation (B) is for "Beginner", meaning that a user new to the package
+should feel comfortable trying this exercise. An exercise designated (I) is
+for "Intermediate", meaning the user may want to have some previous background
+in DifferentialEquations.jl or try some (B) exercises first. The additional
+(E) designation is for "Experienced", which are portions of exercises which may
+take some work.
+
+## Overview
+
+The exercises are described as follows:
+
+- Exercise 1 is solving a simple stiff ordinary differential equation. This is an
+  introductory exercise to get users acquainted with the syntax.
+- Exercise 2 takes the user through solving a stiff ordinary differential equation
+  and using the ModelingToolkit.jl to automatically convert the function to a
+  symbolic form to derive the analytical Jacobian to speed up the solver. The
+  same biological system is then solved with stochasticity, utilizing
+  EnsembleProblems to understand 95% bounds on the solution. Finally,
+  probabilistic programming is employed to perform Bayesian parameter estimation
+  of the parameters against data.
+- Exercise 3 takes the user through defining hybrid delay differential equation,
+  that is a differential equation with events, and using differentiable programming
+  techniques (automatic differentiation) to to perform gradient-based parameter
+  estimation.
+- Exercise 4 takes the user through differential-algebraic equation (DAE)
+  modeling, the concept of index, and using both mass-matrix and implicit
+  ODE representations. This will require doing a bit of math, but the student
+  will understand how to change their equations to make their DAE numerically
+  easier for the integrators.
+- Exercise 5 has one build an acausal model, a DAE system through a component-based
+  modeling approach. Using a tutorial model of an RC circuit (resistor and capacitor)
+  plus some information about inductors, the user then builds new ModelingToolkit
+  components for an inductor and generates an RLC circuit to be simulated.
+- Exercise 6 takes the user through optimizing a PDE solver, utilizing
+  automatic sparsity pattern recognition, automatic conversion of numerical
+  codes to symbolic codes for analytical construction of the Jacobian,
+  preconditioned GMRES, and setting up a solver for IMEX and GPUs, and compute
+  adjoints of PDEs.
+- Exercise 7 focuses on a chaotic orbit, utilizing parallel ensembles across
+  supercomputers and GPUs to quickly describe phase space.
+- Exercise 8 takes the user through training a neural stochastic differential
+  equation, using GPU-accleration and adjoints through Flux.jl's neural
+  network framework to build efficient training codes.
+- Exercise 9 is a deep dive into controls analysis on nonlinear models. The
+  user starts by building an acausal model of a DC motor, which is augmented
+  with a PI-controller that is tuned to control the actions of the motor.
+
+This exercise worksheet is meant to be a living document leading new users through
+a deep dive of the SciML feature set. If you further suggestions
+or want to contribute new problems, please 
+[open an issue or PR at the SciMLWorkshop.jl repository](https://github.com/SciML/SciMLWorkshop.jl).