How to build a constraint programming solver in Julia. Part 1: Solving Sudoku using backtracking.

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Another month and another set of SciML updates! This month we have been
focusing a lot on simplifying our interfaces and cleaning our tutorials.
We can demonstrate that no user-intervention is required for adjoints.
Also, the ModelingToolkit.jl symbolic modeling language has really come
into fruition, allowing component-based models and automated parallelism.
Indeed, let’s jump right into an example.

ModelingToolkit DAEs and Component-Based Modeling

ModelingToolkit.jl
has added the ability to build differential-algebraic equations
through acausal component-based models. As an example, let’s say
we built two Lorenz equations:

using ModelingToolkit, OrdinaryDiffEq

@parameters t σ ρ β
@variables x(t) y(t) z(t)
@derivatives D'~t

eqs = [D(x) ~ σ*(y-x),
      D(y) ~ x*(ρ-z)-y,
      D(z) ~ x*y - β*z]

lorenz1 = ODESystem(eqs,name=:lorenz1)
lorenz2 = ODESystem(eqs,name=:lorenz2)


We can then define an implicit equation that couples the two equations
together and solve the system:

@variables a
@parameters γ…

High Performance Analytics Toolkit (HPAT) is a Julia-based framework for big data analytics on clusters. - IntelLabs/HPAT.jl