A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solvers
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January 2017

DiffEqCallbacks.jl: Prebuilt Callbacks for extending the solvers of DifferentialEquations.jl

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DifferentialEquations.jl has an expressive callback system which allows for customizable transformations of te solver behavior. DiffEqCallbacks.jl is a library of pre-built callbacks which makes it easy to transform the solver into a domain-specific simulation tool.

Tutorials and Documentation

For information on using the package, see the stable documentation. Use the in-development documentation for the version of the documentation, which contains the unreleased features.

Manifold Projection Example

Here we solve the harmonic oscillator:

u0 = ones(2)
function f(du,u,p,t)
  du[1] = u[2]
  du[2] = -u[1]
prob = ODEProblem(f,u0,(0.0,100.0))

However, this problem is supposed to conserve energy, and thus we define our manifold to conserve the sum of squares:

function g(resid,u,p,t)
  resid[1] = u[2]^2 + u[1]^2 - 2
  resid[2] = 0

To build the callback, we just call

cb = ManifoldProjection(g)

Using this callback, the Runge-Kutta method Vern7 conserves energy. Note that the standard saving occurs after the step and before the callback, and thus we set save_everystep=false to turn off all standard saving and let the callback save after the projection is applied.

sol = solve(prob,Vern7(),save_everystep=false,callback=cb)
@test sol[end][1]^2 + sol[end][2]^2  2