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ParameterizedFunctions.jl

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ParameterizedFunctions.jl is a component of the SciML ecosystem which allows for easily defining parameterized ODE models in a simple syntax.

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.

Example

The following are valid ODE definitions.

using DifferentialEquations, ParameterizedFunctions

# Non-Stiff ODE

lotka_volterra = @ode_def begin
  d🐁  = α*🐁  - β*🐁*🐈
  d🐈 = -γ*🐈 + δ*🐁*🐈
end α β γ δ

p = [1.5,1.0,3.0,1.0]; u0 = [1.0;1.0]
prob = ODEProblem(lotka_volterra,u0,(0.0,10.0),p)
sol = solve(prob,Tsit5(),reltol=1e-6,abstol=1e-6)

# Stiff ODE

rober = @ode_def begin
  dy₁ = -k₁*y₁+k₃*y₂*y₃
  dy₂ =  k₁*y₁-k₂*y₂^2-k₃*y₂*y₃
  dy₃ =  k₂*y₂^2
end k₁ k₂ k₃

prob = ODEProblem(rober,[1.0,0.0,0.0],(0.0,1e5),[0.04,3e7,1e4])
sol = solve(prob)

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

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