ParameterizedFunctions.jl: Simple High-Level ODE Definitions

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

Installation

To install ParameterizedFunctions.jl, use the Julia package manager:

using Pkg
Pkg.add("ParameterizedFunctions")

Example

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)

Latex

Latexify directly works on the generated expression. Example:

using ParameterizedFunctions, Latexify

lotka_volterra = @ode_def begin
    dx = a * x - b * x * y
    dy = -c * y + d * x * y
end a b c d

latexify(lotka_volterra.sys)

Generates:

L"\begin{align}
\frac{\mathrm{d} x\left( t \right)}{\mathrm{d}t} =& a x\left( t \right) - b x\left( t \right) y\left( t \right) \\
\frac{\mathrm{d} y\left( t \right)}{\mathrm{d}t} =&  - c y\left( t \right) + d x\left( t \right) y\left( t \right)
\end{align}
"`

Contributing

Please refer to the SciML ColPrac: Contributor's Guide on Collaborative Practices for Community Packages for guidance on PRs, issues, and other matters relating to contributing to SciML.
See the SciML Style Guide for common coding practices and other style decisions.
There are a few community forums:
- The #diffeq-bridged and #sciml-bridged channels in the Julia Slack
- The #diffeq-bridged and #sciml-bridged channels in the Julia Zulip
- On the Julia Discourse forums
- See also SciML Community page

Reproducibility

The documentation of this SciML package was built using these direct dependencies,

Status `~/work/ParameterizedFunctions.jl/ParameterizedFunctions.jl/docs/Project.toml`
  [e30172f5] Documenter v1.3.0
  [65888b18] ParameterizedFunctions v5.17.0 `~/work/ParameterizedFunctions.jl/ParameterizedFunctions.jl`

and using this machine and Julia version.

Julia Version 1.10.2
Commit bd47eca2c8a (2024-03-01 10:14 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)

A more complete overview of all dependencies and their versions is also provided.

Status `~/work/ParameterizedFunctions.jl/ParameterizedFunctions.jl/docs/Manifest.toml`
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Info Packages marked with ⌃ have new versions available and may be upgradable.

You can also download the manifest file and the project file.