Reduced Compile Time, Optimizing Runtime, and Low Dependency Usage

While DifferentialEquations.jl’s defaults strike a balance between runtime and compile time performance, users should be aware that there are many options for controlling the dependency sizing and the compilation caching behavior to further refine this trade-off. The following methods are available for such controls.

Controlling Function Specialization and Precompilation

By default, DifferentialEquations.jl solvers make use of function wrapping techniques in order to fully precompile the solvers and thus decrease the compile time. However, in some cases you may wish to control this behavior, pushing more towards faster runtimes or faster compile times. This can be done by using the specialization arguments of the AbstractDEProblem constructors.

For example, with the ODEProblem we have ODEProblem{iip,specialize}(...). This second type parameter controls the specialization level with the following choices:

SciMLBase.AutoSpecialize: the default. Uses a late wrapping scheme to hit a balance between runtime and compile time.
SciMLBase.NoSpecialize: this will never specialize on the constituent functions, having the least compile time but the highest runtime.
SciMLBase.FullSpecialize: this will fully re-specialize the solver on the given ODE, achieving the fastest runtimes while increasing the compile times. This is what is recommended when benchmarking and when running long computations, such as in optimization loops.

For more information on the specialization levels, please see the SciMLBase documentation on specialization levels.

DifferentialEquations.jl and its ODE package OrdinaryDiffEq.jl precompile some standard problem types and solvers. The problem types include the three specialization levels described above and the default setting. The solvers include some

standard solvers for non-stiff problems such as Tsit5()
standard solvers for stiff problems such as Rosenbrock23()
standard solvers with stiffness detection such as AutoTsit5(Rosenbrock23())
low-storage methods for conservation laws such as SSPRK43() (precompilation disabled by default)

To adapt the amount of precompilation, you can use Preferences.jl. For example, to turn off precompilation for non-default problem types (specialization levels) and all stiff/implicit/low-storage solvers, you can execute the following code in your active project.

using Preferences, UUIDs
set_preferences!(UUID("1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"), "PrecompileNonStiff" => true)
set_preferences!(UUID("1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"), "PrecompileStiff" => false)
set_preferences!(UUID("1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"), "PrecompileAutoSwitch" => false)
set_preferences!(UUID("1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"), "PrecompileLowStorage" => false)
set_preferences!(UUID("1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"), "PrecompileDefaultSpecialize" => true)
set_preferences!(UUID("1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"), "PrecompileAutoSpecialize" => false)
set_preferences!(UUID("1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"), "PrecompileFunctionWrapperSpecialize" => false)
set_preferences!(UUID("1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"), "PrecompileNoSpecialize" => false)

This will create a LocalPreferences.toml file next to the currently active Project.toml file.

Decreasing Dependency Size by Direct Dependence on Specific Solvers

DifferentialEquations.jl is a large library containing the functionality of many different solver and add-on packages. However, often you may want to cut down on the size of the dependency and only use the parts of the library which are essential to your application. This is possible due to SciML’s modular package structure.

Common Example: Using only OrdinaryDiffEq.jl

One common example is using only the ODE solvers OrdinaryDiffEq.jl. The solvers all reexport SciMLBase.jl (which holds the problem and solution types) and so OrdinaryDiffEq.jl is all that’s needed. Thus replacing

using DifferentialEquations

with

#Add the OrdinaryDiffEq Package first!
#using Pkg; Pkg.add("OrdinaryDiffEq")
using OrdinaryDiffEq

will work if these are the only features you are using.

Generalizing the Idea

In general, you will always need SciMLBase.jl, since it defines all of the fundamental types, but the solvers will automatically reexport it. For solvers, you typically only require that solver package. So SciMLBase+Sundials, SciMLBase+LSODA, etc. will get you the common interface with that specific solver setup. SciMLBase.jl is a very lightweight dependency, so there is no issue here!

For the add-on packages, you will normally need SciMLBase, the solver package you choose, and the add-on package. So for example, for predefined callbacks you would likely want SciMLBase+OrdinaryDiffEq+DiffEqCallbacks. If you aren’t sure which package a specific command is from, then use @which. For example, from the callback docs we have:

using DifferentialEquations
function fitz(du, u, p, t)
    V, R = u
    a, b, c = p
    du[1] = c * (V - V^3 / 3 + R)
    du[2] = -(1 / c) * (V - a - b * R)
end
u0 = [-1.0; 1.0]
tspan = (0.0, 20.0)
p = (0.2, 0.2, 3.0)
prob = ODEProblem(fitz, u0, tspan, p)
cb = ProbIntsUncertainty(0.2, 1)
ensemble_prob = EnsembleProblem(prob)
sim = solve(ensemble_prob, Euler(), trajectories = 100, callback = cb, dt = 1 / 10)

EnsembleSolution Solution of length 100 with uType:
ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Tuple{Float64, Float64, Float64}, ODEFunction{true, SciMLBase.AutoSpecialize, FunctionWrappersWrappers.FunctionWrappersWrapper{Tuple{FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, Tuple{Float64, Float64, Float64}, Float64}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Tuple{Float64, Float64, Float64}, Float64}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{Float64}, Tuple{Float64, Float64, Float64}, ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Tuple{Float64, Float64, Float64}, ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}}, false}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Euler, OrdinaryDiffEq.InterpolationData{ODEFunction{true, SciMLBase.AutoSpecialize, FunctionWrappersWrappers.FunctionWrappersWrapper{Tuple{FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, Tuple{Float64, Float64, Float64}, Float64}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Tuple{Float64, Float64, Float64}, Float64}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{Float64}, Tuple{Float64, Float64, Float64}, ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Tuple{Float64, Float64, Float64}, ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}}, false}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.EulerCache{Vector{Float64}, Vector{Float64}}}, DiffEqBase.Stats, Nothing}

If we wanted to know where ProbIntsUncertainty(0.2,1) came from, we can do:

@which ProbIntsUncertainty(0.2, 1)

ProbIntsUncertainty(σ, order) in DiffEqCallbacks at /root/.julia/packages/DiffEqCallbacks/OK721/src/probints.jl:33

This says it’s in the DiffEqCallbacks.jl package. Thus in this case, we could have done

using OrdinaryDiffEq, DiffEqCallbacks
function fitz(du, u, p, t)
    V, R = u
    a, b, c = p
    du[1] = c * (V - V^3 / 3 + R)
    du[2] = -(1 / c) * (V - a - b * R)
end
u0 = [-1.0; 1.0]
tspan = (0.0, 20.0)
p = (0.2, 0.2, 3.0)
prob = ODEProblem(fitz, u0, tspan, p)
cb = ProbIntsUncertainty(0.2, 1)
ensemble_prob = EnsembleProblem(prob)
sim = solve(ensemble_prob, Euler(), trajectories = 100, callback = cb, dt = 1 / 10)

EnsembleSolution Solution of length 100 with uType:
ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Tuple{Float64, Float64, Float64}, ODEFunction{true, SciMLBase.AutoSpecialize, FunctionWrappersWrappers.FunctionWrappersWrapper{Tuple{FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, Tuple{Float64, Float64, Float64}, Float64}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Tuple{Float64, Float64, Float64}, Float64}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{Float64}, Tuple{Float64, Float64, Float64}, ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Tuple{Float64, Float64, Float64}, ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}}, false}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Euler, OrdinaryDiffEq.InterpolationData{ODEFunction{true, SciMLBase.AutoSpecialize, FunctionWrappersWrappers.FunctionWrappersWrapper{Tuple{FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, Tuple{Float64, Float64, Float64}, Float64}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Tuple{Float64, Float64, Float64}, Float64}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{Float64}, Tuple{Float64, Float64, Float64}, ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}, FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}, Tuple{Float64, Float64, Float64}, ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 1}}}}, false}, UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, OrdinaryDiffEq.EulerCache{Vector{Float64}, Vector{Float64}}}, DiffEqBase.Stats, Nothing}

instead of the full using DifferentialEquations. Note that due to the way Julia dependencies work, any internal function in the package will work. The only dependencies you need to explicitly using are the functions you are specifically calling. Thus, this method can be used to determine all of the DiffEq packages you are using.