`reinit!` dominates runtime and allocations in integrator update loop

[jClugstor]

Not exactly a bug per se ...
In an example of a function that reinitializes, updates the state of, and solves an integrator that was created with an MTK system, reinit! takes up all of the allocations, and more than half of the runtime, when reinit_dae = true and reset_dt = true.

Code example:

using ModelingToolkit, OrdinaryDiffEq, Setfield
using ModelingToolkit: t_nounits as t, D_nounits as D
using SymbolicIndexingInterface
using BenchmarkTools
using Test
function Pin(; name)
    @variables v(t) i(t) [connect = Flow]
    sys = System(Equation[], t, [v, i], []; name)
    sys = @set sys.connector_type = ModelingToolkit.connector_type(sys)
    return sys
end
function Ground(; name)
    @named g = Pin()
    eqs = [g.v ~ 0]
    System(eqs, t, [], []; systems=[g], name)
end
function OnePort(; name)
    @named p = Pin()
    @named n = Pin()
    @variables v(t) i(t)
    eqs = [
        v ~ p.v - n.v
        0 ~ p.i + n.i
        i ~ p.i
    ]
    System(eqs, t, [v, i], []; systems=[p, n], name)
end
function Resistor(; name, R=1.0)
    @named oneport = OnePort()
    @unpack v, i = oneport
    @parameters R = R # Sets the default resistance
    eqs = [v ~ i * R]
    extend(System(eqs, t, [], [R]; name), oneport)
end
function Capacitor(; name, C=1.0)
    @named oneport = OnePort()
    @unpack v, i = oneport
    @parameters C = C
    eqs = [D(v) ~ i / C]
    extend(System(eqs, t, [], [C]; name), oneport)
end
function ConstantVoltage(; name, V=1.0)
    @named oneport = OnePort()
    @unpack v = oneport
    @parameters V = V
    eqs = [V ~ v]
    extend(System(eqs, t, [], [V]; name), oneport)
end
function Circuit(; name)
    @named C1 = Capacitor(C=1e-3)
    @named C2 = Capacitor(C=2e-3)
    @named C3 = Capacitor(C=3e-3)
    @named R1 = Resistor(R=1.)
    @named R2 = Resistor(R=2.)
    @named R3 = Resistor(R=3.)
    @named source = ConstantVoltage(V=5.0)
    @named ground = Ground()
    eqs = [
        connect(source.n, ground.g)
        connect(source.p, R1.p)
        connect(R1.n, C1.p, R2.p)
        connect(C1.n, ground.g)
        connect(R2.n, C2.p, R3.p)
        connect(C2.n, ground.g)
        connect(R3.n, C3.p)
        connect(C3.n, ground.g)
    ]
    System(eqs, t; systems=[C1, C2, C3, R1, R2, R3, source, ground], name)
end
@named circuit = Circuit()
circuit = mtkcompile(circuit)
u0 = [circuit.C1.v => 0.; circuit.C2.v => 0.; circuit.C3.v => 0.]
set_u0! = setsym(circuit, [circuit.C1.v; circuit.C2.v; circuit.C3.v])
prob = ODEProblem(circuit, u0, (0., 1e-2))
integrator = init(prob, Trapezoid())
v = [1.; 2.; 3.]
function update!(integrator, u0, set_u0!)
    reinit!(integrator; erase_sol=false, reset_dt=true, reinit_dae=true)
    set_u0!(integrator, u0)
    integrator.saveiter = 0
    integrator.saveiter_dense = 0
    savevalues!(integrator)
    solve!(integrator)
    return
end

Allocations from reset_dt = true:
These are an OrdinaryDiffEq issue, SciML/OrdinaryDiffEq.jl#3231

Allocations from reinit_dae:
Many of these are from late_binding_u0_p

• OOPSetter, from the setp_oop in late_binding_u0_p
• all_symbols, which has allocations from parameters and all_variable_symbols.

The rest of the allocations are from initialize_dae!, which calls get_initial_values, which then calls update_initializeprob! and initprobpmap_split. Both of these call a RuntimeGenerated function which allocates.

We can see these allocations in this flamegraph:

As for the performance implications, profiling shows that over half of the run time is taken up by the reinit! call, and most of the time in reinit! is taken up by the functions that allocate.

I would like to try to see how many of these allocations we can eliminate, and especially see if we can make reinit! faster.

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

(initialization_allocations) pkg> st
Status `~/Documents/Work/dev/ErrorCorp/initialization_allocations/Project.toml`
  [6e4b80f9] BenchmarkTools v1.6.3
  [0ca39b1e] Chairmarks v1.3.1
  [961ee093] ModelingToolkit v11.17.0
  [7771a370] ModelingToolkitBase v1.24.0 `~/.julia/dev/ModelingToolkit/lib/ModelingToolkitBase`
  [1dea7af3] OrdinaryDiffEq v6.108.0
  [bbf590c4] OrdinaryDiffEqCore v3.22.0 `~/Documents/Work/dev/OrdinaryDiffEq.jl/lib/OrdinaryDiffEqCore`
  [efcf1570] Setfield v1.1.2
  [2efcf032] SymbolicIndexingInterface v0.3.46

• Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

Status `~/Documents/Work/dev/ErrorCorp/initialization_allocations/Manifest.toml`
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  [0ca39b1e] Chairmarks v1.3.1
  [fb6a15b2] CloseOpenIntervals v0.1.13
⌅ [861a8166] Combinatorics v1.0.2
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  [6bb917b9] ModelingToolkitTearing v1.10.0
  [2e0e35c7] Moshi v0.3.7
  [46d2c3a1] MuladdMacro v0.2.4
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  [d8a4904e] MutableArithmetics v1.6.7
  [d41bc354] NLSolversBase v8.0.0
  [77ba4419] NaNMath v1.1.3
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Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

• Output of versioninfo()

julia> versioninfo()
Julia Version 1.12.5
Commit 5fe89b8ddc1 (2026-02-09 16:05 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 16 × AMD Ryzen 7 6800U with Radeon Graphics
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, znver3)
  GC: Built with stock GC
Threads: 16 default, 1 interactive, 16 GC (on 16 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_VSCODE_REPL = 1
  JULIA_PKG_SERVER = https://juliahub.com

Additional context

Add any other context about the problem here.

[oscardssmith]

For slowness/allocation in calculating an appropriate initial dt, please file an OrdinaryDiffEq.jl issue.

[jClugstor]

True, that part isn't really MTK.

[jClugstor]

An even simpler example is

using ModelingToolkit, OrdinaryDiffEq
using ModelingToolkit: t_nounits as t, D_nounits as D

# Simplest possible MTK system: du/dt = -u
@variables u(t)
@mtkbuild sys = ODESystem([D(u) ~ -u], t)

prob = ODEProblem(sys, [u => 1.0], (0.0, 1.0))
integrator = init(prob, Tsit5())

# Warm up
reinit!(integrator)
solve!(integrator)

# reinit! allocates even on this minimal MTK system
println("Allocations from reinit!: ", @allocated(reinit!(integrator)), " bytes")
@profview_allocs reinit!(integrator) sample_rate = 1.0

[AayushSabharwal]

Interesting. Why does it hit the symbolic path?

[jClugstor]

reinit! always passed an empty array of pairs as p, so it was always hitting the symbolic path in late_binding_update_u0_p.

#4411 got rid of the allocations from late_binding_update_u0_p, so now I think the only thing on the MTK / Symbolics side is from _initialize_dae! / get_initial_values.

Time profile shows several runtime dispatches:

And allocation profiling shows some allocations happening inside some of the RuntimeGenerated functions

[jClugstor]

Cthulhu says that the type of initializeprob isn't inferred, which causes runtime dispatches to several places, like initlizeprobmap and update_initializeprob!

[AayushSabharwal]

Are you looking at typed code or typed IR? The typed code often lies.

[AayushSabharwal]

reinit! always passed an empty array of pairs as p, so it was always hitting the symbolic path in late_binding_update_u0_p.

Interesting. Was I the one behind that? 😅 That seems wrong.

[jClugstor]

Interesting. Was I the one behind that? 😅 That seems wrong.

Sorry man, it was you :-) . https://github.com/SciML/OrdinaryDiffEq.jl/blame/6b88ece57b3474d2e2b8a4ef78c93133e1d70f6d/lib/OrdinaryDiffEqCore/src/integrators/integrator_interface.jl#L468

At least you left a nice comment explaining why. I think since that was added, you updated late_binding_update_u0_p though, so it doesn't seem relevant anymore.

Are you looking at typed code or typed IR? The typed code often lies.

I was looking at typed code, but I'll take a look at the IR, thanks.

[AayushSabharwal]

Interesting. The remake infrastructure is so tangled at this point 😅 I'm not sure if that comment is still valid at this point.

[AayushSabharwal]

I was looking at typed code, but I'll take a look at the IR, thanks.

I'd recommend turning on optimizations too. It eliminates some dynamic dispatch.

[jClugstor]

This is Cthulhu typed IR with optimizations on

which corresponds to

initializeprob = prob.f.initialization_data.initializeprob
iu0 = state_values(initializeprob) 

at
https://github.com/SciML/OrdinaryDiffEq.jl/blob/6b88ece57b3474d2e2b8a4ef78c93133e1d70f6d/lib/OrdinaryDiffEqCore/src/initialize_dae.jl#L117

so it looks like for some reason prob.f.initialization_data is Union{Nothing, SciMLBase.OverrideInitData}. That doesn't seem right, plus trying to get initializeprob from nothing would error.

To make sure that Cthulhu isn't tricking me I tried @code_typed and got the same thing:

julia> @code_typed optimize=true DiffEqBase.initialize_dae!(integrator)
CodeInfo(
1 ── %1  =   builtin SciMLBase.getfield(integrator, :sol)::ODESolution{Float64, 2, Vector{Vector{Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Vector{Float64}}}, Nothing, ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, MTKParameters{StaticArraysCore.SVector{0, Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, ODEFunction{true, SciMLBase.AutoSpecialize, FunctionWrappersWrappers.FunctionWrappersWrapper{Tuple{FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, MTKParameters{StaticArraysCore.SVector{0, Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, Float64}}}, false}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkitBase.ObservedFunctionCache{System, Nothing}, Nothing, System, Union{Nothing, SciMLBase.OverrideInitData}, Union{Nothing, SciMLBase.ODENLStepData}}, Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, SciMLBase.StandardODEProblem}, Tsit5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}, OrdinaryDiffEqCore.InterpolationData{ODEFunction{true, SciMLBase.AutoSpecialize, FunctionWrappersWrappers.FunctionWrappersWrapper{Tuple{FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, MTKParameters{StaticArraysCore.SVector{0, Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, Float64}}}, false}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkitBase.ObservedFunctionCache{System, Nothing}, Nothing, System, Union{Nothing, SciMLBase.OverrideInitData}, Union{Nothing, SciMLBase.ODENLStepData}}, Vector{Vector{Float64}}, Vector{Float64}, Vector{Vector{Vector{Float64}}}, Nothing, OrdinaryDiffEqTsit5.Tsit5Cache{Vector{Float64}, Vector{Float64}, Vector{Float64}, typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), Static.False}, Nothing}, SciMLBase.DEStats, Nothing, Nothing, Nothing, Nothing}
│    %2  =   builtin SciMLBase.getfield(%1, :prob)::ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, MTKParameters{StaticArraysCore.SVector{0, Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, ODEFunction{true, SciMLBase.AutoSpecialize, FunctionWrappersWrappers.FunctionWrappersWrapper{Tuple{FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, MTKParameters{StaticArraysCore.SVector{0, Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, Float64}}}, false}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkitBase.ObservedFunctionCache{System, Nothing}, Nothing, System, Union{Nothing, SciMLBase.OverrideInitData}, Union{Nothing, SciMLBase.ODENLStepData}}, Base.Pairs{Symbol, Union{}, Nothing, @NamedTuple{}}, SciMLBase.StandardODEProblem}
│    %3  =   builtin SciMLBase.getfield(%2, :f)::ODEFunction{true, SciMLBase.AutoSpecialize, FunctionWrappersWrappers.FunctionWrappersWrapper{Tuple{FunctionWrappers.FunctionWrapper{Nothing, Tuple{Vector{Float64}, Vector{Float64}, MTKParameters{StaticArraysCore.SVector{0, Float64}, Vector{Float64}, Tuple{}, Tuple{}, Tuple{}, Tuple{}}, Float64}}}, false}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, ModelingToolkitBase.ObservedFunctionCache{System, Nothing}, Nothing, System, Union{Nothing, SciMLBase.OverrideInitData}, Union{Nothing, SciMLBase.ODENLStepData}}
│    %4  =   builtin SciMLBase.getfield(%3, :initialization_data)::Union{Nothing, SciMLBase.OverrideInitData}
│    %5  =   builtin (%4 === SciMLBase.nothing)::Bool
│    %6  = intrinsic Core.Intrinsics.not_int(%5)::Bool
└───       goto #9 if not %6
2 ── %8  =   builtin SciMLBase.getfield(%3, :initialization_data)::Union{Nothing, SciMLBase.OverrideInitData}
│    %9  =   builtin SciMLBase.typeof(%8)::Union{Type{Nothing}, Type{SciMLBase.OverrideInitData{IProb, UIProb, IProbMap, IProbPmap, M, OOP}} where {IProb, UIProb, IProbMap, IProbPmap, M, OOP<:Union{Val{true}, Val{false}}}}
│    %10 =   builtin (isa)(%9, Type{Nothing})::Bool
└───       goto #4 if not %10
3 ──       goto #8
4 ── %13 = π (%9, Type{SciMLBase.OverrideInitData{IProb, UIProb, IProbMap, IProbPmap, M, OOP}} where {IProb, UIProb, IProbMap, IProbPmap, M, OOP<:Union{Val{true}, Val{false}}})
└───       goto #5
5 ── %15 =    invoke Base._fieldindex_nothrow(%13::DataType, :initializeprob::Symbol)::Int64
└───       goto #6
6 ── %17 = intrinsic Base.slt_int(0, %15)::Bool
└───       goto #7
7 ──       goto #8
8 ┄─ %20 = φ (#3 => false, #7 => %17)::Bool
└───       goto #10
9 ──       goto #10
10 ┄ %23 = φ (#8 => %20, #9 => false)::Bool
└───       goto #15 if not %23
11 ─ %25 =   builtin SciMLBase.getfield(%3, :initialization_data)::Union{Nothing, SciMLBase.OverrideInitData}
│    %26 =   builtin (isa)(%25, Nothing)::Bool
└───       goto #13 if not %26
12 ─ %28 = π (%25, Nothing)
│            builtin Base.getfield(%28, :initializeprob)::Union{}
└───       unreachable
13 ─ %31 = π (%25, SciMLBase.OverrideInitData)
│    %32 =   builtin Base.getfield(%31, :initializeprob)::Any

[jClugstor]

hmm,

struct ODEFunction{
        iip, specialize, F, TMM, Ta, Tt, TJ, JVP, VJP, JP, SP, TW, TWt, WP, TPJ,
        VJP_P,
        O, TCV,
        SYS, ID <: Union{Nothing, OverrideInitData}, NLP <: Union{Nothing, ODENLStepData},

still, it's a small union so it seems like it should still be inferred?