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Symbolic Indexing Mismatch Between ODESolution and integrator #100

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jonathanfischer97 opened this issue Sep 25, 2024 · 4 comments
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@jonathanfischer97
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Inconsistent Results from Symbolic Indexing in ODESolution vs SavingCallback

There appears to be a discrepancy between the values obtained through symbolic indexing of an ODEProblem solution and those saved using a SavingCallback with symbolic indexing of the integrator. This occurs when using SymbolicIndexingInterface.jl within the context of solving ODEs with ModelingToolkit and DifferentialEquations.

Specifically, when solving an ODE system and saving a variable (in this case, 'x') using two different methods:

  1. Directly from the ODESolution using sol[:x]
  2. Using a SavingCallback with integrator[:x]

The results show a noticeable difference, suggesting that the symbolic indexing within the SavingCallback may not be accurately capturing the state of the system at each time point.

Expected behavior

The values saved using the SavingCallback with symbolic indexing (integrator[:x]) should match those obtained directly from the ODESolution (sol[:x]) at corresponding time points, as both methods are intended to access the same state variable 'x' throughout the solution process.

Minimal Reproducible Example 👇

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

# Define a simple ODE system (Lotka-Volterra equations)
@parameters α β γ δ
@variables x(t) y(t)
eqs = [D(x) ~- β * y) * x
       D(y) ~* x - γ) * y]
@mtkbuild odesys = ODESystem(eqs, t)


odeprob = ODEProblem(
    odesys, [x => 1.0, y => 1.0], (0.0, 10.0), [α => 1.5, β => 1.0, γ => 3.0, δ => 1.0])

# Save x in the ODESolution
sol = solve(odeprob, Tsit5(); saveat = 0.1)



# Now save x using SavingCallback and symbolic indexing 
symbolically_saved_x_values = SavedValues(Float64, Float64)

# Save x using symbolic indexing of the integrator
symbolic_save_func = (u, t, integrator) -> integrator[:x]

cb = SavingCallback(symbolic_save_func, symbolically_saved_x_values, saveat=0.1)

symbolic_sol = solve(odeprob, Tsit5(); callback=cb, save_on = false, saveat = 0.1)




using Plots 

# Plot the ODESolution with symbolic indexing of x
Plots.plot(sol.t, sol[:x], label = "ODESolution", title = "Symbolic indexing of ODESolution versus SavingCallback")

# Plot the SavedValues where x was indexed symbolically in the callback
Plots.plot!(symbolically_saved_x_values.t, symbolically_saved_x_values.saveval, label = "SavingCallback")

image

This issue suggests a potential problem with how SymbolicIndexingInterface.jl interacts with the integrator object within SavingCallback, possibly related to caching or how the symbolic indexing is resolved during the callback execution.

However, I'm not quite sure and this issue may be better placed under the other packages used here. This might have more to do with DiffEqCallbacks than the symbolic indexing. The discrepancy goes away when using numerical indexing in the save_func, like save_func = (u, t, integrator) -> u[1].

Environment (please complete the following information):

  • Output of using Pkg; Pkg.status()
  [c7e460c6] ArgParse v1.2.0
  [6e4b80f9] BenchmarkTools v1.5.0
⌃ [0f109fa4] BifurcationKit v0.3.6
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  [1313f7d8] DataFramesMeta v0.15.3
  [85a47980] Dictionaries v0.4.2
  [459566f4] DiffEqCallbacks v3.9.1
  [0c46a032] DifferentialEquations v7.14.0
  [0703355e] DimensionalData v0.28.1
  [b4f34e82] Distances v0.10.11
  [31c24e10] Distributions v0.25.111
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  [f6369f11] ForwardDiff v0.10.36
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  [961ee093] ModelingToolkit v9.41.0
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  [8913a72c] NonlinearSolve v3.14.0
  [510215fc] Observables v0.5.5
  [5fb14364] OhMyREPL v0.5.28
  [67456a42] OhMyThreads v0.6.2
  [1dea7af3] OrdinaryDiffEq v6.89.0
  [91a5bcdd] Plots v1.40.8
  [c3e4b0f8] Pluto v0.19.46
  [2dfb63ee] PooledArrays v1.4.3
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  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
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  [efcf1570] Setfield v1.1.1
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  [9672c7b4] SteadyStateDiffEq v2.4.0
  [2efcf032] SymbolicIndexingInterface v0.3.30
  [d1185830] SymbolicUtils v3.7.1
  [0c5d862f] Symbolics v6.13.0
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  [adafc99b] CpuId v0.3.1
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  [77a26b50] DiffEqNoiseProcess v5.23.0
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⌅ [f151be2c] EnzymeCore v0.7.8
  [90fa49ef] ErrorfreeArithmetic v0.5.2
  [6912e4f1] Espresso v0.6.3
  [86b6b26d] Evolutionary v0.11.2 `~/.julia/dev/Evolutionary`
⌃ [429591f6] ExactPredicates v2.2.5
  [460bff9d] ExceptionUnwrapping v0.1.10
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  [6a86dc24] FiniteDiff v2.24.0
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  [1eca21be] FoldingTrees v1.2.1
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v0.10.36
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⌅ [fb4132e2] FuzzyCompletions v0.5.4
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⌃ [28b8d3ca] GR v0.73.5
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  • Output of versioninfo()
Julia Version 1.10.5
Commit 6f3fdf7b362 (2024-08-27 14:19 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 36 × Intel(R) Core(TM) i9-10980XE CPU @ 3.00GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, cascadelake)
Threads: 18 default, 0 interactive, 9 GC (on 36 virtual cores)
Environment:
  LD_LIBRARY_PATH = /tmp/.mount_cursorxxQOLW/usr/lib:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 18
@jonathanfischer97 jonathanfischer97 added the bug Something isn't working label Sep 25, 2024
@AayushSabharwal
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AayushSabharwal commented Sep 25, 2024

This is not a bug. Notice that the callback function has the signature (u, t, integrator). The state values at the time the callback is triggered are given by u, not the integrator. This is because the integrator will step past the callback, then interpolate backward. The interpolated values are passed as u, and the time that the callback is triggered is given by t. If you print t and integrator.t inside the callback, they won't be the same.

The discrepancy goes away when using numerical indexing in the save_func, like save_func = (u, t, integrator) -> u[1].

Note how you're indexing u here and it works. integrator.u[1] will fail.

@jonathanfischer97
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Ah gotcha, my mistake. Is there anyway to easily use symbolic indexing within the saving function?

My original use case was basically defining an observable (just a ratio of sums of different variables) within the saving callback, so that I wouldn't have to save the full solution array only to reduce it afterwards.

@AayushSabharwal
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You can use the function returned by getu inside the callback function. That way you avoid the cost of symbolic lookup while retaining the ability to refer to values by names.

@jonathanfischer97
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What would be the recommended way of saving an observable like x + y within the SavingCallback?

  • Because if I define a symbolic getter get_x_plus_y = getu(odeprob, odeprob.f.sys.x + odeprob.f.sys.y yielding a SymbolicIndexingInterface.TimeDependentObservedFunction, I can call this fine on an ODESolution to get the observed value.
  • But can't on u within the saving callback because u is just a Vector and doesn't implement the observable method.

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