`solve` throws `MethodError: cannot convert BasicSymbolc to a Float64` for `ODEProblem` created from `Basis`

[Zinoex]

Describe the bug 🐞
Solving an ODEProblem constructed from Basis throws ERROR: LoadError: MethodError: Cannot convert an object of type SymbolicUtils.BasicSymbolic{Real} to an object of type Float64.

Expected behavior
No errors thrown, solution returned.

Minimal Reproducible Example 👇
This is the SciML SINDy example with the two last lines added.

using DataDrivenDiffEq
using LinearAlgebra
using OrdinaryDiffEq
using DataDrivenSparse
using StableRNGs

rng = StableRNG(1337)

function pendulum(u, p, t)
    x = u[2]
    y = -9.81sin(u[1]) - 0.3u[2]^3 - 3.0 * cos(u[1]) - 10.0 * exp(-((t - 5.0) / 5.0)^2)
    return [x; y]
end

u0 = [0.99π; -1.0]
tspan = (0.0, 15.0)
prob = ODEProblem(pendulum, u0, tspan)
sol = solve(prob, Tsit5(), saveat = 0.01);

X = sol[:, :] + 0.2 .* randn(rng, size(sol));
ts = sol.t;

prob = ContinuousDataDrivenProblem(X, ts, GaussianKernel(),
    U = (u, p, t) -> [exp(-((t - 5.0) / 5.0)^2)],
    p = ones(2))

@variables u[1:2] c[1:1]
@parameters w[1:2]
u = collect(u)
c = collect(c)
w = collect(w)

h = Num[sin.(w[1] .* u[1]); cos.(w[2] .* u[1]); polynomial_basis(u, 5); c]

basis = Basis(h, u, parameters = w, controls = c);
println(basis) # hide

sampler = DataProcessing(split = 0.8, shuffle = true, batchsize = 30, rng = rng)
λs = exp10.(-10:0.1:0)
opt = STLSQ(λs)
res = solve(prob, basis, opt,
    options = DataDrivenCommonOptions(data_processing = sampler, digits = 1))

system = get_basis(res)
params = get_parameter_values(system)
println(system) # hide
println(params) # hide

recovered_model = ODEProblem(system, u0, tspan, params)
recovered_sol = solve(recovered_model)

Error & Stacktrace ⚠️

ERROR: LoadError: MethodError: Cannot `convert` an object of type SymbolicUtils.BasicSymbolic{Real} to an object of type Float64
The function `convert` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  (::Type{T})(::SymbolicUtils.Symbolic) where T<:Union{AbstractFloat, Integer, Complex{<:AbstractFloat}, Complex{<:Integer}}
   @ Symbolics ~/.julia/packages/Symbolics/lJiB2/src/Symbolics.jl:180
  convert(::Type{T}, ::Union{Static.StaticBool{N}, Static.StaticFloat64{N}, Static.StaticInt{N}} where N) where T<:Number
   @ Static ~/.julia/packages/Static/YQhfT/src/Static.jl:434
  convert(::Type{T}, ::AbstractChar) where T<:Number
   @ Base char.jl:185
  ...

Stacktrace:
  [1] setindex!(A::Memory{Float64}, x::SymbolicUtils.BasicSymbolic{Real}, i1::Int64)
    @ Base ./genericmemory.jl:243
  [2] unsafe_copyto!(dest::Memory{Float64}, doffs::Int64, src::Memory{Any}, soffs::Int64, n::Int64)
    @ Base ./genericmemory.jl:153
  [3] unsafe_copyto!
    @ ./genericmemory.jl:133 [inlined]
  [4] _copyto_impl!
    @ ./array.jl:308 [inlined]
  [5] copyto!
    @ ./array.jl:294 [inlined]
  [6] copyto!
    @ ./array.jl:319 [inlined]
  [7] copyto_axcheck!
    @ ./abstractarray.jl:1167 [inlined]
  [8] Array
    @ ./array.jl:626 [inlined]
  [9] convert(::Type{Vector{Float64}}, a::Vector{Any})
    @ Base ./array.jl:618
 [10] setproperty!(x::OrdinaryDiffEqCore.ODEIntegrator{…}, f::Symbol, v::Vector{…})
    @ Base ./Base.jl:52
 [11] initialize!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, cache::OrdinaryDiffEqTsit5.Tsit5ConstantCache)
    @ OrdinaryDiffEqTsit5 ~/.julia/packages/OrdinaryDiffEqTsit5/o07IY/src/tsit_perform_step.jl:111
 [12] initialize!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, cache::OrdinaryDiffEqCore.DefaultCache{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/qzTLI/src/perform_step/composite_perform_step.jl:38
 [13] __init(prob::ODEProblem{…}, alg::CompositeAlgorithm{…}, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}; saveat::Tuple{}, tstops::Tuple{}, d_discontinuities::Tuple{}, save_idxs::Nothing, save_everystep::Bool, save_on::Bool, save_discretes::Bool, save_start::Bool, save_end::Nothing, callback::Nothing, dense::Bool, calck::Bool, dt::Float64, dtmin::Float64, dtmax::Float64, force_dtmin::Bool, adaptive::Bool, gamma::Rational{…}, abstol::Nothing, reltol::Nothing, qmin::Rational{…}, qmax::Int64, qsteady_min::Int64, qsteady_max::Int64, beta1::Nothing, beta2::Nothing, qoldinit::Rational{…}, controller::Nothing, fullnormalize::Bool, failfactor::Int64, maxiters::Int64, internalnorm::typeof(DiffEqBase.ODE_DEFAULT_NORM), internalopnorm::typeof(opnorm), isoutofdomain::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), unstable_check::typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), verbose::Bool, timeseries_errors::Bool, dense_errors::Bool, advance_to_tstop::Bool, stop_at_next_tstop::Bool, initialize_save::Bool, progress::Bool, progress_steps::Int64, progress_name::String, progress_message::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), progress_id::Symbol, userdata::Nothing, allow_extrapolation::Bool, initialize_integrator::Bool, alias::ODEAliasSpecifier, initializealg::OrdinaryDiffEqCore.DefaultInit, kwargs::@Kwargs{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/qzTLI/src/solve.jl:578
 [14] __init (repeats 2 times)
    @ ~/.julia/packages/OrdinaryDiffEqCore/qzTLI/src/solve.jl:11 [inlined]
 [15] #__solve#62
    @ ~/.julia/packages/OrdinaryDiffEqCore/qzTLI/src/solve.jl:6 [inlined]
 [16] __solve
    @ ~/.julia/packages/OrdinaryDiffEqCore/qzTLI/src/solve.jl:1 [inlined]
 [17] #__solve#3
    @ ~/.julia/packages/OrdinaryDiffEqDefault/MdlB6/src/default_alg.jl:48 [inlined]
 [18] __solve
    @ ~/.julia/packages/OrdinaryDiffEqDefault/MdlB6/src/default_alg.jl:47 [inlined]
 [19] #__solve#49
    @ ~/.julia/packages/DiffEqBase/p82Yh/src/solve.jl:741 [inlined]
 [20] __solve
    @ ~/.julia/packages/DiffEqBase/p82Yh/src/solve.jl:732 [inlined]
 [21] #solve_call#33
    @ ~/.julia/packages/DiffEqBase/p82Yh/src/solve.jl:127 [inlined]
 [22] solve_call
    @ ~/.julia/packages/DiffEqBase/p82Yh/src/solve.jl:84 [inlined]
 [23] #solve_up#39
    @ ~/.julia/packages/DiffEqBase/p82Yh/src/solve.jl:547 [inlined]
 [24] solve_up
    @ ~/.julia/packages/DiffEqBase/p82Yh/src/solve.jl:540 [inlined]
 [25] #solve#38
    @ ~/.julia/packages/DiffEqBase/p82Yh/src/solve.jl:530 [inlined]
 [26] solve(::ODEProblem{Vector{…}, Tuple{…}, false, Vector{…}, ODEFunction{…}, @Kwargs{}, SciMLBase.StandardODEProblem})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/p82Yh/src/solve.jl:520
 [27] top-level scope
    @ ~/<path_to_proj>/mwe.jl:50
in expression starting at /<path_to_proj>/mwe.jl:50
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `~/<path_to_proj>/Project.toml`
  [2445eb08] DataDrivenDiffEq v1.9.2
  [5b588203] DataDrivenSparse v0.1.3
  [1dea7af3] OrdinaryDiffEq v6.102.1
  [860ef19b] StableRNGs v1.0.3

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

Status `~/<path_to_proj>/Manifest.toml`
  [47edcb42] ADTypes v1.18.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.42
  [79e6a3ab] Adapt v4.4.0
  [66dad0bd] AliasTables v1.1.3
  [dce04be8] ArgCheck v2.5.0
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.20.0
  [4c555306] ArrayLayouts v1.11.2
  [a9b6321e] Atomix v1.1.2
  [198e06fe] BangBang v0.4.4
  [9718e550] Baselet v0.1.1
  [e2ed5e7c] Bijections v0.2.2
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [8e7c35d0] BlockArrays v1.7.2
  [70df07ce] BracketingNonlinearSolve v1.4.0
  [2a0fbf3d] CPUSummary v0.2.7
  [d360d2e6] ChainRulesCore v1.26.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
⌅ [861a8166] Combinatorics v1.0.2
  [a80b9123] CommonMark v0.9.1
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.18.1
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.6.0
  [6add18c4] ContextVariablesX v0.1.3
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [2445eb08] DataDrivenDiffEq v1.9.2
  [5b588203] DataDrivenSparse v0.1.3
  [82cc6244] DataInterpolations v8.6.1
⌅ [864edb3b] DataStructures v0.18.22
  [e2d170a0] DataValueInterfaces v1.0.0
  [244e2a9f] DefineSingletons v0.1.2
  [8bb1440f] DelimitedFiles v1.9.1
  [2b5f629d] DiffEqBase v6.190.2
  [459566f4] DiffEqCallbacks v4.9.0
  [77a26b50] DiffEqNoiseProcess v5.24.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.7.8
  [8d63f2c5] DispatchDoctor v0.4.26
  [31c24e10] Distributions v0.25.120
  [ffbed154] DocStringExtensions v0.9.5
  [5b8099bc] DomainSets v0.7.16
⌃ [7c1d4256] DynamicPolynomials v0.6.3
  [06fc5a27] DynamicQuantities v1.10.0
  [4e289a0a] EnumX v1.0.5
  [f151be2c] EnzymeCore v0.8.14
  [d4d017d3] ExponentialUtilities v1.27.0
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  [6a86dc24] FiniteDiff v2.28.1
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v1.2.1
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.5.2
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  [c145ed77] GenericSchur v0.5.5
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⌅ [70703baa] JuliaSyntax v0.4.10
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  [ba0b0d4f] Krylov v0.10.2
  [b964fa9f] LaTeXStrings v1.4.0
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  [5078a376] LazyArrays v2.6.3
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  [7ed4a6bd] LinearSolve v3.40.2
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  [d8e11817] MLStyle v0.4.17
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  [d125e4d3] ManualMemory v0.1.8
  [bb5d69b7] MaybeInplace v0.1.4
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  [e1d29d7a] Missings v1.2.0
  [961ee093] ModelingToolkit v10.24.0
  [2e0e35c7] Moshi v0.3.7
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⌃ [102ac46a] MultivariatePolynomials v0.5.9
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  [9a2c21bd] NonlinearSolveQuasiNewton v1.9.0
  [26075421] NonlinearSolveSpectralMethods v1.4.0
  [6fe1bfb0] OffsetArrays v1.17.0
  [429524aa] Optim v1.13.2
  [bac558e1] OrderedCollections v1.8.1
  [1dea7af3] OrdinaryDiffEq v6.102.1
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.5.0
  [6ad6398a] OrdinaryDiffEqBDF v1.10.1
  [bbf590c4] OrdinaryDiffEqCore v1.34.0
  [50262376] OrdinaryDiffEqDefault v1.8.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.16.1
  [9286f039] OrdinaryDiffEqExplicitRK v1.4.0
  [e0540318] OrdinaryDiffEqExponentialRK v1.8.0
  [becaefa8] OrdinaryDiffEqExtrapolation v1.9.0
  [5960d6e9] OrdinaryDiffEqFIRK v1.16.0
  [101fe9f7] OrdinaryDiffEqFeagin v1.4.0
  [d3585ca7] OrdinaryDiffEqFunctionMap v1.5.0
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.5.0
  [9f002381] OrdinaryDiffEqIMEXMultistep v1.7.0
  [521117fe] OrdinaryDiffEqLinear v1.6.0
  [1344f307] OrdinaryDiffEqLowOrderRK v1.6.0
  [b0944070] OrdinaryDiffEqLowStorageRK v1.7.0
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.14.1
  [c9986a66] OrdinaryDiffEqNordsieck v1.4.0
  [5dd0a6cf] OrdinaryDiffEqPDIRK v1.6.0
  [5b33eab2] OrdinaryDiffEqPRK v1.4.0
  [04162be5] OrdinaryDiffEqQPRK v1.4.0
  [af6ede74] OrdinaryDiffEqRKN v1.5.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.18.1
  [2d112036] OrdinaryDiffEqSDIRK v1.7.0
  [669c94d9] OrdinaryDiffEqSSPRK v1.7.0
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.6.0
  [358294b1] OrdinaryDiffEqStabilizedRK v1.4.0
  [fa646aed] OrdinaryDiffEqSymplecticRK v1.7.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.5.0
  [79d7bb75] OrdinaryDiffEqVerner v1.6.0
  [90014a1f] PDMats v0.11.35
  [d96e819e] Parameters v0.12.3
  [e409e4f3] PoissonRandom v0.4.6
  [f517fe37] Polyester v0.7.18
  [1d0040c9] PolyesterWeave v0.2.2
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.34
⌅ [aea7be01] PrecompileTools v1.2.1
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  [1fd47b50] QuadGK v2.11.2
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  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.1
  [ae5879a3] ResettableStacks v1.1.1
  [79098fc4] Rmath v0.8.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.15
  [9dfe8606] SCCNonlinearSolve v1.5.0
  [94e857df] SIMDTypes v0.1.0
  [0bca4576] SciMLBase v2.120.0
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  [c0aeaf25] SciMLOperators v1.7.2
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  [90137ffa] StaticArrays v1.9.15
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  [10745b16] Statistics v1.11.1
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  [2efcf032] SymbolicIndexingInterface v0.3.45
⌃ [19f23fe9] SymbolicLimits v0.2.3
⌅ [d1185830] SymbolicUtils v3.32.0
  [0c5d862f] Symbolics v6.55.0
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  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.5+0
  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.59.0+0
  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

• Output of versioninfo()

Julia Version 1.11.7
Commit f2b3dbda30a (2025-09-08 12:10 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 12 × 13th Gen Intel(R) Core(TM) i7-1365U
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, goldmont)
Threads: 1 default, 0 interactive, 1 GC (on 12 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_VSCODE_REPL = 1

Additional context
Issue emerged after #554 was fixed; however, it is likely that #554 was just the first error hit.