MethodError while solving PDE

[ranjanan]

Describe the bug 🐞

When solving the Fitzhugh Nagumo equation on https://docs.sciml.ai/ModelOrderReduction/dev/tutorials/deim_FitzHugh-Nagumo/ using the single argument solve call, I get a MethodError. I don't get the error when I specify the solver.

Expected behavior

Creation of a PDESolution object like the following:

julia> solve(prob, Tsit5())
PDESolution:
  Return Code:
    Success
  Dependent variables:
    w(x, t): (16, 232) sized solution
    v(x, t): (16, 232) sized solution
  Domain:
    t ∈ (0.0, 14.0) with 232 non-uniform points. average step size 0.06060606060606061
    x ∈ (0.0, 1.0) with 16 points, step size 0.06666666666666667
  From system:
    Equations:
L"\begin{align}
-0.05 + 0.015 \frac{\mathrm{d}}{\mathrm{d}t} v\left( x, t \right) - 0.000225 \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} v\left( x, t \right) + w\left( x, t \right) - v\left( x, t \right) \left( 1 - v\left( x, t \right) \right) \left( -0.1 + v\left( x, t \right) \right) &= 0 \\
-0.05 - 0.5 v\left( x, t \right) + \frac{\mathrm{d}}{\mathrm{d}t} w\left( x, t \right) + 2 w\left( x, t \right) &= 0
\end{align}
"
    Boundary/Initial Conditions:
L"\begin{align}
v\left( x, 0 \right) &= 0 \\
w\left( x, 0 \right) &= 0 \\
\frac{\mathrm{d}}{\mathrm{d}x} v\left( 0, t \right) &=  - 50000 t^{3} e^{ - 15 t} \\
\frac{\mathrm{d}}{\mathrm{d}x} v\left( 1, t \right) &= 0
\end{align}
"

Minimal Reproducible Example 👇

using ModelingToolkit
@independent_variables x t 
@variables v(..) w(..)
Dx = Differential(x)
Dxx = Dx^2
Dt = Differential(t)
const L = 1.0
const ε = 0.015
const b = 0.5
const γ = 2.0
const c = 0.05
f(v) = v * (v - 0.1) * (1.0 - v)
i₀(t) = 50000.0t^3 * exp(-15.0t)
eqs = [ε * Dt(v(x, t)) ~ ε^2 * Dxx(v(x, t)) + f(v(x, t)) - w(x, t) + c,
    Dt(w(x, t)) ~ b * v(x, t) - γ * w(x, t) + c]
bcs = [v(x, 0.0) ~ 0.0,
    w(x, 0) ~ 0.0,
    Dx(v(0, t)) ~ -i₀(t),
    Dx(v(L, t)) ~ 0.0]
domains = [x ∈ (0.0, L),
    t ∈ (0.0, 14.0)]
ivs = [x, t]
dvs = [v(x, t), w(x, t)]
pde_sys = PDESystem(eqs, bcs, domains, ivs, dvs; name = Symbol("FitzHugh-Nagumo"))

using MethodOfLines
N = 15 # equidistant discretization intervals
dx = (L - 0.0) / N
dxs = [x => dx]
order = 2
discretization = MOLFiniteDifference(dxs, t; approx_order = order)
ode_sys, tspan = symbolic_discretize(pde_sys, discretization)
simp_sys = structural_simplify(ode_sys)
ode_prob = ODEProblem(simp_sys, nothing, tspan)
solve(ode_prob)

Error & Stacktrace ⚠️

julia> solve(prob)
ERROR: MethodError: no method matching SciMLBase.PDETimeSeriesSolution(::SciMLBase.PDETimeSeriesSolution{…}, ::MethodOfLines.MOLMetadata{…})

Closest candidates are:
  SciMLBase.PDETimeSeriesSolution(::SciMLBase.AbstractODESolution{T}, ::MethodOfLines.MOLMetadata) where T
   @ MethodOfLines ~/.julia/packages/MethodOfLines/iJ5Ue/src/interface/solution/timedep.jl:11

Stacktrace:
 [1] wrap_sol(sol::SciMLBase.PDETimeSeriesSolution{…}, metadata::MethodOfLines.MOLMetadata{…})
   @ SciMLBase ~/.julia/packages/SciMLBase/jU6iu/src/solutions/pde_solutions.jl:115
 [2] wrap_sol(sol::SciMLBase.PDETimeSeriesSolution{…})
   @ SciMLBase ~/.julia/packages/SciMLBase/jU6iu/src/solutions/basic_solutions.jl:95
 [3] solve(::ODEProblem{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{})
   @ DiffEqBase ~/.julia/packages/DiffEqBase/slKc5/src/solve.jl:1003
 [4] solve(::ODEProblem{Vector{…}, Tuple{…}, true, ModelingToolkit.MTKParameters{…}, ODEFunction{…}, @Kwargs{}, MethodOfLines.MOLMetadata{…}})
   @ DiffEqBase ~/.julia/packages/DiffEqBase/slKc5/src/solve.jl:993
 [5] top-level scope
   @ REPL[14]:1
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

(ROM_FitzhughNagumo) pkg> st
Project ROM_FitzhughNagumo v0.1.0
Status `~/.julia/dev/ROM_FitzhughNagumo/Project.toml`
  [0c46a032] DifferentialEquations v7.14.0
  [94925ecb] MethodOfLines v0.11.3
⌃ [961ee093] ModelingToolkit v9.32.0
Info Packages marked with ⌃ have new versions available and may be upgradable.

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

julia> Pkg.status(; mode = PKGMODE_MANIFEST)
Project ROM_FitzhughNagumo v0.1.0
Status `~/.julia/dev/ROM_FitzhughNagumo/Manifest.toml`
  [47edcb42] ADTypes v1.7.1
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.37
  [79e6a3ab] Adapt v4.0.4
  [66dad0bd] AliasTables v1.1.3
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.16.0
  [4c555306] ArrayLayouts v1.10.3
  [13072b0f] AxisAlgorithms v1.1.0
  [aae01518] BandedMatrices v1.7.4
  [e2ed5e7c] Bijections v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [764a87c0] BoundaryValueDiffEq v5.9.1
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.6
  [00ebfdb7] CSTParser v3.4.3
  [d360d2e6] ChainRulesCore v1.24.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [861a8166] Combinatorics v1.0.2
  [a80b9123] CommonMark v0.8.12
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
⌅ [187b0558] ConstructionBase v1.5.6
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [bcd4f6db] DelayDiffEq v5.48.1
  [2b5f629d] DiffEqBase v6.155.0
  [459566f4] DiffEqCallbacks v3.9.1
  [77a26b50] DiffEqNoiseProcess v5.23.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [0c46a032] DifferentialEquations v7.14.0
  [a0c0ee7d] DifferentiationInterface v0.5.17
  [b4f34e82] Distances v0.10.11
  [31c24e10] Distributions v0.25.111
  [ffbed154] DocStringExtensions v0.9.3
  [5b8099bc] DomainSets v0.7.14
⌅ [7c1d4256] DynamicPolynomials v0.5.7
⌅ [06fc5a27] DynamicQuantities v0.13.2
  [4e289a0a] EnumX v1.0.4
  [f151be2c] EnzymeCore v0.7.8
  [d4d017d3] ExponentialUtilities v1.26.1
  [e2ba6199] ExprTools v0.1.10
⌅ [6b7a57c9] Expronicon v0.8.5
  [9d29842c] FastAlmostBandedMatrices v0.1.3
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [29a986be] FastLapackInterface v2.0.4
  [1a297f60] FillArrays v1.13.0
  [64ca27bc] FindFirstFunctions v1.4.1
  [6a86dc24] FiniteDiff v2.24.0
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v0.10.36
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.4.12
  [46192b85] GPUArraysCore v0.1.6
  [c145ed77] GenericSchur v0.5.4
  [c27321d9] Glob v1.3.1
  [86223c79] Graphs v1.11.2
  [3e5b6fbb] HostCPUFeatures v0.1.17
  [34004b35] HypergeometricFunctions v0.3.24
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [a98d9a8b] Interpolations v0.15.1
  [8197267c] IntervalSets v0.7.10
  [3587e190] InverseFunctions v0.1.16
  [92d709cd] IrrationalConstants v0.2.2
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.6.0
  [682c06a0] JSON v0.21.4
  [98e50ef6] JuliaFormatter v1.0.60
  [ccbc3e58] JumpProcesses v9.13.7
  [ef3ab10e] KLU v0.6.0
  [ba0b0d4f] Krylov v0.9.6
  [b964fa9f] LaTeXStrings v1.3.1
  [2ee39098] LabelledArrays v1.16.0
  [984bce1d] LambertW v0.4.6
  [23fbe1c1] Latexify v0.16.5
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.2.1
  [2d8b4e74] LevyArea v1.0.0
  [d3d80556] LineSearches v7.3.0
  [7ed4a6bd] LinearSolve v2.34.0
  [2ab3a3ac] LogExpFunctions v0.3.28
  [bdcacae8] LoopVectorization v0.12.171
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [a3b82374] MatrixFactorizations v3.0.1
  [bb5d69b7] MaybeInplace v0.1.4
  [94925ecb] MethodOfLines v0.11.3
  [e1d29d7a] Missings v1.2.0
⌃ [961ee093] ModelingToolkit v9.32.0
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.6
  [d8a4904e] MutableArithmetics v1.4.6
  [d41bc354] NLSolversBase v7.8.3
  [2774e3e8] NLsolve v4.5.1
  [77ba4419] NaNMath v1.0.2
  [8913a72c] NonlinearSolve v3.14.0
  [6fe1bfb0] OffsetArrays v1.14.1
  [429524aa] Optim v1.9.4
  [bac558e1] OrderedCollections v1.6.3
  [1dea7af3] OrdinaryDiffEq v6.89.0
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.1.0
  [6ad6398a] OrdinaryDiffEqBDF v1.1.2
  [bbf590c4] OrdinaryDiffEqCore v1.5.1
  [50262376] OrdinaryDiffEqDefault v1.1.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.1.0
  [9286f039] OrdinaryDiffEqExplicitRK v1.1.0
  [e0540318] OrdinaryDiffEqExponentialRK v1.1.0
  [becaefa8] OrdinaryDiffEqExtrapolation v1.1.0
  [5960d6e9] OrdinaryDiffEqFIRK v1.1.1
  [101fe9f7] OrdinaryDiffEqFeagin v1.1.0
  [d3585ca7] OrdinaryDiffEqFunctionMap v1.1.1
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.1.0
  [9f002381] OrdinaryDiffEqIMEXMultistep v1.1.0
  [521117fe] OrdinaryDiffEqLinear v1.1.0
  [1344f307] OrdinaryDiffEqLowOrderRK v1.2.0
  [b0944070] OrdinaryDiffEqLowStorageRK v1.2.1
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.2.1
  [c9986a66] OrdinaryDiffEqNordsieck v1.1.0
  [5dd0a6cf] OrdinaryDiffEqPDIRK v1.1.0
  [5b33eab2] OrdinaryDiffEqPRK v1.1.0
  [04162be5] OrdinaryDiffEqQPRK v1.1.0
  [af6ede74] OrdinaryDiffEqRKN v1.1.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.2.0
  [2d112036] OrdinaryDiffEqSDIRK v1.1.0
  [669c94d9] OrdinaryDiffEqSSPRK v1.2.0
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.1.0
  [358294b1] OrdinaryDiffEqStabilizedRK v1.1.0
  [fa646aed] OrdinaryDiffEqSymplecticRK v1.1.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.1.0
  [79d7bb75] OrdinaryDiffEqVerner v1.1.1
  [a7812802] PDEBase v0.1.14
  [90014a1f] PDMats v0.11.31
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.24
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [43287f4e] PtrArrays v1.2.1
  [1fd47b50] QuadGK v2.11.0
  [74087812] Random123 v1.7.0
  [e6cf234a] RandomNumbers v1.6.0
  [c84ed2f1] Ratios v0.4.5
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.27.0
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [79098fc4] Rmath v0.7.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
  [0bca4576] SciMLBase v2.52.2
  [c0aeaf25] SciMLOperators v0.3.10
  [53ae85a6] SciMLStructures v1.5.0
  [efcf1570] Setfield v1.1.1
  [727e6d20] SimpleNonlinearSolve v1.12.0
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
  [47a9eef4] SparseDiffTools v2.20.0
  [0a514795] SparseMatrixColorings v0.4.0
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.4.0
  [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.7
  [1e83bf80] StaticArraysCore v1.4.3
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.3
  [4c63d2b9] StatsFuns v1.3.1
  [9672c7b4] SteadyStateDiffEq v2.4.0
  [789caeaf] StochasticDiffEq v6.69.0
  [7792a7ef] StrideArraysCore v0.5.7
  [c3572dad] Sundials v4.25.0
  [2efcf032] SymbolicIndexingInterface v0.3.30
⌃ [19f23fe9] SymbolicLimits v0.2.1
⌅ [d1185830] SymbolicUtils v2.1.3
⌅ [0c5d862f] Symbolics v5.36.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
⌅ [8ea1fca8] TermInterface v0.4.1
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.24
  [0796e94c] Tokenize v0.5.29
  [d5829a12] TriangularSolve v0.2.1
  [410a4b4d] Tricks v0.1.9
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1986cc42] Unitful v1.21.0
  [a7c27f48] Unityper v0.1.6
  [3d5dd08c] VectorizationBase v0.21.70
  [19fa3120] VertexSafeGraphs v0.2.0
  [efce3f68] WoodburyMatrices v1.0.0
  [1d5cc7b8] IntelOpenMP_jll v2024.2.1+0
  [856f044c] MKL_jll v2024.2.0+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
⌅ [f50d1b31] Rmath_jll v0.4.3+0
⌅ [fb77eaff] Sundials_jll v5.2.2+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+4
  [05823500] OpenLibm_jll v0.8.1+2
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.52.0+1
  [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> versioninfo()
Julia Version 1.10.5
Commit 6f3fdf7b362 (2024-08-27 14:19 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin22.4.0)
  CPU: 8 × Apple M2
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, apple-m1)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_PKG_USE_CLI_GIT = true
  JULIA_PKG_SERVER = internal.juliahub.com

Additional context

Add any other context about the problem here.