Symbolic regression fails

[sdwfrost]

Describe the bug 🐞

Symbolic regression fails on a problem where Sindy and DMD work.

Expected behavior

A data-driven solution should be found.

Minimal Reproducible Example 👇

# Load libraries
using OrdinaryDiffEq
using DataDrivenDiffEq
using DataDrivenSparse
using DataDrivenSR
using ModelingToolkit

# Define the SIR model
function sir_ode(u,p,t)
    (s,i,r) = u
    (β,γ) = p
    ds = -β*s*i
    di = β*s*i - γ*i
    dr = γ*i
    [ds,di,dr]
end

p = [0.5,0.25]
u0 = [0.99, 0.01, 0.0]
tspan = (0.0, 40.0)
δt = 1

solver = ExplicitRK()
sir_prob = ODEProblem(sir_ode, u0, tspan, p)
sir_sol = solve(sir_prob, solver, saveat = δt)

# Define the data-driven problem
dd_prob = DataDrivenProblem(sir_sol)

# Define the basis
@parameters t
@variables (u(t))[1:3]
Ψ = Basis([u; u[1]*u[2]], u, independent_variable = t)

## Sparse regression (works)
res_sparse = solve(dd_prob, Ψ, STLSQ(),digits=1)

## Symbolic regression
eqsearch_options = SymbolicRegression.Options(binary_operators = [+, *],
                                              loss = L1DistLoss(),
                                              verbosity = -1, progress = false, npop = 30,
                                              timeout_in_seconds = 60.0)
eqs = EQSearch(eq_options = eqsearch_options)
res_sr = solve(dd_prob, Ψ, eqs)

Error & Stacktrace ⚠️

ERROR: BoundsError: attempt to access 0-element Vector{Any} at index [1]
Stacktrace:
[1] getindex
@ ./essentials.jl:13 [inlined]

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

  [3c9adf31] DataDrivenDMD v0.1.1
⌃ [2445eb08] DataDrivenDiffEq v1.0.2
  [7fed8a53] DataDrivenSR v0.1.2
  [5b588203] DataDrivenSparse v0.1.2
  [31c24e10] Distributions v0.25.112
⌅ [961ee093] ModelingToolkit v8.46.1
⌃ [1dea7af3] OrdinaryDiffEq v6.58.2
  [91a5bcdd] Plots v1.40.8
⌅ [8254be44] SymbolicRegression v0.14.5
  [9a3f8284] Random

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

⌅ [47edcb42] ADTypes v0.1.6
⌅ [c3fe647b] AbstractAlgebra v0.27.10
  [621f4979] AbstractFFTs v1.5.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.38
⌅ [79e6a3ab] Adapt v3.7.2
  [66dad0bd] AliasTables v1.1.3
  [dce04be8] ArgCheck v2.3.0
  [ec485272] ArnoldiMethod v0.4.0
⌃ [4fba245c] ArrayInterface v7.7.1
  [30b0a656] ArrayInterfaceCore v0.1.29
  [a9b6321e] Atomix v0.1.0
⌅ [15f4f7f2] AutoHashEquals v0.2.0
  [198e06fe] BangBang v0.4.3
  [9718e550] Baselet v0.1.1
  [e2ed5e7c] Bijections v0.1.9
  [d1d4a3ce] BitFlags v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.6
  [00ebfdb7] CSTParser v3.4.3
  [49dc2e85] Calculus v0.5.2
  [082447d4] ChainRules v1.71.0
  [d360d2e6] ChainRulesCore v1.25.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [944b1d66] CodecZlib v0.7.6
  [35d6a980] ColorSchemes v3.27.0
⌅ [3da002f7] ColorTypes v0.11.5
  [c3611d14] ColorVectorSpace v0.10.0
  [5ae59095] Colors v0.13.0
  [861a8166] Combinatorics v1.0.2
  [a80b9123] CommonMark v0.8.15
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [34da2185] Compat v4.16.0
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [f0e56b4a] ConcurrentUtilities v2.4.2
⌅ [187b0558] ConstructionBase v1.5.6
  [6add18c4] ContextVariablesX v0.1.3
  [d38c429a] Contour v0.6.3
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [3c9adf31] DataDrivenDMD v0.1.1
⌃ [2445eb08] DataDrivenDiffEq v1.0.2
  [7fed8a53] DataDrivenSR v0.1.2
  [5b588203] DataDrivenSparse v0.1.2
⌅ [82cc6244] DataInterpolations v3.12.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [244e2a9f] DefineSingletons v0.1.2
  [8bb1440f] DelimitedFiles v1.9.1
⌃ [2b5f629d] DiffEqBase v6.130.0
⌅ [459566f4] DiffEqCallbacks v2.35.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [b4f34e82] Distances v0.10.12
  [31c24e10] Distributions v0.25.112
  [ffbed154] DocStringExtensions v0.9.3
⌅ [5b8099bc] DomainSets v0.5.14
⌅ [a40a106e] DynamicExpressions v0.4.3
⌅ [7c1d4256] DynamicPolynomials v0.4.6
  [4e289a0a] EnumX v1.0.4
  [460bff9d] ExceptionUnwrapping v0.1.10
  [d4d017d3] ExponentialUtilities v1.26.1
  [e2ba6199] ExprTools v0.1.10
  [c87230d0] FFMPEG v0.4.2
  [cc61a311] FLoops v0.2.2
  [b9860ae5] FLoopsBase v0.1.1
⌅ [7034ab61] FastBroadcast v0.2.8
  [9aa1b823] FastClosures v0.3.2
  [29a986be] FastLapackInterface v2.0.4
⌅ [1a297f60] FillArrays v0.13.11
  [6a86dc24] FiniteDiff v2.26.0
  [53c48c17] FixedPointNumbers v0.8.5
  [9c68100b] FoldsThreads v0.1.2
  [59287772] Formatting v0.4.3
  [f6369f11] ForwardDiff v0.10.37
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.4.12
⌅ [46192b85] GPUArraysCore v0.1.5
  [28b8d3ca] GR v0.73.8
  [c145ed77] GenericSchur v0.5.4
  [c27321d9] Glob v1.3.1
  [86223c79] Graphs v1.12.0
  [42e2da0e] Grisu v1.0.2
⌅ [0b43b601] Groebner v0.2.11
⌅ [d5909c97] GroupsCore v0.4.2
  [cd3eb016] HTTP v1.10.9
  [3e5b6fbb] HostCPUFeatures v0.1.17
  [34004b35] HypergeometricFunctions v0.3.24
  [7869d1d1] IRTools v0.4.14
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [22cec73e] InitialValues v0.3.1
  [18e54dd8] IntegerMathUtils v0.1.2
  [8197267c] IntervalSets v0.7.10
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.2
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.8
  [692b3bcd] JLLWrappers v1.6.1
  [682c06a0] JSON v0.21.4
  [0f8b85d8] JSON3 v1.14.1
  [98e50ef6] JuliaFormatter v1.0.62
  [b14d175d] JuliaVariables v0.2.4
⌃ [ccbc3e58] JumpProcesses v9.10.1
⌅ [ef3ab10e] KLU v0.4.1
  [63c18a36] KernelAbstractions v0.9.29
  [ba0b0d4f] Krylov v0.9.8
  [929cbde3] LLVM v9.1.3
  [b964fa9f] LaTeXStrings v1.4.0
⌃ [2ee39098] LabelledArrays v1.15.1
⌅ [984bce1d] LambertW v0.4.6
⌅ [23fbe1c1] Latexify v0.15.21
  [10f19ff3] LayoutPointers v0.1.17
  [50d2b5c4] Lazy v0.15.1
  [0fc2ff8b] LeastSquaresOptim v0.8.5
  [d3d80556] LineSearches v7.3.0
⌃ [7ed4a6bd] LinearSolve v2.7.0
  [2ab3a3ac] LogExpFunctions v0.3.28
  [e6f89c97] LoggingExtras v1.1.0
  [bdcacae8] LoopVectorization v0.12.171
⌅ [30fc2ffe] LossFunctions v0.8.1
  [d8e11817] MLStyle v0.4.17
⌅ [f1d291b0] MLUtils v0.3.1
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [739be429] MbedTLS v1.1.9
  [442fdcdd] Measures v0.3.2
  [c03570c3] Memoize v0.4.4
⌅ [e9d8d322] Metatheory v1.3.5
  [128add7d] MicroCollections v0.2.0
  [e1d29d7a] Missings v1.2.0
⌅ [961ee093] ModelingToolkit v8.46.1
  [46d2c3a1] MuladdMacro v0.2.4
⌅ [102ac46a] MultivariatePolynomials v0.4.7
  [d8a4904e] MutableArithmetics v1.5.2
  [d41bc354] NLSolversBase v7.8.3
  [2774e3e8] NLsolve v4.5.1
⌅ [872c559c] NNlib v0.8.21
  [77ba4419] NaNMath v1.0.2
  [71a1bf82] NameResolution v0.1.5
⌅ [8913a72c] NonlinearSolve v1.10.1
  [6fe1bfb0] OffsetArrays v1.14.1
  [4d8831e6] OpenSSL v1.4.3
  [429524aa] Optim v1.9.4
  [bac558e1] OrderedCollections v1.6.3
⌃ [1dea7af3] OrdinaryDiffEq v6.58.2
  [90014a1f] PDMats v0.11.31
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [b98c9c47] Pipe v1.3.0
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.3
  [91a5bcdd] Plots v1.40.8
  [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
  [8162dcfd] PrettyPrint v0.2.0
  [27ebfcd6] Primes v0.5.6
  [49802e3a] ProgressBars v1.5.1
  [92933f4c] ProgressMeter v1.10.2
  [43287f4e] PtrArrays v1.2.1
  [1fd47b50] QuadGK v2.11.1
  [fb686558] RandomExtensions v0.4.4
  [e6cf234a] RandomNumbers v1.6.0
  [c1ae055f] RealDot v0.1.0
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
⌅ [731186ca] RecursiveArrayTools v2.38.0
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [42d2dcc6] Referenceables v0.1.3
  [29dad682] RegularizationTools v0.6.0
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.0
  [79098fc4] Rmath v0.8.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
⌅ [0bca4576] SciMLBase v1.97.0
  [e9a6253c] SciMLNLSolve v0.1.9
  [c0aeaf25] SciMLOperators v0.3.11
  [6c6a2e73] Scratch v1.2.1
  [efcf1570] Setfield v1.1.1
  [605ecd9f] ShowCases v0.1.0
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
⌅ [727e6d20] SimpleNonlinearSolve v0.1.23
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [66db9d55] SnoopPrecompile v1.0.3
  [a2af1166] SortingAlgorithms v1.2.1
⌃ [47a9eef4] SparseDiffTools v2.4.1
  [dc90abb0] SparseInverseSubset v0.1.2
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.4.0
  [171d559e] SplittablesBase v0.1.15
  [860ef19b] StableRNGs v1.0.2
⌅ [aedffcd0] Static v0.8.10
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.8
  [1e83bf80] StaticArraysCore v1.4.3
  [82ae8749] StatsAPI v1.7.0
⌅ [2913bbd2] StatsBase v0.33.21
  [4c63d2b9] StatsFuns v1.3.2
  [7792a7ef] StrideArraysCore v0.5.7
  [09ab397b] StructArrays v0.6.18
  [856f2bd8] StructTypes v1.11.0
⌅ [2efcf032] SymbolicIndexingInterface v0.2.2
⌅ [8254be44] SymbolicRegression v0.14.5
⌅ [d1185830] SymbolicUtils v0.19.11
⌅ [0c5d862f] Symbolics v4.14.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [62fd8b95] TensorCore v0.1.1
⌅ [8ea1fca8] TermInterface v0.2.3
  [8290d209] ThreadingUtilities v0.5.2
  [ac1d9e8a] ThreadsX v0.1.12
  [a759f4b9] TimerOutputs v0.5.25
  [0796e94c] Tokenize v0.5.29
  [3bb67fe8] TranscodingStreams v0.11.3
  [28d57a85] Transducers v0.4.84
  [a2a6695c] TreeViews v0.3.0
  [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
  [d9a01c3f] Underscores v3.0.0
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.21.0
  [45397f5d] UnitfulLatexify v1.6.4
  [013be700] UnsafeAtomics v0.2.1
  [d80eeb9a] UnsafeAtomicsLLVM v0.2.1
  [41fe7b60] Unzip v0.2.0
  [3d5dd08c] VectorizationBase v0.21.71
  [19fa3120] VertexSafeGraphs v0.2.0
⌃ [e88e6eb3] Zygote v0.6.41
  [700de1a5] ZygoteRules v0.2.5
  [6e34b625] Bzip2_jll v1.0.8+2
  [83423d85] Cairo_jll v1.18.2+1
  [ee1fde0b] Dbus_jll v1.14.10+0
  [2702e6a9] EpollShim_jll v0.0.20230411+0
  [2e619515] Expat_jll v2.6.2+0
⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
  [a3f928ae] Fontconfig_jll v2.13.96+0
  [d7e528f0] FreeType2_jll v2.13.2+0
  [559328eb] FriBidi_jll v1.0.14+0
  [0656b61e] GLFW_jll v3.4.0+1
  [d2c73de3] GR_jll v0.73.8+0
  [78b55507] Gettext_jll v0.21.0+0
  [7746bdde] Glib_jll v2.80.5+0
  [3b182d85] Graphite2_jll v1.3.14+0
  [2e76f6c2] HarfBuzz_jll v8.3.1+0
  [aacddb02] JpegTurbo_jll v3.0.4+0
  [c1c5ebd0] LAME_jll v3.100.2+0
  [88015f11] LERC_jll v4.0.0+0
  [dad2f222] LLVMExtra_jll v0.0.34+0
  [1d63c593] LLVMOpenMP_jll v18.1.7+0
  [dd4b983a] LZO_jll v2.10.2+1
⌅ [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.11.0+0
  [7e76a0d4] Libglvnd_jll v1.6.0+0
  [7add5ba3] Libgpg_error_jll v1.50.0+0
  [94ce4f54] Libiconv_jll v1.17.0+1
  [4b2f31a3] Libmount_jll v2.40.1+0
  [89763e89] Libtiff_jll v4.7.0+0
  [38a345b3] Libuuid_jll v2.40.1+0
  [e7412a2a] Ogg_jll v1.3.5+1
  [458c3c95] OpenSSL_jll v3.0.15+1
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.3+0
  [36c8627f] Pango_jll v1.54.1+0
  [30392449] Pixman_jll v0.43.4+0
  [c0090381] Qt6Base_jll v6.7.1+1
  [629bc702] Qt6Declarative_jll v6.7.1+2
  [ce943373] Qt6ShaderTools_jll v6.7.1+1
  [e99dba38] Qt6Wayland_jll v6.7.1+1
  [f50d1b31] Rmath_jll v0.5.1+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.21.0+1
  [2381bf8a] Wayland_protocols_jll v1.31.0+0
  [02c8fc9c] XML2_jll v2.13.4+0
  [aed1982a] XSLT_jll v1.1.41+0
  [ffd25f8a] XZ_jll v5.6.3+0
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  [c834827a] Xorg_libSM_jll v1.2.4+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.11+0
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
  [a3789734] Xorg_libXdmcp_jll v1.1.4+0
  [1082639a] Xorg_libXext_jll v1.3.6+0
  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
  [d1454406] Xorg_libXinerama_jll v1.1.4+4
  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
  [ea2f1a96] Xorg_libXrender_jll v0.9.11+0
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.0+0
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.6+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.0+0
  [3161d3a3] Zstd_jll v1.5.6+1
  [35ca27e7] eudev_jll v3.2.9+0
  [214eeab7] fzf_jll v0.53.0+0
  [1a1c6b14] gperf_jll v3.1.1+0
  [a4ae2306] libaom_jll v3.9.0+0
  [0ac62f75] libass_jll v0.15.2+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.3+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.44+0
  [f27f6e37] libvorbis_jll v1.3.7+2
  [009596ad] mtdev_jll v1.1.6+0
⌅ [1270edf5] x264_jll v2021.5.5+0
⌅ [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+1
  [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
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.8.0+1
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2

• Output of versioninfo()

Julia Version 1.10.3
Commit 0b4590a5507 (2024-04-30 10:59 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin22.4.0)
  CPU: 10 × Apple M1 Max
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, apple-m1)
Threads: 8 default, 0 interactive, 4 GC (on 8 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 8