Barely nontrivial boundary conditions work on CPU but not GPU

[nicholaskl97]

Describe the bug 🐞

Some boundary conditions lead to NaNs after optimization on GPU. As shown in the MRE below, the boundary condition u(0) ~ 0 works on GPU (and CPU, not shown), but the boundary condition u(0)^2 ~ 0 only works on CPU, not GPU.

Expected behavior

If a PDESystem works on CPU, it should also work on GPU. u(0)^2 ~ 0 shouldn't result in NaN. Users should be able to specify the equivalent boundary conditions u(0) ~ 0 and u(0)^2 ~ 0 and get similar results.

Minimal Reproducible Example 👇

using NeuralPDE
using Lux, LuxCUDA, Optimization, OptimizationOptimisers, Random, ComponentArrays

Random.seed!(200)

@parameters x
@variables u(..)

eq = [u(x) ~ 0.0]

bc1 = [u(0.0) ~ 0.0]
bc2 = [u(0.0)^2 ~ 0.0]

domain = [x ∈ (-1.0, 1.0)]

# Define neural network discretization
dim_state = 1
dim_hidden = 10
dim_output = 1
chain = Chain(
            Dense(dim_state, dim_hidden, tanh),
            Dense(dim_hidden, dim_hidden, tanh),
            Dense(dim_hidden, 1)
        )

ps = first(Lux.setup(Random.default_rng(), chain))
const gpud = gpu_device()
ps = ps |> ComponentArray |> gpud |> f64

strategy = QuasiRandomTraining(1000)

# u(0) ~ 0 works fine on GPU
discretization1 = PhysicsInformedNN(chain, strategy; init_params = ps)
@named pde_system1 = PDESystem(eq, bc1, domain, [x], [u(x)])

prob1 = discretize(pde_system1, discretization1)
res1 = Optimization.solve(prob1, OptimizationOptimisers.Adam(); maxiters = 10)

@assert !any(isnan.(res1.u))

# u(0)^2 ~ 0 yields NaN parameters on GPU
@named pde_system2 = PDESystem(eq, bc2, domain, [x], [u(x)])

prob2 = discretize(pde_system2, discretization1)
res2 = Optimization.solve(prob2, OptimizationOptimisers.Adam(); maxiters = 10)

@assert all(isnan.(res2.u))

# u(0)^2 ~ 0 works fine on CPU
discretization3 = PhysicsInformedNN(chain, strategy)
@named pde_system3 = PDESystem(eq, bc2, domain, [x], [u(x)])

prob3 = discretize(pde_system3, discretization3)
res3 = Optimization.solve(prob3, OptimizationOptimisers.Adam(); maxiters = 10)

@assert !any(isnan.(res3.u))

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `~/julia_projects/NeuralPDEtests/Project.toml`
  [b0b7db55] ComponentArrays v0.15.19
⌃ [b2108857] Lux v1.2.3
  [d0bbae9a] LuxCUDA v0.3.3
  [961ee093] ModelingToolkit v9.51.0
  [315f7962] NeuralPDE v5.17.0
  [7f7a1694] Optimization v4.0.5
  [42dfb2eb] OptimizationOptimisers v0.3.4
Info Packages marked with ⌃ have new versions available and may be upgradable.

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

Status `~/julia_projects/NeuralPDEtests/Manifest.toml`
  [47edcb42] ADTypes v1.10.0
  [621f4979] AbstractFFTs v1.5.0
  [80f14c24] AbstractMCMC v5.6.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.38
  [79e6a3ab] Adapt v4.1.1
  [0bf59076] AdvancedHMC v0.6.4
  [66dad0bd] AliasTables v1.1.3
  [dce04be8] ArgCheck v2.3.0
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.17.1
  [4c555306] ArrayLayouts v1.10.4
  [a9b6321e] Atomix v0.1.0
  [13072b0f] AxisAlgorithms v1.1.0
  [39de3d68] AxisArrays v0.4.7
  [ab4f0b2a] BFloat16s v0.5.0
  [198e06fe] BangBang v0.4.3
  [9718e550] Baselet v0.1.1
  [e2ed5e7c] Bijections v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [8e7c35d0] BlockArrays v1.1.1
  [70df07ce] BracketingNonlinearSolve v1.1.0
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.6
  [00ebfdb7] CSTParser v3.4.3
  [052768ef] CUDA v5.5.2
  [1af6417a] CUDA_Runtime_Discovery v0.3.5
  [7057c7e9] Cassette v0.3.14
  [082447d4] ChainRules v1.72.1
  [d360d2e6] ChainRulesCore v1.25.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
⌅ [3da002f7] ColorTypes v0.11.5
⌃ [5ae59095] Colors v0.12.11
  [861a8166] Combinatorics v1.0.2
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  [38540f10] CommonSolve v0.2.4
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  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
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  [77dc65aa] FunctionWrappersWrappers v0.1.3
⌅ [d9f16b24] Functors v0.4.12
⌅ [0c68f7d7] GPUArrays v10.3.1
⌅ [46192b85] GPUArraysCore v0.1.6
⌅ [61eb1bfa] GPUCompiler v0.27.8
  [c145ed77] GenericSchur v0.5.4
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  [86223c79] Graphs v1.12.0
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  [3e5b6fbb] HostCPUFeatures v0.1.17
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  [34004b35] HypergeometricFunctions v0.3.25
  [7869d1d1] IRTools v0.4.14
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  [ef3ab10e] KLU v0.6.0
  [63c18a36] KernelAbstractions v0.9.29
  [5ab0869b] KernelDensity v0.6.9
  [ba0b0d4f] Krylov v0.9.8
  [5be7bae1] LBFGSB v0.4.1
  [929cbde3] LLVM v9.1.3
  [8b046642] LLVMLoopInfo v1.0.0
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.5
  [73f95e8e] LatticeRules v0.0.1
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.2.2
  [1d6d02ad] LeftChildRightSiblingTrees v0.2.0
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.3.0
  [7ed4a6bd] LinearSolve v2.37.0
  [6fdf6af0] LogDensityProblems v2.1.2
  [996a588d] LogDensityProblemsAD v1.13.0
  [2ab3a3ac] LogExpFunctions v0.3.28
  [e6f89c97] LoggingExtras v1.1.0
  [bdcacae8] LoopVectorization v0.12.171
⌃ [b2108857] Lux v1.2.3
  [d0bbae9a] LuxCUDA v0.3.3
⌃ [bb33d45b] LuxCore v1.1.0
⌃ [82251201] LuxLib v1.3.7
  [c7f686f2] MCMCChains v6.0.6
  [be115224] MCMCDiagnosticTools v0.3.12
⌃ [7e8f7934] MLDataDevices v1.5.3
  [e80e1ace] MLJModelInterface v1.11.0
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [bb5d69b7] MaybeInplace v0.1.4
  [128add7d] MicroCollections v0.2.0
  [e1d29d7a] Missings v1.2.0
  [961ee093] ModelingToolkit v9.51.0
  [4886b29c] MonteCarloIntegration v0.2.0
  [0987c9cc] MonteCarloMeasurements v1.2.1
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.7
  [d8a4904e] MutableArithmetics v1.6.0
  [d41bc354] NLSolversBase v7.8.3
  [872c559c] NNlib v0.9.24
  [5da4648a] NVTX v0.3.5
  [77ba4419] NaNMath v1.0.2
  [c020b1a1] NaturalSort v1.0.0
  [315f7962] NeuralPDE v5.17.0
  [8913a72c] NonlinearSolve v4.2.0
  [be0214bd] NonlinearSolveBase v1.3.3
  [5959db7a] NonlinearSolveFirstOrder v1.1.0
  [9a2c21bd] NonlinearSolveQuasiNewton v1.0.0
  [26075421] NonlinearSolveSpectralMethods v1.0.0
  [6fe1bfb0] OffsetArrays v1.14.1
  [429524aa] Optim v1.10.0
⌅ [3bd65402] Optimisers v0.3.4
  [7f7a1694] Optimization v4.0.5
  [bca83a33] OptimizationBase v2.4.0
  [42dfb2eb] OptimizationOptimisers v0.3.4
  [bac558e1] OrderedCollections v1.6.3
  [90014a1f] PDMats v0.11.31
  [d96e819e] Parameters v0.12.3
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
  [2dfb63ee] PooledArrays v1.4.3
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.24
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [08abe8d2] PrettyTables v2.4.0
  [27ebfcd6] Primes v0.5.6
  [33c8b6b6] ProgressLogging v0.1.4
  [92933f4c] ProgressMeter v1.10.2
  [43287f4e] PtrArrays v1.2.1
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  [8a4e6c94] QuasiMonteCarlo v0.3.3
  [74087812] Random123 v1.7.0
  [e6cf234a] RandomNumbers v1.6.0
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  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [79098fc4] Rmath v0.8.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
  [0bca4576] SciMLBase v2.62.0
  [19f34311] SciMLJacobianOperators v0.1.1
  [c0aeaf25] SciMLOperators v0.3.12
  [53ae85a6] SciMLStructures v1.5.0
  [30f210dd] ScientificTypesBase v3.0.0
  [6c6a2e73] Scratch v1.2.1
  [91c51154] SentinelArrays v1.4.7
  [efcf1570] Setfield v1.1.1
  [727e6d20] SimpleNonlinearSolve v2.0.0
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [ed01d8cd] Sobol v1.5.0
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⌃ [09ab397b] StructArrays v0.6.18
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  [410a4b4d] Tricks v0.1.9
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  [013be700] UnsafeAtomics v0.2.1
  [d80eeb9a] UnsafeAtomicsLLVM v0.2.1
  [3d5dd08c] VectorizationBase v0.21.71
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  [02a925ec] cuDNN v1.4.0
  [4ee394cb] CUDA_Driver_jll v0.10.3+0
  [76a88914] CUDA_Runtime_jll v0.15.4+0
  [62b44479] CUDNN_jll v9.4.0+0
  [7bc98958] Cubature_jll v1.0.5+0
  [f5851436] FFTW_jll v3.3.10+1
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  [1e29f10c] demumble_jll v1.3.0+0
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  [0dad84c5] ArgTools v1.1.2
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  [7b1f6079] FileWatching v1.11.0
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  [b77e0a4c] InteractiveUtils v1.11.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.11.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
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  [05823500] OpenLibm_jll v0.8.1+2
  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
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  [8e850ede] nghttp2_jll v1.59.0+0
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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 1.11.1
Commit 8f5b7ca12ad (2024-10-16 10:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 20 × 12th Gen Intel(R) Core(TM) i9-12900H
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, alderlake)
Threads: 20 default, 0 interactive, 10 GC (on 20 virtual cores)
Environment:
  JULIA_NUM_THREADS = auto
  JULIA_EDITOR = code

Additional context

@ChrisRackauckas, we spoke about this on a call on Thursday. It came up while working on GPU support for NeuralLyapunov.