GPUVern7 Float32 dense output is ~60 ulps off at mid-step for a constant RHS (visible at tstops)

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Valutazione

Difficoltà
4/5
Tempo stimato
3-5 giorni
Idoneità per principianti
62/100
Tipo di issue
Bug
Chiarezza
Abbastanza chiara
Stato di attività
Attiva
Stack tecnologico
julia
Ambito
backend, testing-qa

Direzione di ricerca

Start by running the provided CPU reproducer and inspect the GPUVern7 interpolant and integ(t) path. Compare the current interpolant with the pre-97e5ac9 source and the tstop tests from PR #544. Done means exact endpoint behavior is preserved, mid-step Float32 error is reduced, and the tstop tests assert an appropriate tolerance.

Scritto dal modello di indicizzazione a partire dal testo della issue.

Descrizione

In Float32, GPUVern7's dense output loses about 60 ulps at mid-step even for a constant right-hand side, where the interpolant should be exact up to rounding. It shows up whenever an adaptive solve stops at a tstop inside a step, because the state there comes from integ(t).

Reproducer (CPU backend, no GPU needed):

using DiffEqGPU, SciMLBase, StaticArrays, KernelAbstractions
for alg in (GPUTsit5(), GPUVern7(), GPUVern9()), stops in (nothing, Float32[0.875])
    prob = ODEProblem{false}((u, p, t) -> SVector(1f0, 1f0), SVector(1f0, 1f0), (0.75f0, 1f0))
    kw = stops === nothing ? (;) : (; tstops = stops)
    sol = solve(EnsembleProblem(prob), alg, EnsembleGPUKernel(CPU(), 0.0); trajectories = 2,
        adaptive = true, dt = prevfloat(0.25f0), abstol = 1f-9, reltol = 1f-6,
        save_everystep = false, kw...)
    u = sol.u[1].u[end][1]
    println(nameof(typeof(alg)), " tstops=", stops, " u_end=", u, " ulps=", round(Int, (u - 1.25f0) / eps(1.25f0)))
end

On master b3d6a17 (Julia 1.12.7), the exact answer is 1.25:

algorithm no tstop tstop at 0.875
GPUTsit5 1.25 (0 ulps) 1.25 (0 ulps)
GPUVern7 1.25 (0 ulps) 1.2500077 (65 ulps)
GPUVern9 1.25 (0 ulps) 1.2499995 (−4 ulps)

The review of https://github.com/SciML/DiffEqGPU.jl/pull/544 reports that substituting the Vern7 interpolant from before https://github.com/SciML/DiffEqGPU.jl/commit/97e5ac9bd03ce7f075432ac9c784031ccc917aa2 ("Restructure Vern7 interpolant with (1-Θ) factors for exact endpoints") into the same environment brought this case from 65 ulps down to 2. That was a source substitution, not a bisect, and I have not reproduced it independently. That commit made the endpoints exact (see https://github.com/SciML/DiffEqGPU.jl/issues/412), so a fix needs to keep exact endpoints while restoring mid-step accuracy.

Found while working on https://github.com/SciML/DiffEqGPU.jl/pull/544. That PR's tstop tests only check that the callback fired and that the state is finite for Vern7/Vern9, rather than fitting a tolerance to this error. They should be tightened once this is fixed.

🤖 Generated with Claude Code (model: claude-opus-5-5[1m])

https://claude.ai/code/session_01SJfy3ez7u4CqvAerKrT5np

Lingua principale
Julia
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Fork
43
Merge medio
1g 20h
PR unite (30g)
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