GlobalDiffEq: add GlobalErrorTransport global error estimation and control#3956
Draft
ChrisRackauckas-Claude wants to merge 5 commits into
Draft
GlobalDiffEq: add GlobalErrorTransport global error estimation and control#3956ChrisRackauckas-Claude wants to merge 5 commits into
ChrisRackauckas-Claude wants to merge 5 commits into
Conversation
Repo transfer of SciML/GlobalDiffEq.jl (GlobalRichardson), keeping its name, UUID, and version lineage. The umbrella OrdinaryDiffEq dependency is replaced by OrdinaryDiffEqTsit5 (precompile workload and tests only), path sources point at the sibling sublibraries, tests read ODEDIFFEQ_TEST_GROUP, and the rendered-API-docs QA check points at the monorepo docs with reexported DiffEqBase names excluded. Adds the Global Error Control docs section and the docs env wiring. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
Carries SciML/GlobalDiffEq.jl#56 (GlobalAdjoint, adjoint_error_estimate; Cao and Petzold 2004, closes SciML/GlobalDiffEq.jl#4) into the monorepo, restructured as the package extension GlobalDiffEqSciMLSensitivityExt on SciMLSensitivity + QuadGK weakdeps. sensealg defaults to nothing and resolves to QuadratureAdjoint(autojacvec = true) when the extension loads; solving without the extension raises an instructive error. Public API and semantics otherwise match the original PR. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
Implements the explicit general linear methods with built-in global error estimation from Constantinescu (2016), SIAM J. Numer. Anal. 54(6) (arXiv:1503.05166; PETSc's TSGLEE23/TSGLEE24/TSGLEE35), addressing SciML/GlobalDiffEq.jl#6 and SciML/GlobalDiffEq.jl#22, as proper OrdinaryDiffEqCore algorithms. The methods propagate the partitioned state (y, ε) where ε is an asymptotically correct global error estimate; solve/init on plain ODEProblems transparently extend to the ArrayPartition form and global_error_estimate(sol) extracts the estimates. The per-step ε increment is an asymptotically correct local error estimate driving standard step-size adaptivity. The paper's method A4 is defective as printed (violates b·c = 1/2, converges at order 1, absent from PETSc) and is deliberately not implemented. Verified locally on the unstable Prince42 problem: solution orders 2/2/3, estimate accuracy orders 3/3/4, est/true-error ratio 1.00. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
Adds the DOPRI5-based order-5 scheme with cheap global error estimation of Makazaga and Murua (BIT 43, 2003) as another tableau in the GLEE general linear framework (SciML/GlobalDiffEq.jl#6, the coefficient- complete published representative of the Dormand-Duckers-Prince RK triple family). Stages 1-7 are the standard DOPRI5 stages, three extra stages propagate an order-6 companion solution, and a generic solution-stage FSAL detection reuses stage 7's evaluation for fsallast, giving exactly 9 function evaluations per step (verified by an nf accounting test). The tableau was verified with exact rational arithmetic against the order and independency conditions. Verified locally on the unstable Prince42 problem: solution order 5, estimate accuracy order 6, est/true-error ratio 1.04, 9.01 f-evals/step. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
Implements the linearized error-transport estimator (SciML/GlobalDiffEq.jl#5; Shampine 1986 / Berzins 1988 / Lang-Verwer 2007): after a dense forward solve, the companion linear ODE ε' = Jε + d(t) driven by the dense-output defect d(t) = f(P(t)) - P'(t) is integrated for the endpoint global error, with matrix-free Jacobian-vector products through DifferentiationInterface (autodiff accepts any ADTypes backend, default AutoForwardDiff). gtol-controlled solves tighten local tolerances via the shared refinement loop in companion.jl, mirroring GlobalAdjoint. global_error_estimate(prob, alg) is the standalone estimator, also added for GlobalAdjoint as an alias of adjoint_error_estimate. Verified locally on Lotka-Volterra vs a 1e-13 reference: estimate to true-error ratios 0.995-0.999 at tolerances 1e-4/1e-6, and gtol=1e-7 control yields 9.8e-9 final error. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
This was referenced Jul 18, 2026
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Important
Ignore this PR until it has been reviewed by @ChrisRackauckas.
Stacked on #, which is stacked on #, #, and #3929. Only the top commit is new here; review that commit. Merge the base PRs first.
Summary
Adds
GlobalErrorTransport— global error estimation andgtol-based control by the linearized error-transport (first variational) equation, addressing SciML/GlobalDiffEq.jl#5 (Berzins' Jacobian-based estimators; also Shampine 1986 and the defect-driven form summarized by Lang and Verwer 2007).P(t), the companion linear ODEε' = J(P(t))ε + d(t)with the dense-output defectd(t) = f(P(t)) − P'(t)is integrated fromε(t₀) = 0;‖ε(T)‖₂estimates the endpoint global error.autodiffkeyword accepts any ADTypes backend (defaultAutoForwardDiff()). New deps: ADTypes, DifferentiationInterface, ForwardDiff.gtol,solve(prob, GlobalErrorTransport(Tsit5(); gtol = ...))tightens local tolerances until the estimate meets the requested global tolerance — the same control loop contract asGlobalAdjoint.global_error_estimate(prob, alg; abstol, reltol, ...)method; for API uniformityglobal_error_estimate(prob, ::GlobalAdjoint)is also added as an alias ofadjoint_error_estimate.src/companion.jland is reused by the next PR in the stack.Version 1.6.0.
Validation (run locally)
ODEDIFFEQ_TEST_GROUP=Core julia --project=lib/GlobalDiffEq -e 'using Pkg; Pkg.test()': pass — Basic 1/1, traits 3/3, Adjoint 14/14, GLEE 37/37, Companion estimators 14/14, BigFloat 2/2ODEDIFFEQ_TEST_GROUP=QA julia --project=lib/GlobalDiffEq -e 'using Pkg; Pkg.test()': pass — 22 passed, 1 pre-existing declared brokengtol = 1e-7control delivered a true endpoint error of 9.8e-9; argument-validation paths tested.🤖 Generated with Claude Code
https://claude.ai/code/session_01MfUh8tgp3iBmMv9nkBqoyY