Fix strict Kantorovich step acceptance

[ChrisRackauckas-Claude]

Please ignore this draft until it has been reviewed by @ChrisRackauckas.

Summary

• Fix strict KantorovichTypeController acceptance to accept a converged step only when every recorded contraction satisfies Θk <= Θreject.
• Keep non-strict mode accepting every converged nonlinear solve.
• Add boundary, rejection, empty-history, and non-strict regression coverage.
• Bump ImplicitDiscreteSolve from 2.1.3 to 2.1.4.

Root cause

The controller documentation says strict mode rejects a step whenever any Θk > Θreject. The implementation used all(Θreject .< Θks), which reversed the inequality: normal well-contracted steps were rejected, while a history in which every contraction exceeded the rejection threshold was accepted.

Why this remains separate from homotopy solving

NonlinearSolve #1071 now provides the controller as KantorovichHomotopy for a genuine HomotopyProblem, and OrdinaryDiffEq's existing HomotopyNonlinearSolveAlg adapter can use it for ODE stage equations. That does not make it a drop-in replacement for this controller:

• HomotopyNonlinearSolveAlg is an OrdinaryDiffEqCore.AbstractNLSolverAlgorithm consumed by the ODE stage-solver machinery, not a NonlinearSolve algorithm accepted by init(::NonlinearProblem, ...). An exact attempted substitution in IDSolve.nlsolve exits with SciMLBase.NonSolverError.
• A general ImplicitDiscreteProblem solves f(u_next, uprev, p, t) = 0 and replaces uprev after every accepted state. It is therefore a sequence of changing nonlinear problems, not one fixed homotopy in t.
• An artificial per-step affine homotopy can preserve the endpoint equation for square problems, but it changes the solve strategy, is not a generic construction for the existing rectangular least-squares cases, and does not match current performance.

Performance check

The closest generic square-problem prototype used

$$H(x, λ) = (1 - λ)(x - u_{prev}) + λ f(x, u_{prev}, p, t)$$

at every discrete step. The recurrence endpoint matched the current solver to about 1e-12. Medians below are from 20 warmed Julia 1.12.6 samples:

Recurrence implementation	Time	Residual calls	Memory	Allocations
current IDSolve	0.592 ms	360	65,904 B	1,357
affine KantorovichHomotopy per step	10.292 ms	1,358	3,288,096 B	47,965
affine HomotopySweep per step	10.444 ms	1,958	3,423,296 B	51,215

The Kantorovich replacement was 17.4x slower and allocated 35x as many objects.

For a scalar path whose residual ignores uprev, a whole-span homotopy is valid and avoids the IDS integrator overhead. In that restricted case, HomotopySweep took 0.205 ms and KantorovichHomotopy took 0.347 ms (current IDS: 0.507 ms), with all endpoints agreeing at floating-point precision. This is consistent with NonlinearSolve #1071's broader comparison: Kantorovich continuation can win on some paths, but it is not a general replacement for Sweep or for the recurrence controller here.

Validation

Run on the rebased branch head 6a73faf817:

• ODEDIFFEQ_TEST_GROUP=Core on Julia 1.10.11: exit 0, all 34 assertions passed; Kantorovich strict acceptance passed 4/4.

• Repository-wide Runic check: exit 0.

• git diff --check: exit 0.

• ODEDIFFEQ_TEST_GROUP=QA on rebased head: JET passed 1/1; Aqua passed 16/17 and failed only the rendered-public-API check on 185 SciMLBase re-exports plus IDSolve (186 names total). This clean-master failure was bisected to Update SciMLTesting QA docs coverage #3867 and remains isolated in #3969; that focused fix passes Julia 1.10 JET 1/1 and Aqua 17/17 plus Runic and diff checks. The umbrella docs fix #3970 is merged in this branch base. No test was skipped, silenced, loosened, or changed.

• Rebased-head GitHub CI completed with 119 successful, 3 skipped, and 7 failed checks. All ImplicitDiscreteSolve Core lanes, its downgrade lane, documentation, Runic, and both benchmark lanes passed. The non-passing checks are independent clean-master baselines or infrastructure:

  • IDS rendered-API QA: #3969. The former root half is fixed by merged #3970.
  • MatrixOperator downgrade failures in BDF, SDIRK, and OrdinaryDiffEqNonlinearSolve: #3917, with shared-workflow prerequisite SciML/.github #118. The exact locked Raise NonlinearSolveBase floor for operator Jacobians #3917 Core suite was independently rerun on Julia 1.11 and exited 0, including the formerly failing 44/44 and 113/113 groups.
  • TaylorSeries resolver conflict: #3965, independently verified at 81/81 locked Core tests.
  • DiffEqDevTools: the self-hosted runner lost communication again; the job-specific rerun endpoint returned HTTP 403.
  • GPU: exited 1 after 22m23s, but the self-hosted failed-step log is unavailable. Equivalence to the independently reproduced clean-master 137-case DAE failure is therefore an inference, tracked by #3922, #3923, and CUDA.jl #3199; no NVIDIA GPU is available locally.

Process notes

The work mapped the exact residual-contraction sampling and Deuflhard step-size formula, extracted the reusable controller into NonlinearSolve, benchmarked it against HomotopySweep and ArcLengthContinuation, tested the proposed direct and affine adapters after NonlinearSolve #1071 merged, and kept this independent predicate bug as a small OrdinaryDiffEq patch.

[ChrisRackauckas-Claude]

Commit f32e1001cd contains the controller-only change on top of prerequisite #3907.

Executed plan and local evidence:

1. Compared the documented predicate (reject if any Θk > Θreject) with the broadcasted implementation and isolated the reversed inequality.
2. Added direct boundary coverage for empty contraction history, Θk == Θreject, the first value above the threshold, and non-strict acceptance.
3. Ran the exact stacked branch through ODEDIFFEQ_TEST_GROUP=Core: every testset passed; the new testset was 4/4.
4. Ran ODEDIFFEQ_TEST_GROUP=QA: JET 1/1, Aqua 18/18, package tests passed.
5. Ran repository-wide Runic --check . and git diff --check: both exit 0.

No test was skipped, disabled, loosened, or converted to warn-only behavior.

[ChrisRackauckas-Claude]

CI note: the red downgrade-sublibraries / test (lib/OrdinaryDiffEqCore) is a current-master baseline dependency-floor failure. This PR job and master job 87111089373 both pin SciMLOperators 1.23.0 while the in-tree OrdinaryDiffEqNonlinearSolve 2.3.0 requires 1.24.3. It fails during Pkg.test(...allow_reresolve=false) resolution before tests execute; neither the isdiscretecache API restoration nor the strict controller test participates. A separate clean-master floor investigation is queued; no test will be skipped or silenced.

[ChrisRackauckas-Claude]

Rebased this PR directly onto current master and removed the unrelated #3907 commit. The branch now contains only b1f6c20788 (strict acceptance fix + regression test + patch bump). Re-ran locally on the exact branch: ODEDIFFEQ_TEST_GROUP=Core julia +1.10 --project=lib/ImplicitDiscreteSolve -e 'using Pkg; Pkg.test()' exited 0 with all 34 assertions passing, including Kantorovich strict acceptance 4/4; Runic on both changed Julia files and git diff --check also exited 0.

[ChrisRackauckas-Claude]

CI note: the red downgrade jobs for lib/StochasticDiffEq (job 87329808979) and lib/OrdinaryDiffEqFIRK (job 87329808768) are the independently reproduced current-master source-floor conflict: the downgrade action pins SciMLOperators = 1.23, while the in-tree OrdinaryDiffEqNonlinearSolve 2.3.0 requires 1.24.3. Clean-master Julia 1.11 reproductions and the first introducing commit are being handled in a separate focused baseline investigation per repository policy. This strict-predicate PR changes only ImplicitDiscreteSolve; it will not mix in those monorepo dependency-floor repairs.

[ChrisRackauckas-Claude]

Feature-specific CI update: ImplicitDiscreteSolve Core now passes on Julia LTS, current stable, and prerelease; its downgrade job passes, as does SimpleImplicitDiscreteSolve downgrade. The sole red ImplicitDiscreteSolve check is QA, which is the independently reproduced current-master removal of the previously released OrdinaryDiffEqCore.isdiscretecache public declaration; the focused restoration is #3907. The controller branch remains limited to the strict-predicate fix.

[ChrisRackauckas-Claude]

Baseline dependency-floor update: the minimal registered-root prerequisite is now draft NonlinearSolve #1079. It patches NonlinearSolve to 4.21.1, permits LinearSolve 4.3/5, and raises the NonlinearSolveBase floor to the operator-capable 2.35. Exact local evidence includes FirstOrder with LinearSolve 4.3 (including operator tests 14/14), LinearSolve 5 operator tests 14/14, QA 15/15, Runic 373/373, and the formerly failing OrdinaryDiffEq nonlinear sets 44/44, 113/113, and 10/10. The focused OrdinaryDiffEq source-floor follow-up remains separate from this controller PR.

[ChrisRackauckas-Claude]

Investigated the failed downgrade-sublibraries / test (lib/DiffEqDevTools) lane.

CI evidence:

• PR #3908 job 87329808771 ran on self-hosted-4vcpu-8gb-vv9dn-runner-8mjh8. Setup, checkout, Julia setup, resolve, and build succeeded. The test step started at 11:05:53Z, but the API still records that step as in_progress with no completion timestamp.
• GitHub attached: “The self-hosted runner lost communication with the server. Verify the machine is running and has a healthy network connection. Anything in your workflow that terminates the runner process, starves it for CPU/Memory, or blocks its network access can cause this error.”
• The logs endpoint returns HTTP 404 BlobNotFound, so there is no Julia exception or failed assertion to inspect.
• PR #3912 job 87336560102 repeated the same incomplete test-step metadata and lost-runner annotation on a different runner, self-hosted-4vcpu-8gb-vv9dn-runner-rq2hh. The two runners survived for different durations, about 44 and 22 minutes respectively.

Clean local reproduction from upstream master commit 5265a6c54232db89d6e57e7a2c69f5f20d55a172:

• Julia 1.11.9, isolated depot and temp directory, the exact v2 downgrade action/skip set, and ODEDIFFEQ_TEST_GROUP=Core.
• The downgrade resolution completed successfully in 2m42.20s, with maximum RSS 2,434,052 KiB.
• The exact test command was Pkg.test(; allow_reresolve = false). A warm-depot definitive rerun exited 0 with Testing DiffEqDevTools tests passed.
• Test wall time was 53m58.65s. Important summaries included Benchmark 15/15, Analyticless Convergence 7/7, Analyticless Stochastic WP 2/2, Stability Region 7/7, Plot Recipes 36/36, and NonlinearSolve WP diagrams 6/6.
• Maximum RSS was 7,807,812 KiB (about 7.45 GiB), with zero swaps.

The local peak leaves only about 0.55 GiB on a nominal 8 GiB runner before the OS and runner service. The evidence is therefore consistent with runner memory pressure terminating the VM/runner connection, not a reproducible Julia source/test regression. I found no source failure to bisect and made no code change. This lane should be rerun on a larger-memory runner or split into lower-peak jobs.

[ChrisRackauckas-Claude]

Rebased the focused predicate fix onto current clean upstream/master (ed6bf86fcc, including #3907) and updated the branch with an explicit force-with-lease after auditing the remote branch. New head: 8b2950d957.

I also tested the proposed replacement with HomotopyNonlinearSolveAlg(KantorovichHomotopy(...)) rather than inferring compatibility from the names:

• Direct substitution is not an accepted API path. IDSolve initializes a NonlinearProblem with alg.nlsolve, while HomotopyNonlinearSolveAlg <: OrdinaryDiffEqCore.AbstractNLSolverAlgorithm is an ODE-stage solver consumed by OrdinaryDiffEqNonlinearSolve.NLSolver. The exact attempted IDSolve(nlsolve = HomotopyNonlinearSolveAlg(HomotopySweep())) run exits with SciMLBase.NonSolverError before solving.
• A whole-span HomotopyProblem is not a semantics-preserving replacement for a general ImplicitDiscreteProblem: after each accepted step the residual changes from f(u_next, uprev, p, t) to one with a new uprev. Only problems whose residual ignores uprev define a fixed path in t.
• I benchmarked the closest generic square-problem adapter, the per-step affine embedding H(x, λ) = (1-λ)(x-uprev) + λ f(x, uprev, p, t), against the existing recurrence solver. All numbers are medians of 20 Julia 1.12.6 samples after warmup:

Recurrence implementation	Time	Residual calls	Memory	Allocations
current IDSolve	0.592 ms	360	65,904 B	1,357
affine KantorovichHomotopy per step	10.292 ms	1,358	3,288,096 B	47,965
affine HomotopySweep per step	10.444 ms	1,958	3,423,296 B	51,215

The Kantorovich adapter reached the same endpoint to about 1e-12, but was 17.4x slower and allocated 35x as many objects. It also does not extend generically to the existing rectangular least-squares cases without choosing an arbitrary rectangular anchor system.

For a scalar fixed path where a whole-span homotopy is valid, direct continuation beat the full IDS integrator overhead, but HomotopySweep was faster than KantorovichHomotopy: 0.205 ms versus 0.347 ms (current IDS: 0.507 ms), all reaching cbrt(2) to floating-point precision. This matches #1071's conclusion that Kantorovich continuation is useful but not a general replacement for Sweep.

Accordingly, this PR remains the small correctness fix for the general recurrence controller; no homotopy adapter code was added.

Post-rebase local validation:

• ODEDIFFEQ_TEST_GROUP=Core on Julia 1.10.11: exit 0, all 34 assertions passed, including strict acceptance 4/4.
• repository-wide Runic check: exit 0.
• git diff --check: exit 0.
• ODEDIFFEQ_TEST_GROUP=QA: JET passed 1/1, then public-doc rendering failed on 186 SciMLBase re-exports. The exact failure reproduces on untouched upstream/master ed6bf86fcc; the mandated separate clean-master bisect/fix investigation is running in parallel. No test was skipped, silenced, or changed.

[ChrisRackauckas-Claude]

One-hour rebased-head CI audit:

• 118 checks succeeded, 3 skipped, 7 failed, and the GPU lane was cancelled at the reusable workflow's 1-hour limit.
• All ImplicitDiscreteSolve Core lanes (LTS/current/prerelease), its downgrade lane, docs, Runic, and both benchmark lanes passed.
• The red IDS/root QA checks are clean-master documentation baselines isolated in Fix ImplicitDiscreteSolve API docs QA #3969 and Document umbrella re-exported API #3970.
• The BDF, SDIRK, and OrdinaryDiffEqNonlinearSolve downgrade failures are the clean-master MatrixOperator/NonlinearSolveBase floor issue in Raise NonlinearSolveBase floor for operator Jacobians #3917, with Reconcile path-source constraints in downgrade tests .github#118 as the shared-workflow prerequisite.
• TaylorSeries is the clean-master resolver conflict fixed by Constrain TaylorSeries test OrderedCollections compat #3965; an independent exact locked run passed 81/81 after applying that fix.
• DiffEqDevTools lost its self-hosted runner; both available rerun mechanisms returned HTTP 403.
• The timed-out GPU lane is independent of this PR. Current master already fails all 137 non-skipped GPU DAE cases; the existing chain is issue GPU DAE tests: 100% failure since GPU CI lane restored (#3813), likely Diagonal mass matrix scalar indexing #3922, partial fix get_differential_vars: check Diagonal.diag, not the full matrix (fixes GPU DAE 100% failure) #3923, and Fix 3-arg QR ldiv! for multi-column right-hand sides JuliaGPU/CUDA.jl#3199.

No completed check implicates the controller predicate or its regression tests. The PR description now contains the benchmark and this full baseline map.

[ChrisRackauckas-Claude]

Rebased after #3970 merged. Current base/head: 298da19f44 / 6a73faf817.

Fresh local validation on this exact head:

• ODEDIFFEQ_TEST_GROUP=Core, Julia 1.10.11: exit 0, 34/34 assertions; strict acceptance 4/4.
• repository-wide Runic 1.7: exit 0.
• git diff --check: exit 0.
• QA: JET 1/1; Aqua 16/17, with only the known 186-name IDS rendered-API baseline tracked by Fix ImplicitDiscreteSolve API docs QA #3969.

The branch was force-updated only after fetching and confirming the remote feature branch still contained solely the prior authored commit; the update used an explicit force-with-lease.

[ChrisRackauckas-Claude]

Fresh post-#3970 CI is complete: 119 success, 3 skipped, 7 failed.

All #3908-relevant checks passed: ImplicitDiscreteSolve Core on LTS/current/pre, IDS downgrade, documentation, Runic, and both benchmark lanes.

The seven failures are independently tracked/classified:

• IDS rendered API QA: Fix ImplicitDiscreteSolve API docs QA #3969.
• BDF, SDIRK, and OrdinaryDiffEqNonlinearSolve downgrade: Raise NonlinearSolveBase floor for operator Jacobians #3917 plus SciML/.github More RK Methods #118. The exact locked Raise NonlinearSolveBase floor for operator Jacobians #3917 suite was rerun locally and exited 0.
• TaylorSeries downgrade resolver: Constrain TaylorSeries test OrderedCollections compat #3965; its locked Core test was independently verified 81/81.
• DiffEqDevTools: self-hosted runner lost communication; job rerun returned HTTP 403.
• GPU: exit 1, but its self-hosted failed-step log is unavailable. Matching the known clean-master DAE failure is an inference; see GPU DAE tests: 100% failure since GPU CI lane restored (#3813), likely Diagonal mass matrix scalar indexing #3922, get_differential_vars: check Diagonal.diag, not the full matrix (fixes GPU DAE 100% failure) #3923, and Fix 3-arg QR ldiv! for multi-column right-hand sides JuliaGPU/CUDA.jl#3199.

No tests were skipped, silenced, loosened, or changed.