feat!: make array-form DAE discretization the v1 default

[ChrisRackauckas-Claude]

Ignore this draft until it has been reviewed by @ChrisRackauckas.

What changed and why

This is the combined MethodOfLines v1 change. Time-dependent PDE systems now discretize to an implicit DAEProblem by default, so array-form equations reach code generation without mtkcompile scalarizing them. Systems that cannot use the first-order DAE path fall back to the compiled ODEProblem path; fallback = false makes that fallback an error. Stationary systems continue to return NonlinearProblems, and every time-dependent solve path retains PDETimeSeriesSolution wrapping.

Discretization strategy selection is removed entirely. MethodOfLines always attempts the array representation and automatically emits pointwise equations for individual patterns that have no array form. The use_ODAE switch is also removed. Callers that need an ODEProblem now use the documented symbolic_discretize + mtkcompile + ODEProblem route explicitly. DAE examples call solve(prob) so OrdinaryDiffEq chooses its default DAE algorithm instead of MethodOfLines documentation hard-coding DFBDF.

The package version moves to 1.0.0. Documentation and tests were migrated according to the problem they need: default DAE solves for implicit examples, and explicit symbolic-to-ODE construction for SSPRK/WENO/staggered examples.

This supersedes the earlier array-discretization PR and subsumes the default flip requested by the older scalar-default PR. The older branch was not replayed because its stale diff would revert newer array-discretization work; its behavioral intent is implemented here by removing the selector entirely.

The branch is rebased through the periodic nonuniform WENO work linked below. That implementation and its seam-coordinate, accuracy, minimal-grid, and unsupported-pattern coverage are preserved under the unconditional array API.

Dependency boundary

This requires the registered DiffEqBase = "7.18.1" fix linked below. ModelingToolkitBase = "1.67" is the tested minimum: 1.66 carries DAEProblem.problem_type through construction but does not yet assemble array residuals, while 1.67 does. The SciMLBase floor supplies DAEProblem.problem_type support.

The newly direct runtime dependency ModelingToolkitBase is MIT licensed. No new solver dependency is introduced; the temporary direct OrdinaryDiffEqBDF test/docs dependency was removed once examples changed to solve(prob).

Verification

Focused runtime behavior on Julia 1.12.6:

problem_type=DAEProblem
algorithm_type=DFBDF  # selected by solve(prob) in the resolved local environment
retcode=Success
max_error=0.0007547373427254089
public_array_strategy=false
public_scalar_strategy=false
legacy_option_names_present=false
ode_problem_type=ODEProblem
ode_retcode=Success

The full rewritten array group passed:

Array discretization             | 3110 / 3110 passed | 27m39.3s
DAEProblem on the array form      |   49 /   49 passed |  1m39.9s
Testing MethodOfLines tests passed

After DiffEqBase 7.18.1 was registered, 68/69 CI checks passed. The remaining WENO
benchmark failed because its explicit SSPRK33 solve still consumed the new
DAEProblem returned by discretize:

Problem type: SciMLBase.DAEProblem
Solver type: OrdinaryDiffEqSSPRK.SSPRK33
Problem types compatible with the chosen solver: SciMLBase.ODEProblem

The benchmark now constructs its RHS/solve problem through symbolic_discretize,
mtkcompile, and ODEProblem, while its dedicated discretization benchmark continues
to exercise discretize. The identical failing leaf passed locally after the change:

run(SUITE["solve"]["burgers"]["stretched"]["N=128"]; samples=1, evals=1)
Trial(25.353 ms)

The resulting CI run passed all 69 checks, including benchmarks, documentation,
downgrade, QA, the complete test matrix, and PDESystemLibrary downstream.

The exact downgrade environment discriminated the ModelingToolkitBase floor with the
same unchanged GROUP=MOL_Interface2 command:

ModelingToolkitBase 1.65 | 3 passed, 1 failed, 2 errored, 8 broken
ModelingToolkitBase 1.66 | 4 passed, 1 failed, 0 errored, 8 broken
ModelingToolkitBase 1.67 | 5 passed, 0 failed, 0 errored, 8 broken | 9m56.0s
Testing MethodOfLines tests passed

Final-tree QA passed with the warmed absolute depot:

QA | 12 passed, 6 existing broken, 18 total | 13m26.0s
Testing MethodOfLines tests passed

The first QA attempt had one Aqua infrastructure failure: its cold, relative-depot persistent-task subprocess exited without creating done.log; the other 11 checks passed. No test or timeout setting changed for the successful retry.

Static checks:

julia +release -m Runic --check .                                            # exit 0
git diff --name-only --diff-filter=ACMRT -z upstream/master...HEAD |
  xargs -0 typos --force-exclude                                              # exit 0
git diff --check upstream/master...HEAD                                       # exit 0

The added source/test comment share is 5.11% (49 comment lines among 958 added lines). The explicit-ODE helper is defined once in test/shared/ode_discretize.jl; no duplicated test bodies or new public definitions were added.

With a local checkout of the required DiffEqBase fix, the unchanged strict docs build completed every example, cross-reference, missing-docstring check, and document check. It then failed external link checking when GitHub returned HTTP 429 for existing source links. Repeated unchanged attempts reached the same external limit; link checking was not disabled or weakened. The initial CI run predated the DiffEqBase 7.18.1 registration and failed at dependency resolution. After registration, a fresh detached checkout resolved DiffEqBase 7.18.1 from General; commit 00788307 retriggered the affected workflows without changing the source tree and commit 972d2586 fixes the sole resulting benchmark failure. All 69 checks on 972d2586 pass.

GROUP=Everything julia +release --project=. -e 'using Pkg; Pkg.test()' ran the
runtime groups on parent commit 545c3231. Representative results were Array
3111/3111, DAE array 49/49, and MOL_Interface2 5 passed / 8 existing broken. It
then failed, before DiffEqBase 7.18.1 was registered, when SciMLTesting created an
isolated QA environment that could only resolve DiffEqBase 7.17.1. The current source
difference is removal of the two legacy-keyword guards; the current tree is covered by
the focused, exact-downgrade, and QA runs above.

The PDESystemLibrary downstream job reaches dependency resolution and fails because its
current MethodOfLines = "0.12" compat excludes 1.0.0. A focused downstream compat and
documented symbolic-to-ODE migration passed 427/427 examples against MethodOfLines 0.12.
Against this v1 branch, the unchanged pre-v1 call shape errored 427/427 times on the
intentional DAEProblem/ODE-solver incompatibility; the migrated v1 run passed 427/427 in
12m19.1s. All nine checks on the supporting downstream draft pass, including Core on
Julia LTS, current, and prerelease, QA, downgrade, Runic, and spelling. The draft is
linked below.

Not run locally: Julia prerelease and GPU jobs.

Reviewer decisions

• The default return-type and public API removals are intentionally breaking and paired with the 1.0.0 bump.
• There is no public or internal whole-system strategy selector. Pointwise generation remains only as the automatic per-equation fallback used by the array implementation.
• There is no use_ODAE compatibility switch. Explicit ODE integrators require the documented symbolic_discretize route.
• DAE examples rely on solve(prob) rather than promising a specific OrdinaryDiffEq default algorithm.
• The compiled ODE fallback can be disabled with fallback = false when implicit DAE construction is required.

Links

• Combined draft: feat!: make array-form DAE discretization the v1 default #650
• Earlier array-discretization PR: feat: DAEProblem path that keeps the array (slice-form) discretization #639
• Older default-flip PR: Make ArrayDiscretization the default discretization strategy #618
• Required DiffEqBase fix: fix: let the despecialization barrier accept unwrapped parameters OrdinaryDiffEq.jl#4297
• PDESystemLibrary v1 compatibility draft: Support MethodOfLines 1 PDESystemLibrary.jl#75
• Periodic nonuniform WENO base commit: 88a568e
• PDESystemLibrary downstream failure: https://github.com/SciML/MethodOfLines.jl/actions/runs/32433332081/job/96629426810
• Pre-fix WENO benchmark failure: https://github.com/SciML/MethodOfLines.jl/actions/runs/32454120471/job/96688018756