[ChrisRackauckas-Claude]

Ignore this PR until reviewed by @ChrisRackauckas.

Blocked on ModelingToolkit 11.42.0 being released. The compat floor here is ModelingToolkit = "11.42", which does not exist yet, so CI cannot resolve until SciML/ModelingToolkit.jl#5091 merges and MTK is released. Everything below was verified locally against that branch.

Closes the ModelOrderReduction half of #29.

The reduced system now carries its own time span, so a problem can be built from it without repeating one:

deim_sys = deim(full_prob, sol, pod_dim)
deim_prob = DAEProblem(deim_sys, nothing; build_initializeprob = false)   # was: ..., full_prob.tspan

Where the span comes from

• The problem method takes prob.tspan. That is the interval the reduction was actually trained on, so it is the honest default for the reduced model.
• The system method takes get_tspan(sys), inheriting whatever the source system carries.
• A source with no time span yields a reduced system with no time span, rather than a fabricated interval. Passing one explicitly still overrides.

The README and the FitzHugh-Nagumo tutorial drop the now-redundant full_prob.tspan argument.

Background

System gained a tspan field in SciML/ModelingToolkit.jl#5085, released as ModelingToolkitBase v1.69.0 (JuliaRegistries/General#167382, merged 10:01Z today). Every time-dependent problem constructor defaults to it. The floor here is MTK 11.42 rather than 11.41 because MTK 11.41 floors ModelingToolkitBase = "1.64", so an 11.41 user can resolve MTKBase 1.68 and not have the field at all; PR 5091 raises that floor to 1.69.

Verification

Julia 1.12.7, against local checkouts of ModelingToolkitBase 1.69.0 and the ModelingToolkit 5091 branch.

=== deim exit 0 (252s)
training parameters and nonautonomous nonlinearities |    4      4   3.1s
ODEProblem sources and scalar code generation        |    9      9  19.0s
nonautonomous linear terms                           |    5      5   3.1s
the reduced system carries a tspan                   |    8      8   2.9s
=== array_structure exit 0 (35s)
array ROM regressions                                |   15     15  24.5s
=== full_order exit 0 (27s)
separate_terms                                       |   15     15   7.1s
FullOrderModel                                       |   17     17   7.6s

Behaviour of the four cases, measured directly:

ROM tspan from problem: (0.0, 0.5)
DAEProblem without tspan: (0.0, 0.5)
solve: Success
relative error: 3.477844813759253e-7
ROM tspan from system:  (0.0, 0.5)
DAEProblem without tspan: (0.0, 0.5)
ROM tspan when source has none: nothing
explicit tspan still works: (0.0, 1.0)

The full Documenter build, with the tutorial now omitting the time span, exits 0.

Runic --check ., typos, and git diff --check all exit 0.

Not verified

• GROUP=QA was not re-run; this PR adds no public name and changes no import.
• Julia LTS and prerelease, and the downgrade configuration, were not run locally. Note the downgrade job will resolve ModelingToolkit at its floor, which is the whole point of moving the floor to 11.42.
• CI on this PR cannot pass until MTK 11.42.0 is registered, as described at the top.

Review notes

• Taking prob.tspan for the problem method is a judgement call. The alternative is the source system's own span, which for a MethodOfLines discretization is the PDE's t domain and usually identical. I went with the problem because that is the interval the snapshots came from, and because a user who solved a sub-interval probably wants the reduced model to describe that sub-interval.
• The test compat in test/Project.toml moves to 11.42 as well, so the test environment cannot silently resolve an older MTK that lacks the field.

🤖 Generated with Claude Code

https://claude.ai/code/session_01H5RuLDtEazwTKPkNbPeZVu