V0.2 Scope#

Summary#

v0.2 is the smallest next release that expands PDELie in a disciplined way.

It does not introduce a new major representation layer.
It does not introduce a new numerical regime.
It does not widen the ecosystem surface.

Instead, it asks a narrower and more important question:

Do the current stable contracts and symmetry pipeline survive contact with a second PDE?

The second PDE for v0.2 is 1D Burgers.

For Milestone 1, the Burgers target is frozen as:

  • viscous 1D Burgers with fixed nu

  • uniform periodic grid on x in [0, 2π)

  • spatial translation as the first stable recovery / verification target

  • no new canonical stable objects

  • no new stable derivative backend

Must Implement#

Stable scope for v0.2#

  • uniform rectilinear grids only

  • synthetic PDE data only

  • polynomial generators only

  • verification-first development

  • Heat remains supported

  • Burgers is added as the second stable PDE

Stable canonical objects for v0.2#

The stable contract set remains the current narrow slice unless a second-PDE requirement forces a minimal extension:

  • FieldBatch

  • DerivativeBatch

  • ResidualBatch

  • ResidualEvaluator

  • GeneratorFamily

  • VerificationReport

No other canonical objects should become stable in v0.2 unless absolutely necessary to support the second-PDE vertical slice.

Concrete v0.2 Target#

Add a second end-to-end stable path:

FieldBatch -> DerivativeBatch -> ResidualBatch -> GeneratorFamily -> VerificationReport

for synthetic 1D Burgers on a uniform periodic grid.

Required components#

  • one synthetic 1D Burgers dataset generator

  • one trusted Burgers residual evaluator

  • derivative support that works within the existing stable numerical assumptions

  • one broadened translation fitting path that works for Heat and Burgers under the current stable slice

  • one finite-transform verification path for the Burgers spatial-translation target

  • one controlled benchmark task comparing behavior on Heat and Burgers

Milestone 1 may retain a minimal internal fitter fallback to the reference spatial-translation direction if the residual-based SVD drifts on Burgers, provided:

  • the public fitter / verifier API does not change

  • the fallback remains specific to the spatial-translation target

  • diagnostics state whether the fallback was used

Required scientific result#

  • recover and verify spatial translation on Burgers under the stable pipeline

  • maintain the existing Heat result without regressions

Development Order#

  1. freeze v0.2 scope

  2. add synthetic 1D Burgers data

  3. add Burgers residual evaluator

  4. broaden the current translation fitting path just enough for the second PDE

  5. add/adjust verification for the Burgers spatial-translation target

  6. add cross-PDE tests and release-gate checks

Explicitly Deferred#

The following are not part of stable v0.2 scope:

  • weak-form derivatives as a stable backend

  • invariant-coordinate pipelines as a stable feature

  • InvariantMap as a stable contract

  • InvariantLibrary as a stable contract

  • DiscoveryResult as a stable contract

  • downstream system-identification workflows as part of the stable API

  • PySINDy integration as a release-defining stable feature

  • operator symmetry

  • NeuralOperator integration

  • broader adapter work (PDEBench, The Well, etc.) as a release-defining goal

  • nonuniform rectilinear support in stable derivative code

  • multi-generator Lie algebra tooling beyond diagnostics

  • broad benchmark zoo

  • manuscript-specific experiment logic

These may be explored experimentally, but they do not define v0.2.

Benchmark Rules for v0.2#

v0.2 should benchmark the current stable symmetry pipeline across two PDEs, not yet benchmark downstream utility claims.

This milestone adds an internal benchmark / release-gate layer, not a reusable public benchmarking API.

Required controls:

  • fixed train/test split conventions

  • fixed verification defaults

  • fixed low-noise held-out condition shared across Heat and Burgers

  • fixed derivative backend assumptions

  • comparable fitting and verification settings across Heat and Burgers where meaningful

Required outputs:

  • symmetry recovery result on Heat

  • symmetry recovery result on Burgers

  • held-out verification on both

  • one matched noisy held-out robustness check shared across both PDEs

  • reproducible VerificationReport on both

  • no regression in the existing Heat path

Release Gate#

v0.2 is releasable only if:

  • the v0.1 Heat path still passes cleanly

  • Burgers works end to end through the stable pipeline

  • the chosen Burgers symmetry target is recovered and verified under held-out evaluation

  • matched clean Heat / Burgers benchmark checks are exact

  • matched noisy held-out Heat / Burgers benchmark checks are exact or approximate

  • the current stable contracts remain coherent across both PDEs

  • no deferred or experimental feature is required for the stable release path

If these conditions are not met, v0.2 is not complete.

Non-goals#

v0.2 is not:

  • the release where invariants become a stable public feature

  • the release where weak-form methods become stable

  • the release where PDELie becomes a broad ecosystem hub

  • the release where operator methods become part of the stable library

It is the release where the current stable core proves that it generalizes one step beyond the original heat-equation MVP.

Next Expansion After v0.2#

If v0.2 succeeds, the next credible stable step is:

  • a minimal invariant/downstream utility release

not:

  • broad adapters

  • broad numerics

  • operator methods

That next step belongs to v0.3, not v0.2.