V0.3 Scope#

Summary#

v0.3 is the first downstream-utility release for PDELie.

It does not introduce a new numerical regime.
It does not widen the ecosystem surface broadly.
It does not bring operator methods into the stable library.

Instead, it asks a narrower and more important question:

Can the current stable symmetry pipeline support one minimal invariant/downstream utility path under controlled benchmark conditions?

v0.3 is therefore the first invariant/downstream utility release, not the first broad ecosystem or operator release.

The downstream target for v0.3 is frozen as:

  • a single-generator invariant workflow only

  • a thin downstream bridge only

  • one controlled benchmark layer only

  • Heat and Burgers remain the only stable PDEs

  • the current stable derivative backend remains spectral_fd

Current State#

Milestone 1 — Complete#

v0.3 Milestone 1 is complete.

Completed scope:

  • stable InvariantMapSpec

  • runtime-only InvariantApplier

  • one frozen invariant application path for the current stable symmetry slice

  • regression protection showing Heat and Burgers still pass the existing stable pipeline

This milestone introduced the first stable invariant-layer contract without broadening the public API beyond the narrow single-generator path.

Milestone 2 — Complete#

v0.3 Milestone 2 is complete.

Completed scope:

  • runtime-only pdelie.discovery.to_pysindy_trajectories

  • one narrow flattened-trajectory bridge for PySINDy only

  • one minimal downstream fit smoke path for the current invariant-transformed stable slice

  • no new stable canonical object

This milestone added a backend-specific runtime bridge, not a canonical PDE-discovery representation.

Milestone 3 — Complete#

v0.3 Milestone 3 is complete.

Completed scope:

  • one internal four-branch downstream benchmark:

    • vanilla

    • known_invariant

    • discovered_invariant

    • nuisance

  • one frozen benchmark-local alignment rule for the current single-generator translation slice

  • one explicit frozen PySINDy configuration for the downstream release gate

  • reproducibility, matched-settings, and release-gate tests

  • no new public API and no new stable canonical object

This milestone proves a controlled downstream utility signal for the current invariant/downstream path relative to a nuisance baseline. It does not claim broader discovery-quality superiority.

Must Implement#

Stable scope for v0.3#

  • uniform rectilinear grids only

  • synthetic PDE data only

  • polynomial generators only

  • single-generator invariant workflows only

  • one thin downstream bridge only

  • one controlled benchmark layer only

  • verification-first development

  • Heat and Burgers remain supported

  • no new numerical backend is required for the stable path

Stable canonical objects for v0.3#

Stable in v0.3:

  • FieldBatch

  • DerivativeBatch

  • ResidualBatch

  • ResidualEvaluator

  • GeneratorFamily

  • VerificationReport

  • InvariantMapSpec

Runtime-only, not canonical:

  • InvariantApplier

Still not stable in v0.3:

  • InvariantLibrary

  • DiscoveryResult

No other canonical objects should become stable in v0.3 unless absolutely necessary to support the frozen invariant/downstream path.

Concrete v0.3 Target#

Add one minimal end-to-end stable downstream path on top of the existing stable symmetry core.

The stable conceptual path becomes:

FieldBatch -> DerivativeBatch -> ResidualBatch -> GeneratorFamily -> InvariantMapSpec -> InvariantApplier -> downstream bridge -> VerificationReport

for Heat and Burgers under the current stable translation-targeted symmetry slice.

Required components#

  • one stable InvariantMapSpec for the single-generator case

  • one runtime InvariantApplier

  • one thin downstream bridge, likely PySINDy

  • one controlled benchmark comparing:

    • vanilla downstream path

    • known-invariant downstream path

    • discovered-invariant downstream path

    • one nuisance / conditioning baseline

  • one release-gate layer that keeps all settings matched across benchmark branches

Required scientific result#

  • the known-invariant and discovered-invariant downstream paths both run end to end under the stable contracts

  • the benchmark is reproducible and matched

  • the invariant-aware downstream path is at least meaningfully distinguishable from a nuisance baseline under matched controls

  • Heat and Burgers remain regression-free under the existing stable symmetry pipeline

v0.3 is a utility release, not yet a broad superiority-claim release.

Frozen Milestones#

Milestone 1 — Invariant layer#

Status: Complete

Frozen scope:

  • stable InvariantMapSpec

  • runtime-only InvariantApplier

  • one narrow application path

  • no downstream bridge yet

  • no benchmark expansion yet

Milestone 2 — Thin downstream bridge#

Status: Complete

Frozen scope:

  • one thin downstream bridge only

  • no broad system-identification framework

  • no new canonical stable object unless absolutely required

  • no benchmark expansion yet beyond the minimal bridge smoke path

  • no weak-form methods

  • no operator methods

  • no broad adapters

Completed outcome:

  • transformed data from the current single-generator invariant path can feed one downstream workflow cleanly under stable contracts

Milestone 3 — Controlled downstream benchmark / release-gate layer#

Status: Complete

Frozen scope:

  • one controlled benchmark comparing:

    • vanilla

    • known-invariant

    • discovered-invariant

    • nuisance baseline

  • matched feature budget

  • matched regularization budget

  • matched split policy

  • reproducible benchmark outputs

  • no broad benchmark zoo

  • no new public benchmark API unless clearly justified

Completed outcome:

  • v0.3 release gate can be stated in terms of a reproducible downstream utility benchmark, not just symmetry recovery

  • known_invariant and discovered_invariant are expected to be numerically equivalent in the frozen Milestone 3 slice

  • the nuisance baseline is the actual utility comparison branch for this release gate

Development Order#

  1. freeze v0.3 scope

  2. implement InvariantMapSpec

  3. implement InvariantApplier

  4. add one thin downstream bridge

  5. add the controlled downstream benchmark layer

  6. add nuisance / conditioning control baseline

  7. add release-gate tests and documentation

Explicitly Deferred#

The following are not part of stable v0.3 scope:

  • weak-form derivatives as a stable backend

  • multi-generator invariant charts

  • InvariantLibrary as a stable contract

  • DiscoveryResult as a stable contract

  • broad system-identification framework work beyond one thin bridge

  • broad adapters (PDEBench, The Well, etc.) as release-defining work

  • operator symmetry

  • NeuralOperator integration

  • nonuniform rectilinear support in stable derivative code

  • multiple downstream backends

  • broad benchmark zoo

  • manuscript-specific experiment logic

These may be explored experimentally, but they do not define v0.3.

Benchmark Rules for v0.3#

v0.3 should benchmark the first stable downstream utility path, not yet claim broad downstream dominance.

Required controls:

  • fixed train/test split conventions

  • fixed verification defaults

  • fixed noise condition where applicable

  • fixed feature budget

  • fixed regularization budget

  • fixed derivative backend assumptions

  • identical benchmark settings across:

    • vanilla

    • known-invariant

    • discovered-invariant

    • nuisance baseline

Required outputs:

  • downstream result for vanilla path

  • downstream result for known-invariant path

  • downstream result for discovered-invariant path

  • downstream result for one nuisance baseline

  • held-out evaluation under matched settings

  • reproducible benchmark outputs

  • no regression in the existing Heat/Burgers symmetry paths

The benchmark must distinguish:

  • correctness of the invariant/downstream mechanism

  • conditioning effects

  • a controlled downstream utility signal relative to the nuisance baseline

Release Gate#

v0.3 is releasable only if:

  • the v0.2 Heat path still passes cleanly

  • the v0.2 Burgers path still passes cleanly

  • the single-generator InvariantMapSpec and InvariantApplier work end to end on the frozen stable path

  • the thin downstream bridge works for the frozen stable task

  • the controlled benchmark runs reproducibly under matched settings

  • the nuisance baseline is included

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

  • the current stable contracts remain coherent after adding the first invariant/downstream layer

If these conditions are not met, v0.3 is not complete.

Non-goals#

v0.3 is not:

  • 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

  • the release where full invariant machinery becomes stable

  • the release where downstream discovery becomes a broad multi-backend framework

It is the release where PDELie proves that its current stable symmetry core can support one disciplined invariant/downstream utility path.

Next Expansion After v0.3#

If v0.3 succeeds, the next credible stable step is one of:

  • broader invariant machinery

  • broader downstream semantics

  • broader numerics

but still not automatically operator methods or broad ecosystem expansion.

Those decisions belong to v0.4+, not v0.3.