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Support quasi-periodic (Periodic × Matérn) product kernels in the state-space SDE registry #669

Description

@thomaspinder

Category: literature · Severity: medium
Location: gpjax/state_space/kernels.py:174 — _to_sde_product_kernel``

Problem

The SDE registry rejects all ProductKernels (kernels.py:175-178), which blocks the canonical quasi-periodic kernel TruncatedPeriodic × Matérn (Solin & Särkkä 2014 §3) whose state dimension is only (2K+1)·d. Both factor SDEs already exist, and the module's own Mauna Loa example (examples/state_space_gps.py:99-100,149-154) documents the gap and substitutes a sum.

Recommendation

Add a product-SDE construction for the Periodic×stationary case (Kronecker of the factor state-space models); keep the explicit rejection only for genuinely unsupported products.

Filed from the 2026-07-02 GPJax codebase audit (medium tier). Companion spec for the high-severity items: plans/2026-07-02-audit-high-severity-remediation-design.md.

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    bugSomething isn't workingdocumentationImprovements or additions to documentationenhancementNew feature or requestjax-compatibilitykernelsv1.0-resolvedNo longer relevant: resolved or made obsolete by the v1.0 conditioning refactor

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