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Add array-form POD Galerkin reduction without DEIM - #202

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ChrisRackauckas merged 1 commit into
SciML:mainfrom
ChrisRackauckas-Claude:feat/pod-galerkin-array-form
Sep 8, 2026
Merged

ChrisRackauckas merged 1 commit into
SciML:mainfrom
ChrisRackauckas-Claude:feat/pod-galerkin-array-form

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Ignore this PR until reviewed by @ChrisRackauckas.

Closes #2.

Summary

  • Add public pod(sys, snapshot, dim) / pod(prob, sol, dim) for POD Galerkin projection without DEIM.
  • For array/field source equations, assemble V' * f(V*ŷ) with V and V' as array parameters so the reduced residual graph stays independent of grid size.
  • Keep one array differential equation and one array reconstruction per source field (same online representation as POD-DEIM).
  • Scalarized sources fall back to full residual Galerkin (online cost scales with full order); use deim when hyper-reduction is required.
  • Share reduced-system assembly through _assemble_reduced_system.

Test plan

  • GROUP=Core julia --project -e 'using Pkg; Pkg.test()'
    • Core/pod.jl: 19 passed
    • Core/array_structure.jl, deim.jl, and other Core files passed
  • CI on this PR
  • Docs build if desired: julia --project=docs docs/make.jl

Made with Cursor

Closes SciML#2. Project source field/array residuals as V'*f(V*ŷ) with
array parameters so the reduced graph stays grid-independent; keep
DEIM for hyper-reduced online cost.

Co-authored-by: Cursor <cursoragent@cursor.com>
@ChrisRackauckas
ChrisRackauckas merged commit 8bc6fd6 into SciML:main Sep 8, 2026
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Model Order Reduction via POD

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