Domain-Validity-Gated Metamorphic Testing of Scientific ML Surrogates
For developers of scientific ML surrogates, the paper provides a principled method to screen metamorphic relations for domain validity, enabling auditable, oracle-free testing that separates model errors from out-of-domain inputs.
The paper addresses the oracle problem in testing scientific ML surrogates by proposing a domain-validity rubric and executable metamorphic relation (MR) assets. On MeshGraphNets, node permutation holds to machine precision, mirror-y is a bounded out-of-distribution stress finding, and absolute conservation is deferred; results hold across architectures and PhysicsNeMo, and on a compressible airfoil task the predicate rejects incompressible continuity on physical grounds.
Scientific machine-learning (SciML) surrogates approximate expensive simulations, but exact expected outputs for arbitrary inputs are unavailable (the oracle problem). Metamorphic testing checks relations across executions, yet a candidate relation is not automatically valid: its preconditions, output mapping, and the numerical floor of the scoring operator determine whether a violation is meaningful. We study how candidate metamorphic relations (MRs) can be screened for domain validity and turned into executable, oracle-free test assets for SciML surrogates. We propose (i) a domain-validity rubric that admits a candidate only when its tolerance dominates the operator's numerical floor and its preconditions hold; (ii) an MR-card executable-asset format recording source cases, transformations, metrics, tolerances, and typed relation-level verdicts; and (iii) a case-study protocol on MeshGraphNets cylinder-flow surrogates, with a claim ledger binding every result to a tracked artifact. On a MeshGraphNets checkpoint, node permutation holds to machine precision, mirror-y is a bounded out-of-distribution stress finding rather than an exact symmetry, and absolute conservation stays deferred while a reference-relative guard passes. The same readings hold across held-out trajectories, a checkpoint roster, three further architectures, and PhysicsNeMo. On a second CFD task (compressible airfoil) the predicate instead rejects incompressible continuity on physical grounds, showing it reasons about domain validity rather than running a fixed checklist. On a second PDE family, FNO Burgers and heat surrogates run full admit/reject/execute verdicts. The evidence spans two CFD tasks and a second PDE family, supporting a validity-aware bridge from candidate MRs to auditable SciML test assets that separates model-level violations from out-of-domain applications.