# Domain-Validity-Gated Metamorphic Testing of Scientific ML Surrogates

arXiv: https://arxiv.org/abs/2606.17529 · HTML: https://mlsanity.com/paper/2606.17529/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 16 Jun 2026.

## Builds on (most cited first, 8 of 8)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Metamorphic Testing: A New Approach for Generating Next Test Cases](https://mlsanity.com/paper/2002.12543/) (2020)
- [Towards a Complete Metamorphic Testing Pipeline](https://mlsanity.com/paper/2310.00338/) (2023)
- [Towards Automated Metamorphic Test Identification for Ocean System Models](https://mlsanity.com/paper/2103.09782/) (2021)
- [Bug or not Bug? Analysing the Reasons Behind Metamorphic Relation Violations](https://mlsanity.com/paper/2305.09640/) (2023)
- [Exploring a Test Data-Driven Method for Selecting and Constraining Metamorphic Relations](https://mlsanity.com/paper/2307.15522/) (2023)

## Abstract (arXiv)

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.