An embodied agent is an intelligent entity that interacts with its environment through a physical body. Currently, the evaluation of embodied agents primarily relies on two paradigms: (1) manually annotated Visual Question Answering (VQA) pairs and (2) high-level task completion metrics, such as success in navigation or manipulation. The former is labor-intensive and subject to variability in annotation quality. The latter may obscure critical vulnerabilities, allowing agents to complete tasks through suboptimal means or safety violations, thereby concealing safety risks and inefficiencies. Given that spatial cognition is the cornerstone for executing embodied tasks, there is a pressing need to assess whether embodied agents possess robust spatial cognition during task execution. Inspired by metamorphic testing principles in software engineering, we propose MetaSpace, a novel framework designed to evaluate the spatial cognition of agents. By leveraging spatiotemporal multimodal states derived from real execution trajectories, MetaSpace automatically generates test cases based on predefined metamorphic relations (MRs) grounded in logical rules and physical laws. Crucially, we encode these MRs as executable rules in a logic programming language (Prolog). Violations of these relations indicate failures in spatial cognition. Our empirical evaluation across three embodied scenarios demonstrates that MetaSpace successfully detects 90,422 spatial cognition errors in state-of-the-art (SOTA) MLLM-driven agents. We introduce the Spatial Cognition (SC) score to quantify performance. Results indicate that all SOTA agents achieve average scores between 0.44 and 0.52, significantly lower than the human benchmark of 0.96.
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.