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Two-dimensional (2D) materials have attracted considerable attention for next-generation electronic, optoelectronic, and catalytic applications; however, their performance is strongly influenced by the presence and stability of atomic-scale defects. Defect formation energy plays an essential role in defect prevalence, lattice stability, and functional behavior. Still, its evaluation remains challenging due to the complexity of defect-induced structural perturbations and the limitations of equilibrium-first-principles approaches. This paper presents an entirely conceptual framework that reframes defect formation energy estimation as a graph-structured inference problem. Leveraging graph neural networks (GNNs), the proposed defect-aware graph neural architecture (DAGNA) represents pristine and defect-perturbed lattices as coupled relational graphs, enabling structured propagation of defect-induced information across spatial scales. Instead of proposing a predictive or validated model, the framework explains how hierarchical message passing, defect-aware embeddings, and physics-constrained aggregation can be organized to regulate information flow under defect perturbations in two-dimensional systems. By synthesizing advances in graph theory, the physics of defects, and materials-focused AI, this work provides an operational decision-making framework for reasoning about defect formation energy without relying on empirical datasets or simulations. This framework contributes to the theoretical foundations of applied artificial intelligence in materials science. It provides a clear, physically grounded architecture for future studies in defect-aware materials modeling and defect engineering.

Active learning is widely used in materials discovery to reduce the number of expensive density functional theory calculations required for surrogate-model training. Its dominant acquisition rule, uncertainty sampling, assumes that the most uncertain configuration will also yield the greatest information gain. Although this logic performs well for many bulk properties, it breaks down for defect formation energies. In this setting, uncertainty sampling repeatedly selects uninformative structures, misallocates computational budget, and fails to reach the defective configurations that govern vacancy, interstitial, and substitutional behavior in technologically important materials. This failure reflects a structural mismatch between the acquisition rule and defect physics. Defect configurations are rare in configuration space, energetics are highly localized, and DFT labels often contain substantial aleatoric noise from finite-size effects, charge corrections, and supercell artifacts. These conditions weaken the link between predictive uncertainty and useful learning signal, while representation bias in models trained mainly on perfect crystals further erodes selectivity. This study develops a failure-mode analysis of uncertainty sampling for defect formation energies, identifying recurrent breakdowns in sampling, representation, calibration, and budget use. It also outlines practical detection principles and defect-aware mitigation strategies, including initialization with defective structures, hybrid acquisition functions, epistemic-only scoring, and budget partitioning. The central implication is that active learning for defect discovery cannot rely on generic uncertainty-based querying. Effective acceleration in this domain requires acquisition strategies designed around the rarity, locality, and noise structure of defect energetics.