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Physics-guided machine learning (PGML) has emerged as a hybrid paradigm in materials science, integrating domain knowledge with data-driven methods to enhance predictive accuracy and generalizability. Conventional approaches typically embed physical principles as soft inputs—either through loss-function regularization or auxiliary features—allowing violations during optimization. This manuscript advances a conceptual reframing in which physics operates as a hard constraint on the model’s hypothesis space rather than as an additive input. By restricting permissible functional forms, symmetries, and conservation relations a priori, the framework enforces physical consistency at the architectural level, altering the interaction dynamics between data and prior knowledge. The reframing yields systems-level insights into epistemic trade-offs: reduced reliance on large datasets, improved extrapolation beyond training regimes, and inherent satisfaction of thermodynamic or mechanical invariants critical to materials behavior. Analytical implications include feedback structures that couple data refinement to constraint satisfaction, revealing emergent robustness in multiscale modeling. This perspective addresses persistent challenges in materials science, such as sparse experimental data and complex microstructure-property relationships, without resorting to empirical validation. The contribution lies in reinterpreting PGML’s epistemic foundation, steering future developments toward constraint-centric designs that prioritize physical fidelity over post-hoc penalization.

In the rapidly evolving field of computational materials engineering, data-driven approaches have transformed the discovery and design of novel materials by leveraging machine learning and high-throughput computations to navigate vast chemical spaces. Traditional methodologies often rely on Euclidean distance metrics to quantify similarities between materials in latent representations, facilitating tasks such as property prediction, inverse design, and autonomous experimentation. However, this assumption overlooks the inherent non-linearities and topological complexities of material spaces, where properties like electronic bandgaps, mechanical strengths, and thermodynamic stabilities emerge from intricate atomic interactions that do not conform to flat geometries. This conceptual gap leads to inefficiencies in representation learning, biased uncertainty quantification, and suboptimal steering in discovery pipelines. Here, we introduce a novel interpretive framework that critiques Euclidean metrics through a manifold-based lens, emphasizing geodesic distances and curvature-aware embeddings to better capture the epistemic structure of materials data. By integrating insights from graph neural networks, multimodal datasets, and closed-loop systems, this framework reveals computational trade-offs in data infrastructures and enhances the interpretability of AI-guided workflows. Implications extend to improved coupling of simulations and experiments, fostering more robust foundation models for materials science and accelerating innovation in energy, electronics, and structural applications without empirical validation.