TY - JOUR
T1 - Material Spaces Are Not Euclidean: A Computational Critique of Distance Metrics in Data-Driven Materials Discovery
AU - Carlos Vega
AU - Maria Hernandez
JF - Journal of Computational and Data-Driven Materials Engineering
JO - J. Comput. Data-Driven Mater. Eng.
SN - 3149-9368
Y1 - 2022
VL - 1
IS - 1
DO - 10.68159/v489956132
SP - 80
N2 - 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.
UR - https://iamrp.net/v489956132
ER -