Spatial Statistics for Screening Molecular Structures.

The dominant paradigm in computational materials discovery relies on heavily parameterized deep architectures, including message-passing graph and equivariant networks, that typically require large density functional theory (DFT)-labeled training sets and produce nonconvex latent representations complicating inverse design, a limitation in the data-scarce regimes common to exploratory screening. Standard formulations also face specific difficulties with chemically disordered configurations and with distinguishing chiral geometries (e.g., E ( 3 ) -invariant models are reflection-blind by construction). These are task- and formulation-dependent tendencies, not universal deficiencies, and are reduced by pre-training, transfer, and equivariant designs. This review presents spatial-statistics feature engineering as a physically rigorous, deployable complement. Molecular structures are encoded as voxelized fields, and two-point auto- and cross-correlations are evaluated deterministically via Fast Fourier Transforms, moving spatial pattern recognition into a closed-form, physics-informed operation. Principal component analysis yields low-dimensional, convex representations supporting lean neural networks and non-parametric surrogates, achieving sub-2% normalized errors from as little as 0.1% of the dataset in reported cases. Demonstrated across periodic crystals, disordered high-entropy alloys, and non-periodic molecules, the framework enables Bayesian active learning and zero-shot extrapolation on commodity hardware, which remains challenging for large-scale architectures at equal data budgets.