Spatial statistics for screening molecular structures
Abstract
The dominant paradigm in computational materials discovery relies on heavily parameterized deep architectures, including message-passing graph networks and equivariant models, that require millions of DFT-labeled training structures and produce non-convex latent representations that complicate continuous optimization for inverse design. These architectures are impractical in data-scarce regimes, which is the typical case in molecular screening, and exhibit well-documented limitations in capturing chemically disordered configurations and chiral geometries. This review presents feature engineering based on spatial statistics as a physically rigorous and immediately deployable alternative. Molecular structures are encoded as voxelized scalar fields, and two-point auto- and cross-correlations are evaluated deterministically via Fast Fourier Transforms, explicitly transferring the burden of spatial pattern recognition from the learning algorithm to a closed-form, physics-informed operation. Principal component analysis of the resulting correlation maps yields low-dimensional, strictly convex representations that support lean neural networks (<100k trainable parameters) and non-parametric surrogate models, achieving sub-2% prediction error with as few as 10 training samples. Demonstrated across periodic crystals, chemically disordered high-entropy alloys, and non-periodic organic molecules, this framework enables Bayesian active learning and zero-shot extrapolation on commodity hardware, which current large-scale architectures cannot replicate at equivalent data budgets.
Versions
Related
- Data driven screening of CaCu5-type magnetic structures
- Preservation of photon statistics upon selective molecular modulation in hollow-core fibers
- Crystalline ASR products: Review of mineral candidates and molecular simulations of their atomic structures, thermodynamic data and thermoelastic properties
- Steering interfacial molecular structures by substrate-molecule charge transfer
- Thermal Stability of Encapsulated Molecular Structures with Extended OH-Hydrogen-Bond Chains
BibTeX
@misc{ray2026spatial,
title = {{Spatial statistics for screening molecular structures}},
author = {Pranoy Ray and Surya R. Kalidindi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.17147},
eprint = {2605.17147},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.17147},
}
RIS
TY - UNPB
TI - Spatial statistics for screening molecular structures
AU - Pranoy Ray
AU - Surya R. Kalidindi
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2605.17147
UR - https://arxiv.org/abs/2605.17147
AB - The dominant paradigm in computational materials discovery relies on heavily parameterized deep architectures, including message-passing graph networks and equivariant models, that require millions of DFT-labeled training structures and produce non-convex latent representations that complicate continuous optimization for inverse design. These architectures are impractical in data-scarce regimes, which is the typical case in molecular screening, and exhibit well-documented limitations in capturing chemically disordered configurations and chiral geometries. This review presents feature engineering based on spatial statistics as a physically rigorous and immediately deployable alternative. Molecular structures are encoded as voxelized scalar fields, and two-point auto- and cross-correlations are evaluated deterministically via Fast Fourier Transforms, explicitly transferring the burden of spatial pattern recognition from the learning algorithm to a closed-form, physics-informed operation. Principal component analysis of the resulting correlation maps yields low-dimensional, strictly convex representations that support lean neural networks (<100k trainable parameters) and non-parametric surrogate models, achieving sub-2% prediction error with as few as 10 training samples. Demonstrated across periodic crystals, chemically disordered high-entropy alloys, and non-periodic organic molecules, this framework enables Bayesian active learning and zero-shot extrapolation on commodity hardware, which current large-scale architectures cannot replicate at equivalent data budgets.
ER -