TY - JOUR
T1 - Theoretical Foundations of Geometric Deep Learning for Amorphous Structures: Beyond the Periodicity Assumption
AU - Thomas Andersen
AU - Lars Nielsen
AU - Mette Sørensen
JF - Journal of Computational and Data-Driven Materials Engineering
JO - J. Comput. Data-Driven Mater. Eng.
SN - 3149-9368
Y1 - 2025
VL - 4
IS - 1
DO - 10.68159/u729969158
SP - 46
N2 - Geometric deep learning has advanced computational materials science, yet most existing approaches remain constrained by the periodicity assumption inherent to crystalline systems. While crystal-based graph neural networks exploit translational symmetry and periodic boundary conditions, amorphous materials—such as glasses, liquids, polymers, and disordered alloys—lack long-range order, exhibit non-repetitive atomic arrangements, and span widely varying system sizes. This mismatch renders periodicity-dependent methods both theoretically inadequate and practically unreliable for disordered structures. This work identifies three key distinctions—non-periodic graph construction, symmetry limited to E(3) equivariance, and non-physical boundary conditions—which collectively give rise to fundamental challenges, including scaling limitations, loss of transferability, and structural representation imbalances. Through theoretical analysis, the limitations of crystal-oriented graph neural networks in amorphous settings are clarified. To address these issues, a new framework is proposed based on size-extensive, E(3)-equivariant architectures that eliminate periodic assumptions and integrate multi-scale encoding of local, intermediate, and global structure with size-normalized aggregation. This formulation provides a principled foundation for geometric deep learning models tailored to amorphous materials and their applications in energy, optics, and structural systems.
UR - https://iamrp.net/u729969158
ER -