Challenges in Non-Polymeric Crystal Structure Prediction: Why a Geometric, Permutation-Invariant Loss is Needed

Crystalline structure prediction is an essential prerequisite for designing materials with targeted properties. Yet, it is still an open challenge in materials design and drug discovery. Despite recent advances in computational materials science, accurately predicting three-dimensional non-polymeric crystal structures remains elusive. In this work, we focus on the molecular assembly problem, where a set S of identical rigid molecules is packed to form a crystalline structure. Such a simplified formulation provides a useful approximation to the actual problem. However, while recent state-of-the-art methods have increasingly adopted sophisticated techniques, the underlying learning objective remains ill-posed. We propose a better formulation that introduces a loss function capturing key geometric molecular properties while ensuring permutation invariance over S. Remarkably, we demonstrate that within this framework, a simple regression model already outperforms prior approaches, including flow matching techniques, on the COD-Cluster17 benchmark, a curated non-polymeric subset of the Crystallography Open Database (COD).