C2NP: A Benchmark for Learning Scale-Dependent Geometric Invariances in 3D Materials Generation

• URL: http://arxiv.org/abs/2601.19076v1
• Date: Tue, 27 Jan 2026 01:25:50 GMT
• Title: C2NP: A Benchmark for Learning Scale-Dependent Geometric Invariances in 3D Materials Generation
• Authors: Can Polat, Erchin Serpedin, Mustafa Kurban, Hasan Kurban,
• Abstract summary: We introduce Crystal-to-Nanoparticle (C2NP), a benchmark for evaluating generative models when moving between infinite crystalline unit cells and finite nanoparticles.<n>C2NP defines two complementary tasks: (i) generating nanoparticles of specified radii from periodic unit cells, testing whether models capture surface truncation and geometric constraints; and (ii) recovering bulk lattice parameters and space-group symmetry from finite particle configurations.
• Score: 2.3982445219832678
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Generative models for materials have achieved strong performance on periodic bulk crystals, yet their ability to generalize across scale transitions to finite nanostructures remains largely untested. We introduce Crystal-to-Nanoparticle (C2NP), a systematic benchmark for evaluating generative models when moving between infinite crystalline unit cells and finite nanoparticles, where surface effects and size-dependent distortions dominate. C2NP defines two complementary tasks: (i) generating nanoparticles of specified radii from periodic unit cells, testing whether models capture surface truncation and geometric constraints; and (ii) recovering bulk lattice parameters and space-group symmetry from finite particle configurations, assessing whether models can infer underlying crystallographic order despite surface perturbations. Using diverse materials as a structurally consistent testbed, we construct over 170,000 nanoparticle configurations by carving particles from supercells derived from DFT-relaxed crystal unit cells, and introduce size-based splits that separate interpolation from extrapolation regimes. Experiments with state-of-the-art approaches, including diffusion, flow-matching, and variational models, show that even when losses are low, models often fail geometrically under distribution shift, yielding large lattice-recovery errors and near-zero joint accuracy on structure and symmetry. Overall, our results suggest that current methods rely on template memorization rather than scalable physical generalization. C2NP offers a controlled, reproducible framework for diagnosing these failures, with immediate applications to nanoparticle catalyst design, nanostructured hydrides for hydrogen storage, and materials discovery. Dataset and code are available at https://github.com/KurbanIntelligenceLab/C2NP.

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