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

2026-01-27

AI Summary

Existing generative models for materials lack systematic evaluation in cross-scale generalization—from infinite periodic crystals to finite nanostructures—and struggle to capture surface effects and size-dependent geometric distortions. This work proposes the C2NP benchmark, which establishes the first systematic generative tasks bridging bulk crystals and nanoparticles: (i) generating nanoparticles of specified radii from unit cells, and (ii) inferring bulk lattice parameters and space groups from given nanoparticles. Leveraging a dataset of over 170,000 DFT-relaxed nanoparticles, the benchmark introduces size-based interpolation and extrapolation splits to assess geometric invariance across scales. Experiments reveal that while mainstream generative models achieve low training losses, they fail catastrophically under distributional shifts, exhibiting large lattice recovery errors and near-zero joint accuracy in structure–symmetry prediction, exposing their reliance on template memorization rather than physically grounded, scalable generalization.

Technology Category

• Natural Language Processing: Generation
• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

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.

Problem

• scale-dependent generalization
• geometric invariance
• 3D materials generation
• nanoparticle synthesis
• crystal-to-nanoparticle transition

Innovation

• scale-dependent generalization
• geometric invariance
• nanoparticle generation
• crystal symmetry recovery
• distribution shift