The use of generative models to sample equilibrium distributions of many-body systems, as first demonstrated by Boltzmann Generators, has attracted substantial interest due to their ability to produce unbiased and uncorrelated samples in `one shot'. Despite their promise and impressive results across the natural sciences, scaling these models to large systems remains a major challenge. In this work, we introduce a Boltzmann Generator architecture that addresses this scalability bottleneck with a focus on applications in materials science. We leverage augmented coupling flows in combination with graph neural networks to base the generation process on local environmental information, while allowing for energy-based training and fast inference. Compared to previous architectures, our model trains significantly faster, requires far less computational resources, and achieves superior sampling efficiencies. Crucially, the architecture is transferable to larger system sizes, which allows for the efficient sampling of materials with simulation cells of unprecedented size. We demonstrate the potential of our approach by applying it to several materials systems, including Lennard-Jones crystals, ice phases of mW water, and the phase diagram of silicon, for system sizes well above one thousand atoms. The trained Boltzmann Generators produce highly accurate equilibrium ensembles for various crystal structures, as well as Helmholtz and Gibbs free energies across a range of system sizes, able to reach scales where finite-size effects become negligible.

翻译：生成模型用于采样多体系统的平衡分布，正如玻尔兹曼生成器首次展示的那样，因其能够“一次性”产生无偏且不相关的样本而引起了广泛关注。尽管这些模型在自然科学领域展现出前景并取得了令人瞩目的成果，但将其扩展到大型系统仍然是一个重大挑战。在本工作中，我们引入了一种玻尔兹曼生成器架构，旨在解决这一可扩展性瓶颈，并重点关注材料科学中的应用。我们利用增强耦合流与图神经网络的结合，将生成过程建立在局部环境信息的基础上，同时支持基于能量的训练和快速推理。与之前的架构相比，我们的模型训练速度显著加快，所需计算资源大大减少，并实现了更优的采样效率。至关重要的是，该架构可迁移到更大的系统尺寸，从而能够高效采样具有前所未有尺寸模拟单元的材料。我们通过将该方法应用于多个材料系统来展示其潜力，包括Lennard-Jones晶体、mW水的冰相以及硅的相图，系统尺寸远超过一千个原子。训练后的玻尔兹曼生成器为各种晶体结构生成了高度精确的平衡系综，并计算了不同系统尺寸下的亥姆霍兹和吉布斯自由能，能够达到有限尺寸效应可忽略的尺度。