张量约化的原子密度表示
Tensor-reduced atomic density representations
AI总结：
本文提出张量约化原子密度表示，通过张量分解将化学元素信息映射至固定维度，使表示大小不随元素数增长，同时保持系统可收敛性，适用于数据分析和回归任务。
摘要：
基于密度且具有欧几里得对称不变性的原子环境表示，已成为机器学习原子间势、更广泛的数据驱动原子建模以及材料数据集可视化和分析中广泛使用的工具。纳入化学元素信息的标准机制是为每种元素创建单独的密度，并在它们之间形成张量积。这导致表示的大小随着元素数量的增加而急剧扩展。图神经网络不显式使用密度表示，通过将化学元素信息以可学习的方式映射到固定维度空间，从而避免了这种扩展。我们利用标准邻域密度描述符的张量结构，将这种方法重新表述为张量分解。由此，我们形成了紧凑的张量约化表示，其大小不依赖于化学元素的数量，但仍具有系统可收敛性，因此适用于广泛的数据分析和回归任务。
英文摘要：
Density based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modelling and the visualisation and analysis of materials datasets.The standard mechanism used to incorporate chemical element information is to create separate densities for each element and form tensor products between them. This leads to a steep scaling in the size of the representation as the number of elements increases. Graph neural networks, which do not explicitly use density representations, escape this scaling by mapping the chemical element information into a fixed dimensional space in a learnable way. We recast this approach as tensor factorisation by exploiting the tensor structure of standard neighbour density based descriptors. In doing so, we form compact tensor-reduced representations whose size does not depend on the number of chemical elements, but remain systematically convergeable and are therefore applicable to a wide range of data analysis and regression tasks.
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