The atomic cluster expansion provides local, complete basis functions that enable efficient parametrization of many-atom interactions. We extend the atomic cluster expansion to incorporate graph basis functions. This naturally leads to representations that enable the efficient description of semilocal interactions in physically and chemically transparent form. Simplification of the graph expansion by tensor decomposition results in an iterative procedure that comprises current message-passing machine learning interatomic potentials. We demonstrate the accuracy and efficiency of the graph atomic cluster expansion for a number of small molecules, clusters, and a general-purpose model for carbon. We further show that the graph atomic cluster expansion scales linearly with the number of neighbors and layer depth of the graph basis functions.

中文翻译：

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超越等变消息传递的半局部交互的图原子簇扩展


原子簇扩展提供了局部、完整的基函数，可以实现多原子相互作用的有效参数化。我们扩展原子簇扩展以合并图基函数。这自然会导致能够以物理和化学透明形式有效描述半局域相互作用的表示。通过张量分解对图展开的简化导致迭代过程，其中包括当前消息传递机器学习原子间势。我们展示了许多小分子、簇和碳通用模型的图原子簇扩展的准确性和效率。我们进一步表明，图原子簇扩展与图基函数的邻居数量和层深度呈线性关系。