发表机构
Courant Institute; New York University; Tandon School of Engineering; The University of Chicago（库朗研究所; 纽约大学; 坦登工程学院; 芝加哥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
NEMORA是FMM的神经等变扩展，可线性复杂度处理数十万个原子，在非局部基准上大幅降低力和能量误差，性能优于或媲美现有长程方法。
AI 中文摘要
等变图神经网络已成为机器学习原子间势的基础架构，能以远低于量子化学方法的计算成本达到其精度。这些模型可准确描述局部原子环境，但有限的空间截断会截断长程信息流，且堆叠消息传递层会导致过平滑和过挤压。现有长程扩展方法要么采用固定的解析传播核，要么将长程通信限制在标量或保度通道，要么仅近似等变，要么产生超线性计算成本。将可学习的长程等变传输与多尺度多体表达性及针对更大系统的高效缩放相结合，仍是核心挑战。我们提出神经等变多极算子（NEMORA），这是用于学习长程张量表示的快速多极方法（FMM）的神经等变扩展。NEMORA将FMM的解析多极展开和平移算子推广为自适应空间层次上的可学习等变对应物，其算子耦合角自由度并形成跨长度尺度的多体相互作用，保留FMM的层次结构和解析径向因子作为物理归纳偏置，同时学习依赖数据的长程耦合。NEMORA的时间和内存复杂度为线性，可处理比其他长程方法更大的系统，达数十万个原子，且可增强受对称性约束和无对称性约束的短程主干模型。在非局部基准测试中，它相对于短程主干模型将力误差降低了一个数量级以上，能量误差降低了三个数量级以内，精度优于或与现有长程扩展方法相当。
英文摘要
Equivariant graph neural networks have emerged as foundational architectures for machine-learned interatomic potentials, approaching quantum-chemical accuracy at a fraction of the computational cost. These models describe local atomic environments accurately, but finite spatial cutoffs truncate long-range information flow, and stacking message-passing layers can lead to over-smoothing and over-squashing. Existing long-range extensions either prescribe a fixed analytical propagation kernel, restrict long-range communication to scalars or degree-preserving channels, are only approximately equivariant, or incur super-linear computational cost. Combining learnable long-range equivariant transport with multiscale many-body expressivity and efficient scaling for larger systems remains a central challenge. We introduce Neural Equivariant Multipole Operators (NEMORA), a neural equivariant extension of the Fast Multipole Method (FMM) for learning long-range tensorial representations. NEMORA generalizes the FMM's analytical multipole expansion and translation operators to learned equivariant counterparts on an adaptive spatial hierarchy. Its operators couple angular degrees and form many-body interactions across length scales, retaining the FMM's hierarchical organization and analytical radial factors as physical inductive biases while learning data-dependent long-range couplings. NEMORA evaluates in linear time and memory complexity, allowing it to treat larger systems than other long-range methods reaching hundreds of thousands of atoms, and it augments both symmetry-constrained and unconstrained short-range backbones. On non-local benchmarks, it reduces force and energy errors relative to the short-range backbones by over an order of magnitude and up to three orders of magnitude, respectively, which is better than or competitive with existing long-range extensions in accuracy.
Comments59 pages, 5 figures, including supplementary material
