arXiv：cs.LG· Jay L. Kaplan, Samuel Varner, Rebecca Willett, Juan J. de Pablo·· 4 小时前
NEMORA：面向长程原子模拟的神经等变多极算子
NEMORA: Neural Equivariant Multipole Operators for Long-Range Atomistic Learning
AI 导读
NEMORA 将快速多极子方法（FMM）的解析多极展开与平移算子泛化为可学习的等变版本，在自适应空间层级上学习长程张量表示。该模型以线性时间与内存复杂度计算，可处理数十万原子量级的更大体系，并能增强受对称约束与不受约束的短程骨干网络。在非局域基准上，其力与能量误差相对短程骨干分别降低一个数量级以上、最高达三个数量级。
正文
Abstract: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.
| Comments: | 59 pages, 5 figures, including supplementary material |
| Subjects: | Machine Learning (cs.LG); Chemical Physics (physics.chem-ph); Computational Physics (physics.comp-ph) |
| Cite as: | arXiv:2610.10776 [cs.LG] |
| (or arXiv:2610.10776v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10776 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Jay Kaplan [view email]
[v1]
Wed, 7 Oct 2026 18:32:31 UTC (3,672 KB)
来源：arXiv：cs.LG · arxiv.org