arXiv：cs.LG· Ridham Patel·· 4 小时前
IKNO：面向旋转鲁棒神经动力学的精确 SO(3) 等变各向同性核
Exact SO(3)-Equivariant Isotropic Kernels for Rotation-Robust Neural Dynamics
AI 导读
研究者提出 Invariant-Conditioned Isotropic Kernel Neural Operator（IKNO），一种从旋转不变的标量与随数据旋转的向量方向构建局部交互的紧凑图模型，用于三维 Navier-Stokes 动力学预测，旋转输入时其预测速度变化以完全相同方式旋转。
正文
Abstract:Neural surrogates for vector-valued partial differential equations can fit training data yet change their predictions when the same physical state is expressed in a rotated coordinate frame. We study this failure on three-dimensional Navier--Stokes dynamics observed at irregularly placed points. We introduce the Invariant-Conditioned Isotropic Kernel Neural Operator (IKNO), a compact graph model that builds local interactions from scalar quantities unchanged by rotation and vector directions that rotate with the data. Consequently, rotating the positions and velocities rotates the predicted velocity change in exactly the same way. On a held-out test set fixed after model design, training unconstrained graph models on randomly rotated examples reduces but does not eliminate their coordinate dependence. In contrast, IKNO is consistent to numerical precision, matches the forecasting accuracy of a general rotation-aware Tensor Field Network with $5.6$ times fewer parameters, and outperforms a parameter-matched graph simulator. These results show that a compact, PDE-specialized model can remove coordinate dependence without sacrificing forecasting accuracy.
| Comments: | Accepted at NeurIPS 2026 Workshop NeurReps (Proceedings Track) |
| Subjects: | Machine Learning (cs.LG); Computational Engineering, Finance, and Science (cs.CE); Machine Learning (stat.ML) |
| Cite as: | arXiv:2610.10626 [cs.LG] |
| (or arXiv:2610.10626v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10626 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Ridham Patel [view email]
[v1]
Wed, 7 Oct 2026 11:05:39 UTC (38 KB)
来源：arXiv：cs.LG · arxiv.org