Exact SO(3)-Equivariant Isotropic Kernels for Rotation-Robust Neural Dynamics
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.
ProofPaper ↗
Key points
- 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.
- 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.
Sources (1)
- [1]Exact SO(3)-Equivariant Isotropic Kernels for Rotation-Robust Neural DynamicsarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 11:05 AM
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.
Extractive summary: sentences quoted from the sources.