Exact SO(3)-Equivariant Isotropic Kernels for Rotation-Robust Neural Dynamics

The paper introduces the Invariant-Conditioned Isotropic Kernel Neural Operator (IKNO), a compact graph model designed to predict vector-valued partial differential equations in a rotation‑robust manner. IKNO constructs local interactions from rotation‑invariant scalar quantities and vector directions that transform consistently with the data, ensuring that rotating input positions and velocities results in a correspondingly rotated predicted velocity change. Experiments on three‑dimensional Navier–Stokes dynamics show that IKNO achieves numerical precision consistency, matches the forecasting accuracy of a larger rotation‑aware Tensor Field Network, and outperforms a parameter‑matched graph simulator.

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