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[Submitted on 7 Oct 2026] Title:Exact SO(3)-Equivariant Isotropic Kernels for Rotation-Robust Neural Dynamics View a PDF of the paper titled Exact SO(3)-Equivariant Isotropic Kernels for Rotation-Robust Neural Dynamics, by Ridham Patel View PDF HTML (experimental) 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) Full-text links: Access Paper: View a PDF of the paper titled Exact SO(3)-Equivariant Isotropic Kernels for Rotation-Robust Neural Dynamics, by Ridham Patel View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.LG new | recent | 2026-10 Change to browse by: cs cs.CE stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)