Learning Manifold and It\^o Dynamics with Branched Neural Rough Differential Equations

In three linesBranched Neural Rough Differential Equations (B-NRDEs) extend NRDEs to capture Itô dynamics on manifolds. They use a Hopf-algebraic framework based on Grossman-Larson and Munthe-Kaas-Wright rooted trees, exactly preserving manifold constraints. Validated on rough Bergomi volatility, SO(3) dynamics forecasting, and SPD covariance matrices.

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