B-NRDEs recast NRDE log-ODE steps via Grossman-Larson and Munthe-Kaas-Wright rooted trees to enable intrinsic Itô and manifold dynamics with a branched signature-kernel objective.
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Approximates manifold heat kernels via PINNs solving the heat equation to enable diffusion models on arbitrary manifolds including S2, SO(3), and SPD(n).
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Learning Manifold and It\^o Dynamics with Branched Neural Rough Differential Equations
B-NRDEs recast NRDE log-ODE steps via Grossman-Larson and Munthe-Kaas-Wright rooted trees to enable intrinsic Itô and manifold dynamics with a branched signature-kernel objective.
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Riemannian Diffusion Models on General Manifolds via Physics-Informed Neural Networks
Approximates manifold heat kernels via PINNs solving the heat equation to enable diffusion models on arbitrary manifolds including S2, SO(3), and SPD(n).