arXiv Machine Learning July 14, 2026 By Munawar Ali, Qi Feng, Charlie Pyle, George Xu

Branched Signature Kernel Solvers for ODEs with rough Single-Trajectory signals

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arXiv:2605. 25826v2 Announce Type: replace-cross Abstract: We develop a branched signature kernel solver for linear and nonlinear ordinary differential equations driven by a \emph{single observed trajectory} of a possibly rough forcing signal--a setting common within earthquake engineering, finance, biology, and structural health monitoring, where only one forcing realization is available, and the solver must respect the underlying physical law without an ensemble of realizations.

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