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

ArXi:2605.25826v1 Announce Type: cross 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 that arises naturally in earthquake engineering, finance, biology, and structural health monitoring, where the forcing is observed exactly once and the solver must respect the underlying physical law without re