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We consider Hamiltonian systems driven by multi-dimensional Gaussianprocesses in rough path sense, which include fractional Brownian motions withHurst parameter $H\in(1/4,1/2]$. We indicate that the phase flow preserves thesymplectic structure almost surely and this property could be inherited bysymplectic Runge--Kutta methods, which are implicit methods in general. If thevector fields belong to $Lip^{\gamma}$, we obtain the solvability ofRunge--Kutta methods and the pathwise convergence rates. For linear and skewsymmetric vector fields, we focus on the midpoint scheme to give correspondingresults. Numerical experiments verify our theoretical analysis.

Symplectic Runge-Kutta Methods for Hamiltonian Systems Driven by Gaussian Rough Paths