We study linear rough partial differential equations in the setting of [Friz
and Hairer, Springer, 2014, Chapter 12]. More precisely, we consider a linear
parabolic partial differential equation driven by a deterministic rough path
W of H\"older regularity α with 1/3<α≤1/2. Based on a stochastic representation of the solution of the rough
partial differential equation, we propose a regression Monte Carlo algorithm
for spatio-temporal approximation of the solution. We provide a full
convergence analysis of the proposed approximation method which essentially
relies on the new bounds for the higher order derivatives of the solution in
space. Finally, a comprehensive simulation study showing the applicability of
the proposed algorithm is presented