$$y_m(t)=mu_m(t)+tau_m(x)+epsilon_m(t)$$
Where $m$ is the $m^{th}$ data or curve; $\mu_m$ is from functional regression; and $\tau_m$ is from Gaussian Process regression with mean 0 covariance matrix $k({\bf\theta})$.
Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York.