This paper deals with the optimization of the short-term production planning of a real cascade of run-of-river hydropower plants. Water inflows and electricity prices are subject to data uncertainty and they are modeled by a finite set of joint scenarios. The optimization problem is written with a two-stage stochastic dynamic mixed-integer linear programming formulation. This problem is solved by replacing the value function of the second stage with a surrogate model. We propose to evaluate the feasibility of fitting the surrogate model by supervised learning during a pre-processing step. The learning data set is constructed by Latin hypercube sampling after discretizing the functional inputs. The surrogate model is chosen among linear models and the dimension of the functional inputs is reduced by principal components analysis. Validation results for one simplified case study are encouraging. The methodology could however be improved to reduce the prediction errors and to be compatible with the time limit of the operational process.