Abstract: A computer-implementable method generates scenario trees for optimal control of systems on the basis of only stochastically describable influencing values. The scenario tree generated describes a recursive decision process, with flexible decision time points, which stably approximates the underlying stochastic processes. A large number of scenarios are generated recursively from the temporally successive branching points of the scenario structure up to the next decision time point and reduced on the basis of a suitable distance dimension. For the theoretically provable achievement of the distribution, a Fortet-Mourier metric and if appropriate a filtration distance should be taken into account for clustering the partial scenarios. The (multidimensional) values at the end of the resulting reduced scenarios result in new branching points.

Abstract: Method of training an artificial neural network, comprising at least one layer with input neurons and one output layer with output neurons which are adapted differently from the input neurons.