Abstract: A method for training a generative adversarial network, in particular a Wasserstein generative adversarial network. The generative adversarial network includes a generator and a discriminator, the generator and the discriminator being artificial neuronal networks. The method includes training the discriminator. In the step of training the discriminator, a parameter of the discriminator is adapted as a function of a loss function, the loss function including a term that represents the violation of the Lipschitz condition as a function of a first input datum and a second input datum and as a function of a first output of the discriminator when processing the first input datum and a second output of the discriminator when processing the second input datum, the second input datum being created starting from the first input datum by applying the method of the virtual adversarial training.

Abstract: A method for training an artificial neural network, in particular a Bayesian neural network, in particular of a recurrent artificial neural network, in particular a VRNN, to predict future sequential time series in time steps as a function of past sequential time series to control an engineering system, using training data sets, a step being provided of adapting a parameter of the artificial neural network as a function of a loss function, the loss function comprising a first term, which includes an estimate of a lower bound (ELBO) of the distances between a prior probability distribution (prior) over at least one latent variable and a posterior probability distribution (inference) over the at least one latent variable, wherein the prior probability distribution (prior) is independent of future sequential time series.

Abstract: A method for training a generative adversarial network, in particular a Wasserstein generative adversarial network. The generative adversarial network includes a generator and a discriminator, the generator and the discriminator being artificial neuronal networks. The method includes training the discriminator. In the step of training the discriminator, a parameter of the discriminator is adapted as a function of a loss function, the loss function including a term that represents the violation of the Lipschitz condition as a function of a first input datum and a second input datum and as a function of a first output of the discriminator when processing the first input datum and a second output of the discriminator when processing the second input datum, the second input datum being created starting from the first input datum by applying the method of the virtual adversarial training.