Just a Single-Layer CNN for Stochastic Modeling: A Discriminator-Free Approach

The advent of machine learning (ML) has significantly transformed hydrology, particularly in the simulation of hydrological flows. However, ML techniques have not been employed to the same extent in stochastic hydrology. In applied sciences, the most common ML-based approach for developing stochastic simulation schemes is the use of generative adversarial networks (GANs), which consist of two sub-models, that is, a generator and a discriminator. Despite their potential, GANs have notable limitations, including high architectural complexity and the requirement to divide observed time series into shorter segments to generate sufficient training examples. This segmentation reduces the effective length of the series, limiting the model’s ability to capture and reproduce long-term dependencies. In this study, we propose a simpler stochastic scheme based on a single convolutional neural network (CNN) used as a generator, replacing the discriminator component of the GAN with a specifically designed cost function. The model is applied to a case study involving measured flow velocity time series and evaluated against traditional stochastic schemes designed for both Markovian and Hurst–Kolmogorov processes. Results show that the CNN-based approach not only offers computational simplicity but also outperforms conventional methods in preserving key statistical characteristics of the observed data.