Mode collapse remains the primary unresolved challenge within generative adversarial networks (GANs). In this work, we introduce an innovative approach that supplements the discriminator by additionally enforcing the similarity between the generated and real distributions. We implement a one-sample test on the generated samples and employ the resulting test statistic to penalize deviations from the real distribution. Our method encompasses a practical strategy to estimate distributions, compute the test statistic via a differentiable function, and seamlessly incorporate test outcomes into the training objective. Crucially, our approach preserves the convergence and theoretical integrity of GANs, as the introduced constraint represents a requisite condition for optimizing the generator training objective. Notably, our method circumvents reliance on regularization or network modules, enhancing compatibility and facilitating its practical application. Empirical evaluations on diverse public datasets validate the efficacy of our proposed approach.

Based on particle swarm optimization (PSO), a new exponential time delay fraction order grey prediction model is proposed in this paper. Firstly, the original data is preprocessed by fractional-order accumulation; on the basis of fractional-order accumulation, it is proved that the initial value of the original sequence satisfies the fixed point theorem. On the basis of GM(1,1) model, a new model is established by adding exponential time delay term. The model is discretized by integral, the least square estimation of the linear parameters and the approximate time response equation are obtained. Finally, PSO is used to search the optimal parameters of the model and the experimental results are verified by Wilcoxon rank sum test. In order to test the good adaptability and strong prediction ability of the new model, two groups of data are verified for the production and consumption of oil and electricity in China. The results show that the new model has better prediction accuracy and adaptability than the other existing six grey models.