Regression loss-assisted conditional style generative adversarial network for virtual sample generation with small data in soft sensing

Existing methods that extend virtual sample pools to address small sample problem caused by sample atypicality and uneven distribution often overlook data sparsity and inverse sample generation challenges, which limits the accuracy of subsequent modeling. To address above problem, we propose a novel regression-assisted conditional style generative adversarial network (RAC-StyleGAN). The proposed method leverages the strengths of StyleGAN in latent space mapping to enhance data diversity and granularity, while incorporating regression-assisted conditions to improve modeling performance. Specifically, RAC-StyleGAN utilizes kernel density estimation and radial basis function interpolation to ensure that the generated output variables are uniformly distributed. Based on the principle of inverse transformation, the interpolated output variables are then used as conditional inputs for the StyleGAN model, generating virtual input variables that faithfully reflect the marginal distribution of the original data. Furthermore, to preserve the complex nonlinear relationships between input and output variables, RAC-StyleGAN integrates a regression loss strategy based on empirical risk minimization into the StyleGAN framework. By fine-tuning the generation process, the soft-sensing model effectively captures the nonlinear mapping between inputs and outputs. Experimental validations on synthetic nonlinear functions, University of California Irvine machine learning (UCI) datasets, and a real-world purified terephthalic acid (PTA) solvent system demonstrate that RAC-StyleGAN effectively generates high-quality virtual samples, significantly enhancing the modeling performance.