Advanced Generative Neural Networks for Predicting Complex 2D Physical Fields With Minimal Data: A VQVAE-Transformer Framework

Abstract This paper introduces a novel generative neural network system for predicting complex, structured 2D physical fields with a focus on achieving high accuracy, stability, and computational efficiency with very limited data. The proposed framework employs a Vector Quantized Variational Autoencoder (VQVAE) combined with a generative model that integrates a unique combination of transformer-based structures, inverted ResNet modules, and mobileSR architectures. This architecture does not exist in its current form and has been specifically optimized for the challenges of turbomachinery applications, where data availability is often limited to less than 100 samples. The system addresses this challenge by minimizing overfitting while maintaining robustness, demonstrating its potential for future use in industrial design and optimization processes. The capabilities of the proposed system are evaluated through two different case studies: a high-temperature heat pump radial compressor, which is the second stage in a three-stage compression system for superheated steam, and the first stage of a three-stage axial compressor used in the military sector, where the rotor geometry is varied. These case studies illustrate the model’s applicability across different technical domains, highlighting its potential to serve as a versatile tool in simulation-driven design processes. We analyze the model’s architecture and provide detailed insights into its ability to produce physically meaningful predictions, thereby demonstrating its utility in scenarios that traditionally rely on computationally intensive simulation models. While the model is capable of predicting 0D performance metrics such as efficiency—similar to traditional Kriging-based surrogate models—the authors argue that this should not be considered its primary application. The benefit of the model here will be very limited. Unlike traditional surrogate modelling, which reduces design variables to scalar values, this model directly predicts full 2D flow fields, providing significantly richer information. As a result, optimization processes should be rethought to take advantage of this additional level of detail. Rather than treating the model as a simple function approximator for efficiency or pressure loss, engineers can leverage its spatially resolved predictions to directly identify and address local flow phenomena. The fast 2D predictions allow for the identification of undesirable flow patterns that remain invisible in traditional 0D metrics.