Enhanced Generative Adversarial Networks: A Hyperbolic Latent Space for Synthesizing High-Fidelity Raman Spectra of Minerals

The scarcity of high-quality data is a significant challenge for machine learning in several sciences. This work presents a novel and reproducible method for synthesizing realistic Raman spectra of minerals by leveraging a Wasserstein Generative Adversarial Network with a Gradient Penalty (WGAN-GP). While our physically-informed generator (https://zenodo.org/records/17213917) based on q-Gaussian functions successfully learned the fundamental structure of spectra, we faced the common GAN challenge of mode collapse and training instability, which limited the utility of our initial model. To overcome this, we tested a new hypothesis: integrating a hyperbolic latent space into the generator's architecture. Unlike a standard Euclidean space, this curved geometry is better suited for capturing the nested, hierarchical features of spectral data. Our experiments confirm that this innovation not only prevents mode collapse but also drastically accelerates training. We demonstrate that our hyperbolic model achieves excellent results in as few as 20 epochs, with critic scores, correlation, and MSE values far surpassing a standard model trained for a much longer period. This research highlights how combining scientific domain knowledge (hyperbolic geometry) with advanced AI models can lead to innovative and highly effective solutions for generating high-fidelity scientific data.