PIGPVAE: Physics-Informed Gaussian Process Variational Autoencoders

Recent advances in generative AI offer promising solutions for synthetic data generation but often rely on large datasets for effective training. To address this limitation, we propose a novel generative model that learns from limited data by incorporating physical constraints into a Variational Autoencoder (VAE) framework. Specifically, we extend VAE with a physics-based generator to capture underlying dynamics, while unmodeled dynamics are learned via a latent Gaussian Process VAE (GPVAE) component. We further introduce a regularization term that balances the physical model and data-driven discrepancy, promoting both interpretability and fidelity to real-world observations. We evaluate the proposed method on both real and simulated data, demonstrating that the Physics-Informed GPVAE (PIGPVAE) outperforms state-of-the-art methods in terms of diversity and accuracy of the generated samples, even under small-data conditions. Additionally, we demonstrate that PIGPVAE can produce realistic samples beyond the observed distribution, highlighting its robustness and usefulness under distribution shifts.