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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.<\/jats:p>","DOI":"10.1007\/s10489-025-06776-9","type":"journal-article","created":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T13:07:45Z","timestamp":1753708065000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["PIGPVAE: physics-informed gaussian process variational autoencoders"],"prefix":"10.1007","volume":"55","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3799-7708","authenticated-orcid":false,"given":"Michail","family":"Spitieris","sequence":"first","affiliation":[]},{"given":"Massimiliano","family":"Ruocco","sequence":"additional","affiliation":[]},{"given":"Abdulmajid","family":"Murad","sequence":"additional","affiliation":[]},{"given":"Alessandro","family":"Nocente","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,28]]},"reference":[{"key":"6776_CR1","doi-asserted-by":"crossref","unstructured":"Rombach R, Blattmann A, Lorenz D, Esser P, Ommer B (2022) High-resolution image synthesis with latent diffusion models. 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