# PIGPVAE: Physics-Informed Gaussian Process Variational Autoencoders

arXiv: https://arxiv.org/abs/2505.19320 · HTML: https://mlsanity.com/paper/2505.19320/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 25 May 2025.

## Builds on (most cited first, 16 of 16)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [Vector Quantized Time Series Generation with a Bidirectional Prior Model](https://mlsanity.com/paper/2303.04743/) (2023)
- [TSGBench: Time Series Generation Benchmark](https://mlsanity.com/paper/2309.03755/) (2023)
- [Scalable Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2010.13472/) (2020)
- [TSGM: A Flexible Framework for Generative Modeling of Synthetic Time Series](https://mlsanity.com/paper/2305.11567/) (2023)
- [Markovian Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2207.05543/) (2022)
- [Bayesian Calibration of Imperfect Computer Models using Physics-Informed Priors](https://mlsanity.com/paper/2201.06463/) (2022)
- [Fully Bayesian Autoencoders with Latent Sparse Gaussian Processes](https://mlsanity.com/paper/2302.04534/) (2023)
- [Learning Physics between Digital Twins with Low-Fidelity Models and Physics-Informed Gaussian Processes](https://mlsanity.com/paper/2206.08201/) (2022)

## Abstract (arXiv)

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 to enhance performance. Specifically, we extend the VAE architecture by incorporating physical models in the generative process, enabling it to capture underlying dynamics more effectively. While physical models provide valuable insights, they struggle to capture complex temporal dependencies present in real-world data. To bridge this gap, we introduce a discrepancy term to account for unmodeled dynamics, represented within a latent Gaussian Process VAE (GPVAE). Furthermore, we apply regularization to ensure the generated data aligns closely with observed data, enhancing both the diversity and accuracy of the synthetic samples. The proposed method is applied to indoor temperature data, achieving state-of-the-art performance. Additionally, we demonstrate that PIGPVAE can produce realistic samples beyond the observed distribution, highlighting its robustness and usefulness under distribution shifts.