PIGPVAE: Physics-Informed Gaussian Process Variational Autoencoders

TL;DR

PIGPVAE is a physics-informed Gaussian process VAE that improves synthetic data generation from limited data by integrating physical models and discrepancy modeling, achieving state-of-the-art results in temperature data.

Contribution

It introduces a novel physics-informed VAE with Gaussian process latent modeling and discrepancy terms to better learn from limited data and handle complex dynamics.

Findings

Achieves state-of-the-art performance on indoor temperature data.

Generates realistic samples beyond observed data distribution.

Enhances data diversity and accuracy with physical constraints.

Abstract

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.