PIGPVAE: Physics-Informed Gaussian Process Variational Autoencoders

TL;DR

PIGPVAE addresses limited data in indoor temperature generation by fusing physics-informed decoding with a latent Gaussian Process discrepancy to capture unmodeled dynamics. The method merges a physics-based VAE (PIVAE) with a GPVAE-style discrepancy, adding a trainable regularization to keep the learned physics faithful to observations. On heating/cooling curves, PIGPVAE outperforms purely data-driven baselines and sustains realistic generation even under distribution shifts, demonstrating interpretability and robustness. This approach offers a scalable path for physics-aware synthetic data in HVAC planning and anomaly detection, particularly when data are scarce.

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.

Figures (13)

• Figure 1: Standard VAE
• Figure 2: GPVAE
• Figure 3: PIVAE
• Figure 4: PIGPVAE
• Figure 5: PIGPVAE model; Reconstructed cooling data. Left plot shows the original data and $\hat{\mathbf{x}}$ (full model) is the PIGPVAE model reconstructions which are a combination of the physical model a nd the learned discrepancies.