用物理约束提升小数据下的生成效果，还能生成分布外的合理数据。
PIGPVAE: Physics-Informed Gaussian Process Variational Autoencoders
- 在变分自编码器中融合物理模型与高斯过程，建模复杂动态
- 在有限数据下实现领先性能，生成样本既多样又准确
- 适合缺乏数据但有物理规律的场景，如环境模拟与系统预测
近年来生成式AI为合成数据生成提供了新思路，但通常依赖大量数据训练。为突破此限制，我们提出一种新生成模型——物理信息高斯过程变分自编码器（PIGPVAE），通过引入物理约束，在数据有限条件下提升性能。具体而言，我们在变分自编码器架构中融入物理模型，增强对底层动态的捕捉能力；针对物理模型难以刻画真实数据中复杂时间依赖的问题，引入差异项以表征未建模动态，该部分由潜变量中的高斯过程建模（即GPVAE）。此外，通过正则化使生成数据更贴近观测数据，提高合成样本的多样性与准确性。所提方法应用于室内温度数据，达到当前最优表现。同时验证了PIGPVAE可生成超出观测分布的真实样本，展现出对分布偏移的鲁棒性与实用性。
原文摘要 · Abstract (English)
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.
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