Reproduce “PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Weiheng Zhong, Hadi Meidani
A Physics-Informed Variational Auto-Encoder (PI-VAE) framework is developed for solving stochastic differential equations (SDEs) and their inverse problems, integrating physical laws into a VAE architecture. The method achieves improved training stability and up to 75% computational efficiency compared to physics-informed GANs, while accurately modeling high-dimensional stochastic processes and operating effectively with limited data.
Key insights
- Incorporating physical laws directly into the VAE's loss function allows the model to learn the underlying distribution of SDE solutions while respecting physical constraints.
- Using Maximum Mean Discrepancy (MMD) as a distance measure in the VAE loss improves performance and stability compared to Kullback-Leibler divergence, Mean Squared Error, or Sinkhorn distance for learning stochastic processes.
- The VAE architecture provides inherently more stable training and greater computational efficiency than GAN-based approaches for physics-informed learning of SDEs.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.