Di-BiLPS: Neural PDE Solver for Extremely Sparse Observations
Researchers propose Di-BiLPS, a unified neural framework for solving forward and inverse partial differential equation (PDE) problems under extremely sparse observational data. The model combines a variational autoencoder for compressing high-dimensional inputs into a latent space, a latent diffusion module for uncertainty modeling, and contrastive learning for representation alignment. Operating entirely in this latent space, Di-BiLPS addresses limitations of classical numerical solvers and existing neural approaches, which degrade severely when data is extremely sparse. The framework aims to improve inference efficiency at high resolutions and maintain accuracy in sparse regimes. The work is published on arXiv under reference 2605.13790.
Key facts
- Di-BiLPS is a neural framework for forward and inverse PDE problems.
- It handles extremely sparse observational data.
- Combines variational autoencoder, latent diffusion, and contrastive learning.
- Operates entirely in a compact latent space.
- Addresses degradation of classical and neural solvers under sparse data.
- Published on arXiv with ID 2605.13790.
- Targets high-resolution inference efficiency.
- Aims to maintain accuracy in extremely sparse regimes.
Entities
Institutions
- arXiv