PDE求解在稀疏观测场景下一直是个难题，Di-BiLPS用潜空间扩散和对比学习解决了精度和效率的双重瓶颈。做科学计算或物理模拟的开发者，尤其是处理传感器数据稀疏的团队，值得关注这个新范式。
Di-BiLPS 是一种新型神经网络框架，专门解决在观测数据极度稀疏（低至3%）时偏微分方程（PDE）的正向和逆向问题。它结合了变分自编码器压缩高维输入、潜变量扩散模块处理不确定性，以及对比学习对齐表征，所有操作在紧凑的潜空间中进行，大幅提升推理效率。实验表明，在多个PDE基准上，Di-BiLPS在极稀疏输入下达到最先进性能，同时计算成本显著降低。此外，该框架支持零样本超分辨率，可在连续时空域进行预测。
Di-BiLPS: Denoising induced Bidirectional Latent-PDE-Solver under Sparse Observations
Partial differential equations (PDEs) are fundamental for modeling complex natural and physical phenomena. In many real-world applications, however, observational data are extremely sparse, which severely limits the applicability of both classical numerical solvers and existing neural approaches. While neural methods have shown promising results under moderately sparse observations, their inference efficiency at high resolutions is limited, and their accuracy degrades substantially in the extremely sparse regime. In this work, we propose the Di-BiLPS, a unified neural framework that effectively handle both forward and inverse PDE problems under extremely sparse observations. Di-BiLPS combines a variational autoencoder to compress high-dimensional inputs into a compact latent space, a latent diffusion module to model uncertainty, and contrastive learning to align representations. Operating entirely in this latent space, the framework achieves efficient inference while retaining flexible input-output mapping. In addition, we introduce a PDE-informed denoising algorithm based on a variance-preserving diffusion process, which further improves inference efficiency. Extensive experiments on multiple PDE benchmarks demonstrate that Di-BiLPS consistently achieves SOTA performance under extremely sparse inputs (as low as 3%), while substantially reducing computational cost. Moreover, Di-BiLPS enables zero-shot super-resolution, as it allows predictions over continuous spatial-temporal domains.