Hao Wu

Weiyan Wang, Xingjian Shi, Ruiqi Shu et al.

In practice, physical spatiotemporal forecasting can suffer from data scarcity, because collecting large-scale data is non-trivial, especially for extreme events. Hence, we propose \method{}, a novel probabilistic framework to realize iterative self-training with new self-ensemble strategies, achieving better physical consistency and generalization on extreme events. Following any base forecasting model, we can encode its deterministic outputs into a latent space and retrieve multiple codebook entries to generate probabilistic outputs. Then BeamVQ extends the beam search from discrete spaces to the continuous state spaces in this field. We can further employ domain-specific metrics (e.g., Critical Success Index for extreme events) to filter out the top-k candidates and develop the new self-ensemble strategy by combining the high-quality candidates. The self-ensemble can not only improve the inference quality and robustness but also iteratively augment the training datasets during continuous self-training. Consequently, BeamVQ realizes the exploration of rare but critical phenomena beyond the original dataset. Comprehensive experiments on different benchmarks and backbones show that BeamVQ consistently reduces forecasting MSE (up to 39%), enhancing extreme events detection and proving its effectiveness in handling data scarcity.

Huanshuo Dong, Hong Wang, Hao Wu et al.

Neural operators have demonstrated considerable effectiveness in accelerating the solution of time-dependent partial differential equations (PDEs) by directly learning governing physical laws from data. However, for PDEs governed by conservation laws(e.g., conservation of mass, energy, or matter), existing neural operators fail to satisfy conservation properties, which leads to degraded model performance and limited generalizability. Moreover, we observe that distinct PDE problems generally require different optimal neural network architectures. This finding underscores the inherent limitations of specialized models in generalizing across diverse problem domains. To address these limitations, we propose Exterior-Embedded Conservation Framework (ECF), a universal conserving framework that can be integrated with various data-driven neural operators to enforce conservation laws strictly in predictions. The framework consists of two key components: a conservation quantity encoder that extracts conserved quantities from input data, and a conservation quantity decoder that adjusts the neural operator's predictions using these quantities to ensure strict conservation compliance in the final output. Since our architecture enforces conservation laws, we theoretically prove that it enhances model performance. To validate the performance of our method, we conduct experiments on multiple conservation-law-constrained PDE scenarios, including adiabatic systems, shallow water equations, and the Allen-Cahn problem. These baselines demonstrate that our method effectively improves model accuracy while strictly enforcing conservation laws in the predictions.