Zhiwei Zhang, Wenxuan Yuan, Xiaoyuan Cheng, Pouria Behnoudfar, Chuanqi Chen, Charlotte Moser, Yuta Tarumi, Jin-Long Wu 等 13 位作者
Koopman representations describe nonlinear dynamics through linear evolution in a transformed space, offering an attractive framework for their linear simplicity and generality. Yet these advantages do not necessarily translate into improved performance in deep latent data assimilation (LDA). We systematically compare seven representative methods and structural baselines across five systems spanning approximately periodic to strongly chaotic dynamics and a broad range of state dimensions. We evaluate forecast and assimilation accuracy, physical state recovery, latent-trajectory behavior, and dynamical consistency, and assess Gaussian error assumptions, objective convexity, and uniqueness of analysis solutions. Our results reveal a trade-off between representational flexibility and optimization tractability. Linear evolution of the latent state can stabilize short-term forecasts but restrict expressiveness in strongly chaotic and high-dimensional systems, without consistently improving assimilation accuracy. Parameterized linear operators offer greater flexibility, yet their joint optimization with the encoder--decoder remains nonconvex. Methods with closed-form analysis updates generally perform better and exhibit greater robustness in our experiments, although matrix inversion remains a computational bottleneck. These findings show that the practical benefits of Koopman structure depend on both sufficient observational information and the choice of assimilation procedure.
Abhishek A. Sabnis, Mihai Mitrea, Lya Lugon, Karine Sartelet, Marc Bocquet, Xiaoyuan Cheng, Shupeng Zhu, Sibo Cheng
Full-field reconstruction of air pollution is essential for evaluating pollution exposure and supporting public health decision-making. However, the complex interactions among pollutants, hard-to-predict weather patterns, and limited monitoring station coverage make this a complex task. We apply deep learning techniques to provide fast and accurate reconstructions from sparse observations of four key pollutants: NO2, O3, PM2.5 and PM10. Models are trained on full-field simulation data and evaluated on real-world observations collected from 9 to 28 monitoring stations in the city of Paris. We introduce a diffusion-based generative framework for multi-pollutant reconstruction and benchmark its performance against deterministic deep learning models. Despite noisy observations and strong spatial variability, the models achieve high structural similarity on simulated validation data and produce realistic spatial patterns on real-world observations, as indicated by power-spectrum analysis. We introduce data augmentation methods that enable transfer to real-world observations without retraining, allowing the models to generalise beyond the training period. These findings highlight the potential of ML models for reliable real-world deployment in air pollution reconstruction tasks.