Precipitation nowcasting, a critical task for weather-sensitive applications, is highly challenging owing to the chaotic nature of atmospheric dynamics. Despite recent progress in deep learning, existing methods are limited in their capacity to model turbulent motions, one of the key drivers of precipitation evolution. Thus, we propose MoCast, the first work that incorporates turbulence knowledge to decompose turbulent motions into solvable components for precipitation nowcasting. Specifically, inspired by the continuity equation, MoCast introduces two core innovations: (1) a physics-guided motion module that learns turbulent motions from physically interpretable mean and fluctuating components based on Reynolds, Helmholtz, and Wavelet decomposition techniques, and (2) a motion-guided source-sink module that learns source-sink features considering the multi-scale impact from motions based on a mixture-of-experts architecture. Extensive experiments on three real-world datasets demonstrate that MoCast achieves the state-of-the-art performance. MoCast and its diffusion-based variant MoCast+ reduce CSI error by an average of 4.9% and 4.5% compared to the best deterministic and probabilistic baselines, respectively.

Accurate air quality forecasting is essential for public health and environmental sustainability, but remains challenging due to the complex pollutant dynamics. Existing deep learning methods often model pollutant dynamics as an instantaneous process, overlooking the intrinsic delays in pollutant propagation. Thus, we propose AirDDE, the first neural delay differential equation framework in this task that integrates delay modeling into a continuous-time pollutant evolution under physical guidance. Specifically, two novel components are introduced: (1) a memory-augmented attention module that retrieves globally and locally historical features, which can adaptively capture delay effects modulated by multifactor data; and (2) a physics-guided delay evolving function, grounded in the diffusion-advection equation, that models diffusion, delayed advection, and source/sink terms, which can capture delay-aware pollutant accumulation patterns with physical plausibility. Extensive experiments on three real-world datasets demonstrate that AirDDE achieves the state-of-the-art forecasting performance with an average MAE reduction of 8.79% over the best baselines.

In multivariate time series (MTS) forecasting, many deep learning based methods have been proposed for modeling dependencies at multiple spatial (inter-variate) or temporal (intra-variate) scales. However, existing methods may fail to model dependencies across multiple spatial-temporal scales (ST-scales, i.e., scales that jointly consider spatial and temporal scopes). In this work, we propose ST-Hyper to model the high-order dependencies across multiple ST-scales through adaptive hypergraph modeling. Specifically, we introduce a Spatial-Temporal Pyramid Modeling (STPM) module to extract features at multiple ST-scales. Furthermore, we introduce an Adaptive Hypergraph Modeling (AHM) module that learns a sparse hypergraph to capture robust high-order dependencies among features. In addition, we interact with these features through tri-phase hypergraph propagation, which can comprehensively capture multi-scale spatial-temporal dynamics. Experimental results on six real-world MTS datasets demonstrate that ST-Hyper achieves the state-of-the-art performance, outperforming the best baselines with an average MAE reduction of 3.8% and 6.8% for long-term and short-term forecasting, respectively. Code is available at https://anonymous.4open.science/ST-Hyper-83E7.

Multi-variate time series (MTS) forecasting is crucial for various applications. Existing methods have shown promising results owing to their strong ability to capture intra- and inter-variate dependencies. However, these methods often overlook lead-lag dependencies at multiple grouping scales, failing to capture hierarchical lead-lag effects in complex systems. To this end, we propose MillGNN, a novel graph neural network-based method that learns multiple grouping scale lead-lag dependencies for MTS forecasting, which can comprehensively capture lead-lag effects considering variate-wise and group-wise dynamics and decays. Specifically, MillGNN introduces two key innovations: (1) a scale-specific lead-lag graph learning module that integrates cross-correlation coefficients and dynamic decaying features derived from real-time inputs and time lags to learn lead-lag dependencies for each scale, which can model evolving lead-lag dependencies with statistical interpretability and data-driven flexibility; (2) a hierarchical lead-lag message passing module that passes lead-lag messages at multiple grouping scales in a structured way to simultaneously propagate intra- and inter-scale lead-lag effects, which can capture multi-scale lead-lag effects with a balance of comprehensiveness and efficiency. Experimental results on 11 datasets demonstrate the superiority of MillGNN for long-term and short-term MTS forecasting, compared with 16 state-of-the-art methods.

Weather forecasting is essential but remains computationally intensive and physically incomplete in traditional numerical weather prediction (NWP) methods.Deep learning (DL) models offer efficiency and accuracy but often ignore physical laws, limiting interpretability and generalization.We propose PhyDL-NWP, a physicsguided deep learning framework that integrates physical equations with latent force parameterization into data-driven models.It predicts weather variables from arbitrary spatiotemporal coordinates, computes physical terms via automatic differentiation, and uses a physics-informed loss to align predictions with governing dynamics.PhyDL-NWP enables resolution-free downscaling by modeling weather as a continuous function and fine-tunes pre-trained models with minimal overhead, achieving up to 170× faster inference with only 55K parameters.Experiments show that PhyDL-NWP improves both forecasting performance and physical consistency.

Although transformer-based methods have achieved great success in multi-scale temporal pattern interaction modeling, two key challenges limit their further development: (1) Individual time points contain less semantic information, and leveraging attention to model pair-wise interactions may cause the information utilization bottleneck. (2) Multiple inherent temporal variations (e.g., rising, falling, and fluctuating) entangled in temporal patterns. To this end, we propose Adaptive Multi-Scale Hypergraph Transformer (Ada-MSHyper) for time series forecasting. Specifically, an adaptive hypergraph learning module is designed to provide foundations for modeling group-wise interactions, then a multi-scale interaction module is introduced to promote more comprehensive pattern interactions at different scales. In addition, a node and hyperedge constraint mechanism is introduced to cluster nodes with similar semantic information and differentiate the temporal variations within each scales. Extensive experiments on 11 real-world datasets demonstrate that Ada-MSHyper achieves state-of-the-art performance, reducing prediction errors by an average of 4.56%, 10.38%, and 4.97% in MSE for long-range, short-range, and ultra-long-range time series forecasting, respectively. Code is available at https://github.com/shangzongjiang/Ada-MSHyper.

With the increasingly serious air pollution, people are paying more and more attention to air quality. However, air quality information is not available for all regions, as the number of air quality monitoring stations in a city is limited. Existing air quality estimation methods only consider the multisource data of partial regions and separately estimate the air qualities of all regions. In this article, we propose a deep citywide multisource data fusion-based air quality estimation (FAIRY) method. FAIRY considers the citywide multisource data and estimates the air qualities of all regions at a time. Specifically, FAIRY constructs images from the citywide multisource data (i.e., meteorology, traffic, factory air pollutant emission, point of interest, and air quality) and uses SegNet to learn the multiresolution features from these images. The features with the same resolution are fused by the self-attention mechanism to provide multisource feature interactions. To get a complete air quality image with high resolution, FAIRY refines low-resolution fused features by employing high-resolution fused features through residual connections. In addition, the Tobler's first law of geography is used to constrain the air qualities of adjacent regions, which can fully use the air quality relevance of nearby regions. Extensive experimental results demonstrate that FAIRY achieves the state-of-the-art performance on the Hangzhou city dataset, outperforming the best baseline by 15.7% on MAE.

The problem of air pollution threatens public health. Air quality forecasting can provide the air quality index hours or even days later, which can help the public to prevent air pollution in advance. Previous works focus on citywide air quality forecasting and cannot solve nationwide city forecasting problems, whose difficulties lie in capturing the latent dependencies between geographically distant but highly correlated cities. In this article, we propose the group-aware graph neural network (GAGNN), a hierarchical model for nationwide city air quality forecasting. The model constructs a city graph and a city group graph to model the spatial and latent dependencies between cities, respectively. GAGNN introduces a differentiable grouping network to discover the latent dependencies among cities and generate city groups. Based on the generated city groups, a group correlation encoding module is introduced to learn the correlations between them, which can effectively capture the dependencies between city groups. After the graph construction, GAGNN implements message passing mechanism to model the dependencies between cities and city groups. The evaluation experiments on two real-world nationwide city air quality datasets, including the China dataset and the US dataset, indicate that our GAGNN outperforms existing forecasting models.

Traffic forecasting is an essential problem in urban planning and computing. The complex dynamic spatial-temporal dependencies among traffic objects (e.g., sensors and road segments) have been calling for highly flexible models; unfortunately, sophisticated models may suffer from poor robustness especially in capturing the trend of the time series (1st-order derivatives with time), leading to unrealistic forecasts. To address the challenge of balancing dynamics and robustness, we propose TrendGCN, a new scheme that extends the flexibility of GCNs and the distribution-preserving capacity of generative and adversarial loss for handling sequential data with inherent statistical correlations. On the one hand, our model simultaneously incorporates spatial (node-wise) embeddings and temporal (time-wise) embeddings to account for heterogeneous space-and-time convolutions; on the other hand, it uses GAN structure to systematically evaluate statistical consistencies between the real and the predicted time series in terms of both the temporal trending and the complex spatial-temporal dependencies. Compared with traditional approaches that handle step-wise predictive errors independently, our approach can produce more realistic and robust forecasts. Experiments on six benchmark traffic forecasting datasets and theoretical analysis both demonstrate the superiority and the state-of-the-art performance of TrendGCN. Source code is available at https://github.com/juyongjiang/TrendGCN.

Multivariate time series (MTS) forecasting plays an important role in the automation and optimization of intelligent applications. It is a challenging task, as we need to consider both complex intra-variable dependencies and inter-variable dependencies. Existing works only learn temporal patterns with the help of single inter-variable dependencies. However, there are multi-scale temporal patterns in many real-world MTS. Single inter-variable dependencies make the model prefer to learn one type of prominent and shared temporal patterns. In this article, we propose a multi-scale adaptive graph neural network (MAGNN) to address the above issue. MAGNN exploits a multi-scale pyramid network to preserve the underlying temporal dependencies at different time scales. Since the inter-variable dependencies may be different under distinct time scales, an adaptive graph learning module is designed to infer the scale-specific inter-variable dependencies without pre-defined priors. Given the multi-scale feature representations and scale-specific inter-variable dependencies, a multi-scale temporal graph neural network is introduced to jointly model intra-variable dependencies and inter-variable dependencies. After that, we develop a scale-wise fusion module to effectively promote the collaboration across different time scales, and automatically capture the importance of contributed temporal patterns. Experiments on six real-world datasets demonstrate that MAGNN outperforms the state-of-the-art methods across various settings.