Macro Forecasting

Long-horizon forecasting of time-dependent partial differential equations (PDEs) is critical for characterizing the sustained evolution of physical systems. While neural operators have emerged as efficient surrogates, they typically learn implicit finite-time transitions from discrete observations. When deployed autoregressively, such propagators often suffer from rapid error accumulation and dynamic drift. To address this, we propose a neural forecasting framework that reformulates PDE rollout as learning a Structured Spectral Propagator (SSP) in a propagation-oriented latent space. Following an analysis-propagation-synthesis design, our framework: (i) maps physical states into a shared, time-consistent spatial representation; (ii) projects this space into a compact propagation state to isolate recurrent dynamics from fine-grained spatial details, thereby decoupling reconstruction fidelity from rollout regularity; and (iii) evolves retained spectral modes using a frequency-conditioned linear backbone complemented by a nonlinear spectral closure to account for truncated interactions. This explicit structuring endows the propagator with a strong inductive bias for coherent modal evolution. Extensive experiments demonstrate that SSP significantly outperforms state-of-the-art baselines, reducing relative $L_2$ errors by up to 48.9\% and exhibiting improved stability in temporal extrapolation beyond the supervised horizon.

Existing soccer commentary models are often designed for pre-segmented clips or localized events. When deployed on untrimmed full-match videos with sliding windows, they can produce delayed, repeated, or poorly synchronized commentary. Recent streaming video-language models make low-latency full-match narration feasible, but they often favor general real-time descriptions rather than professional, event-grounded soccer commentary. They may describe nearby actions while failing to mention key events such as goals, cards, substitutions, and offsides correctly and on time. In this paper, we introduce **SoccerNarrate**, a data, model, and evaluation framework that bridges low-latency streaming narration with event-grounded professional soccer commentary. First, we construct **SoccerNarrate-Data**, a large-scale time-anchored dataset with word-level ASR alignment, quality filtering, and entity calibration. Second, we perform **macro-window preference alignment(MWPA)**, which aligns the model with complete event-level commentary semantics by comparing causal multi-step rollouts from the same streaming prefix while keeping second-level inference unchanged. We further use event-mismatched human commentaries as counterfactual negatives to emphasize event semantics over commentary style. Third, we introduce **SoccerNarrate-Eval**, an event-centric benchmark based on temporally constrained event entailment. Full-match experiments show that SoccerNarrate improves event coverage and event-aligned precision over strong offline and streaming baselines. Data and models will be released.

Accurate traffic prediction is essential for urban planning but remains challenging due to the irregular patterns caused by unexpected events. While Spatio-Temporal Graph Neural Networks (STGNNs) effectively model periodic data, they often struggle with these aperiodic fluctuations. To address this, we propose SIMBAD, which improves generalization on irregular patterns via two key mechanisms: 1) adaptive regulation of periodic signals to prioritize recent signals, and 2) dynamic spatial modeling that adjusts influence between connected nodes based on contextual relations. Built upon simple similarity metrics to adapt to aperiodic patterns, SIMBAD outperforms existing methods on real-world benchmark datasets, demonstrating superior performance in predicting unseen and irregular traffic events.

State-of-the-art machine learning weather prediction systems achieve strong upper-air forecast skill but degrade at longer lead times, with mesoscale structures progressively vanishing and ensemble forecasts becoming under-dispersive. While these limitations are often attributed to the training objective, we find that message-passing processors significantly contribute to this degradation. Repeated neighborhood aggregation at each autoregressive step acts as a smoothing operator that, over rollout steps, suppresses high-frequency information in latent space. This effect is particularly limiting in regional weather prediction, where fine-scale structures are already partially unresolved, further eroding mesoscale variability and hindering long-horizon forecasting. We propose GraphMet, a graph-based weather model motivated by Koopman theory that replaces stacked message-passing layers with a single linear Koopman operator step. GraphMet learns linear evolution in a spectral latent basis while preserving the encoder, decoder, and multi-scale icosahedral mesh structure. A two-term spectral objective jointly learns a stable Koopman basis and preserves latent geometry, enabling efficient long-range propagation without repeated nonlinear aggregation. Empirically, GraphMet reduces the 15-day activity and improves regional RMSE by 11-14% at 5km resolution, and enables efficient probabilistic forecasting with lower inference cost than state-of-the-art methods. Our code available at : https://anonymous.4open.science/w/GraphMet-54ED/.

Multivariate time-series forecasting requires reliable cross-series interaction, yet many attention- and mixing-based models couple heterogeneous variables without explicit entry-stage alignment. Such uncalibrated early interaction can lead to poorly conditioned optimization and degraded generalization when cross-series statistics drift. We propose First-layer Statistical Calibration (FISC), a simple framework that imposes statistical calibration constraints only on the first cross-series coupling layer while leaving deeper coupling layers learnable without repeated calibration. FISC estimates training-set cross-series statistics, converts them into a statistical affinity matrix, and convexly fuses this matrix with learnable coupling parameters. A row-wise simplex projection then yields a nonnegative row-stochastic mixing operator, providing bounded and interpretable entry-layer interaction. By restricting calibration to the first layer, FISC calibrates the entrance interaction without repeatedly constraining deeper feature transformations. To reduce temporal redundancy, FISC further combines a time-domain branch with a data-adaptive orthogonal-domain branch derived from training-time temporal statistics. Experiments on standard long- and short-term forecasting benchmarks show that FISC improves forecasting accuracy while maintaining favorable efficiency. Ablations and non-stationarity analyses further show that first-layer-only calibration consistently outperforms no calibration, last-layer calibration, and all-layer calibration, supporting a simple principle for robust cross-series learning: constrain the entrance interaction with training-set statistics, while letting deeper representations remain data-adaptive.

The quadratic attention cost of Vision Transformers (ViTs) forces a sharp compromise between discretization and rollout horizon, and binds tightest in the fine-scale PDE regime where shocks, reaction fronts, and material interfaces occupy a small, time-varying fraction of the domain. Further, conventional neural surrogates do not adapt to localized features dynamically. We propose WAMRViT, a ViT that tokenizes its input as a balanced quadtree under a wavelet-inspired refinement criterion, encodes position and refinement level jointly via a 3D rotary positional embedding with a soft level axis, and regrids in cell space at inference to remain stable over long rollouts. A multi-scale variant additionally keeps each leaf at its native source resolution and defers the per-level resolution differential to the model. Unlike prior adaptive-tokenization work, the tokenizer imposes no a priori token count; we evaluate under fully adaptive topology over long autoregressive rollouts; and WAMRViT is the first machine-learning surrogate to natively tokenize multi-level Adaptive Mesh Refinement (AMR) data. We demonstrate that on uniform-grid datasets, WAMRViT exceeds a finest-patch uniform backbone on the region of interest while using a fraction of the tokens, with a structural interpolation cost on the global metric that the multi-scale variant closes at the initial rollout steps. On a complex AMR combustion problem whose extremely fine scale features uniform-grid baselines cannot represent natively and must project onto a coarser grid, WAMRViT operates directly on the adaptive cells and substantially reduces finest-level error at matched parameters. Code: https://anonymous.4open.science/r/wamrvit-review-74E1

Quantifying uncertainty in time series forecasting is particularly demanding because sequential data exhibit temporal dependence and are prone to distributional changes. Conformal inference has emerged as a powerful uncertainty quantification approach through the construction of prediction sets. Recent advances have introduced online conformal methods that adaptively adjust prediction thresholds through feedback mechanisms. However, the existing feedback mechanism typically relies solely on miscoverage indicators (actual feedback)—whether the true label falls within the interval at each time step—while overlooking the empirical prediction threshold (estimated feedback) that is derived from the oracle conformal method. In this paper, we propose $\textit{Dynamic Dual-feedback Conformal Inference}$ (DDCI), which incorporates a dual-feedback mechanism consisting of $\textit{actual feedback}$ and $\textit{estimated feedback}$. The former drives the primary adjustment of the intervals based on true observations, while the latter dampens excessive expansions or contractions by leveraging empirical thresholds from conformal inference during updates. By balancing these two signals, DDCI achieves more stable and narrower prediction intervals in sequential settings while adhering to the target coverage rate in practice.

Real-world time series typically exhibit non-uniform information density across temporal positions, frequency structures, and forecasting horizons: critical dynamics are concentrated in local segments, different frequency components carry different structural information, and different horizons require different modeling complexity. However, most existing methods still allocate computation approximately uniformly across these dimensions, leading to redundant computation in low-information regions and insufficient modeling of key patterns. To address this, we propose BucpTSF, an information-density-driven structured framework for time series forecasting. Specifically, BucpTSF reorganizes raw sequences into hierarchically heterogeneous multi-level token representations through information-density-aware temporal representation reorganization, captures key cross-token dependencies with low overhead via frequency-selective structured token interaction, and further introduces horizon-conditioned structured extrapolation to adaptively balance dynamic modeling and structural extrapolation bias for different horizons, thereby improving the accuracy and stability of long-term forecasting. Extensive experiments on real-world datasets show that BucpTSF consistently outperforms strong baselines under various forecasting settings, validating the effectiveness of information-density-driven non-uniform computation allocation for time series forecasting.

Accurate real-time forecasting of atmospheric pollutants is essential for reducing exposure risks and improving public health. Traditional numerical forecasting systems suffer from incomplete parameterizations, uncertain inputs, and high computational cost. Existing deep learning approaches improve efficiency, but often entangle meteorological and pollutant variables within unified forecasting frameworks, limiting flexibility and pollutant-specific representation learning. To address these challenges, we propose AirMPA, a decoupled autoregressive framework for meteorology-to-pollution forecasting. AirMPA predicts 13 atmospheric pollutants at 0.4$^\circ$ spatial resolution and 12-h temporal resolution using meteorological fields, emission priors, and historical pollutant concentrations. The model is built on an improved Swin-Transformer architecture with zonal release attention and dual-branch fusion, enabling more effective modeling of global transport continuity and heterogeneous pollutant dynamics. During training, AirMPA uses ERA5 reanalysis as meteorological forcing, while during inference it directly ingests forecast fields from external meteorological models, enabling stable autoregressive prediction up to 5 days ahead. Experiments show that AirMPA consistently outperforms Aurora and surpasses CAMS in approximately 90\% of pollutant--lead-time evaluation cases over the 5-day forecast horizon, while outperforming CAMS on all variables beyond 48 h. These results demonstrate the potential of decoupled meteorology-to-pollution forecasting for global air quality prediction.

Neural surrogate benchmarks for spatiotemporal PDEs are dominated by idealized test beds with periodic boundaries and synthetic dynamics. Architecture rankings established on these benchmarks do not transfer to real atmospheric chemistry, and standard regression metrics conceal the failure modes that determine operational utility. AQBench evaluates ten architectures across five model families on high-resolution WRF-Chem simulations of $PM_2.5$, $NO_2$, and $CO$ over the Indian subcontinent, against five operationally-grounded objectives: long-horizon stability, exceedance detection, extreme-episode bias, advection-diffusion residuals, and multi-pollutant forecasting. Three findings emerge. Spectral neural operators, the strongest family on canonical PDE benchmarks, rank in the bottom four on 168 hour RMSE here. Models that lead on aggregate regression underestimate during extreme pollution episodes and miss the majority of true exceedance events. Joint training on $PM_2.5$, $NO_2$, and $CO$ improves $PM_2.5$ accuracy across most architectures with no parameter increase, with Transolver gaining 21\% at 168th hour. The dataset, evaluation framework, and trained baselines are released.