Spatio-Temporal Forecasting

Multivariate ocean forecasting must exploit shared evolution in a coupled ocean system while adapting to the heterogeneous statistical and dynamical characteristics of different prediction variables and locations. Fully shared models may lack the flexibility to handle this heterogeneity, whereas fully independent models discard the common ocean context shared across variables. The key question is how to retain shared context in a unified model while allowing computation to specialize according to the prediction target and local state. We propose OceanMoE, a structured conditional sparse Mixture-of-Experts framework that combines sharing and specialization for multivariate ocean forecasting. OceanMoE fuses cross-variable information to construct target-specific local representations and uses them to perform content-conditioned sparse routing at each spatial location, with the number of active experts adapted to router confidence. In the decoder, routing is augmented with a learned geographic bias parameterized by spherical-harmonic spatial bases, while shared residual and seasonal pathways provide common cross-variable and month-dependent context. Experiments on long-horizon autoregressive ORAS5 forecasting show that OceanMoE lowers aggregate forecasting error in both evaluated settings and maintains lower geometric-mean normalized RMSE than the corresponding baselines over most later rollout months. Routing analyses further show that expert allocation varies with prediction targets and spatial locations. These results support structured conditional computation as a modeling strategy for balancing shared ocean context with adaptive specialization.

Multi-modal spatio-temporal forecasting (MM-STF) supports weather nowcasting, traffic prediction, and earth-system modeling by combining heterogeneous sources such as physical fields, satellite imagery, and in-situ sensors. Three obstacles persist: (i) modalities have different spatio-temporal sampling rates, forcing lossy interpolation onto a unified grid; (ii) modalities are frequently missing at deployment due to sensor outages or revisit gaps, while most methods train with full availability; and (iii) autoregressive decoders accumulate errors over long horizons, amplified by multi-modal conditioning. We propose AsyncCouple-Flow to address these issues jointly. A Modality-Aware Token Sparsification (MATS) module performs scale-aware tokenization and uses a shared importance scorer to select top-k tokens per timestep, producing equal-length sequences. An Asynchronous Cross-Modal Coupling Graph (ACCG) replaces fixed cross-attention with a learnable graph whose edges encode time offsets, semantic similarity, and modality-specific physical priors, enabling fusion under arbitrary asynchrony and missingness. A Flow-Matching Forecasting Head models multi-step prediction as a conditional ODE, trained with stochastic modality dropout and integrated jointly to avoid autoregressive drift. Experiments on ERA5+GOES+ISD weather forecasting and PEMS-BAY traffic prediction with multi-source side information show that AsyncCouple-Flow outperforms state-of-the-art baselines and remains robust with up to two missing modalities. The code will be released upon acceptance.

Statistical post-processing improves ensemble weather forecasts, but generating calibrated predictions at locations without observations remains challenging. This study compares statistical and machine-learning-based methods for post-processing ECMWF 2-m temperature and 10-m wind speed forecasts at observed and unobserved stations in Germany. We consider EMOS-based approaches, distributional regression networks, Transformers, and graph neural networks under both limited and extended predictor settings. For temperature, we also investigate linear forecast combinations and propose an altitude-aware linear pool (ALP). The results show that post-processing improves upon the raw ensemble in most settings, but no single method performs best across all variables, station groups, and evaluation metrics. The proposed ALP provides a small but significant improvement over the standard linear pool at unobserved locations.

Large language models (LLMs) have shown promise for spatio-temporal forecasting, but existing approaches often rely on regularly sampled token sequences and struggle with irregular observations because of temporal asynchrony, representation-space misalignment, and limited context windows. We propose LLMODE, a token-efficient framework for irregular spatio-temporal forecasting with a frozen LLM backbone. LLMODE first uses a graph-aware ODE encoder to reconstruct irregular graph observations as a continuous-time latent trajectory. A Fixed-Budget Perceiver Resampler then compresses this variable-length trajectory into a fixed number of dynamic memory tokens. In parallel, compact statistical descriptors are encoded and resampled into context memory tokens. A dual-source gated cross-attention module injects both memories into the frozen LLM, enabling controlled utilization of external spatio-temporal evidence. Experiments on three real-world urban datasets and two physical-dynamics benchmarks show competitive overall performance, with clearer advantages under sparse or dynamically complex irregular sampling. Additional evaluations on unseen urban regions further demonstrate strong zero-shot generalization without adaptation.

Data assimilation (DA) uses Bayesian inference to update the state of a numerical forecast model with observed data. In this study, we propose a fundamentally different, unified approach to atmospheric data assimilation. We use latent video flow-matching to sample temporally consistent trajectories from a prior trained using ERA5 reanalysis (69 variables over an 8-day window). We also use posterior sampling to assimilate real observation sources, such as those from the NOAA Integrated Global Radiosonde Archive and the Integrated Surface Database. Because the prior generates a continuous trajectory, it naturally propagates information between observed and unobserved frames. Therefore, we can perform various DA tasks, such as filtering and smoothing, simply by changing the observed frames. Moreover, we generate full-state ensemble forecasts directly from sparse observations, achieving performance competitive with state-of-the-art observation-to-forecast models.

Compound flooding in managed coastal systems is influenced by hydrological conditions and water-management activity observed across multiple monitoring stations. Current forecasting models can capture temporal dependencies with low average errors, but global error metrics may conceal poor reproduction of prolonged high-water plateaus that are relevant to flood early warning. Because hydrometeorological and operational signals are distributed across heterogeneous gages, single-site records do not fully represent high-water dynamics. Nevertheless, unconstrained fusion of cross-site signals can degrade the stability of local temporal forecasts. This work proposes an anchored forecasting framework that incorporates cross-site information through state- and lead-dependent bounded residual corrections. A multi-source regime representation constructed from hydrometeorological and operational observations adaptively calibrates inter-site relationships and correction scales, enabling targeted cross-site adjustment while preserving the local temporal forecast as a stable anchor. Beyond conventional global error statistics, we evaluate event-scale high-water characteristics through the temporal alignment of forecasted and observed high-water processes. Experiments demonstrate that selectively integrating multi-station dynamic conditions improves the prediction reliability of sustained high-water plateaus while maintaining high accuracy during routine hydrological conditions, supporting flood early warning and water-management decision support.

Short-term precipitation nowcasting is important for hydrometeorological early warning, especially when intense convective rainfall may trigger urban flooding, flash floods, and other high-impact hazards. A key challenge in warning-oriented nowcasting is that radar precipitation fields contain strongly coupled multi-scale structures, while forecast quality often degrades at later lead times, making it difficult to preserve intense precipitation cores and their spatial organization over the full warning-relevant horizon. To address this problem, we propose QWRF-Net, a quantum-wavelet framework with rectified flow for short-term precipitation nowcasting. The core idea is to improve the conditional representation of precipitation by explicitly decomposing latent features into wavelet sub-bands and then performing differentiated quantum-inspired modulation in the decomposed latent space, before generating future sequences through a rectified-flow-based non-autoregressive decoder. Experiments on the KNMI radar and SEVIR benchmarks under a unified evaluation protocol show that QWRF-Net achieves favorable overall performance, with relatively consistent gains at medium-to-high precipitation thresholds, on an extreme-event subset, and in preserving intense precipitation cores and fine-scale structures. Ablation results further indicate that wavelet-based scale disentanglement, differentiated sub-band modulation, and flow-based generation provide complementary benefits within the proposed framework. Overall, these results suggest that jointly enhancing multi-scale precipitation representation and stable multi-step generation is a promising direction for warning-oriented short-term precipitation nowcasting. The observed improvements may also provide a more useful precipitation basis for downstream hydrological and warning-related applications.

Emergency Departments (EDs) are critical access points in healthcare systems, yet they face persistent pressure from unpredictable patient demand, seasonal surges, and non-urgent visits. Effective ED planning requires forecasts at multiple decision-making levels: hospitals need local demand estimates for staffing and bed management, regions require forecasts to coordinate healthcare units, and national authorities need system-wide projections for capacity planning. However, most existing approaches forecast ED demand independently at a single level, ignoring the hierarchy linking hospitals, regions, and national systems. This can produce incoherent predictions, where hospital-level forecasts do not aggregate consistently to regional or national demand. We propose HierSTT, a hierarchical Transformer-based framework for coherent multi-level ED forecasting. HierSTT jointly predicts hospital, regional, and national level demand in a single end-to-end model. A Temporal Fusion Transformer captures national dynamics, while spatio-temporal Transformer encoder-decoder modules model regional and hospital demand conditioned on higher-level forecasts. A coherence-aware loss penalizes cross-level inconsistencies during training. We further introduce a nationwide Portuguese ED dataset covering 81 hospitals across 5 regional health administrations, with heterogeneous covariates at each level. Experiments show that HierSTT reduces average WAPE by 32% relative to the best non-hierarchical deep learning baseline and outperforms all classical hierarchical reconciliation methods, while producing near-coherent predictions across levels. Additional resources associated with this work are available at https://github.com/FilipaLino/HierSTT.

Camera-only 4D occupancy forecasting enables autonomous vehicles to predict future 3D semantic scenes solely from historical multi-view images, which is critical for driving safety. Even though current methods have achieved good performance, the strong spatial-temporal modeling between the input multi-view frames is still underexplored, which limits the performance of those methods in future 4D forecasting. To address this gap, we introduce a novel framework, InterOCF, for 4D occupancy forecasting that jointly models temporal dynamics in both 3D voxel-based representations and multi-view segmentation sequences, while explicitly incorporating feature interaction between the 2D and 3D branches. Our framework incorporates three core components: 1) A 3D Spatio-Temporal (3DST) module that learns volumetric dynamics from historical voxel states to predict future voxel states; 2) A 2D Spatio-Temporal (2DST) module employing an auxiliary multi-view temporal segmentation forecasting task to enhance temporal semantic dynamics; 3) A Spatio-Temporal Interaction Modeling (STIM) module that enables feature interaction between 2D and 3D representations. Experiments on the nuScenes, Lyft-Level5, and nuScenes-Occupancy datasets show that InterOCF consistently outperforms existing baseline approaches.

Federated learning has emerged as a promising paradigm for spatio-temporal forecasting (STF), enabling collaborative model training without sharing raw observations. Existing federated STF methods primarily regard cross-client heterogeneity as an optimization challenge and mitigate it through personalized approaches. However, such heterogeneity fundamentally stems from diverse \emph{environmental conditions}, and these methods capture environment-specific forecasting patterns, hardly generalizing under environmental shifts. Our key insight is that the environmental diversity across federated clients should be exploited, as they provide \emph{complementary observations of the same underlying spatio-temporal system}. Based on this insight, we propose \method, a novel federated de-confounding framework that \textbf{treats clients as distinct causal environments}. \method leverages the client heterogeneity as distributed environmental evidence and learns a global prototype codebook to capture shared environmental regimes. We further derive a theoretical federated de-confounding bound that is linearly controlled by the averaged confounding strength. Extensive experiments demonstrate that \method consistently outperforms federated baselines, while providing transferable, interpretable, and communication-efficient environmental representations.

Real-world traffic data exhibit heterogeneous spatial correlations and nonlinear temporal dynamics, posing substantial challenges for accurate spatio-temporal forecasting. Existing approaches have developed increasingly sophisticated graph, attention, and decomposition architectures, while the influence of the underlying nonlinear function approximator has received comparatively less attention. In this work, we propose STKAN, a spatio-temporal forecasting architecture that introduces Taylor-polynomial Kolmogorov--Arnold Network modules into spatial and temporal token mixing. STKAN first constructs high-level spatial representations through a learnable soft node-group assignment mechanism, applies group-wise spatial mixing, and subsequently models temporal dependencies over the compressed sequence. Spatial and temporal self-attention layers are further employed to capture long-range interactions. Experiments on five traffic forecasting benchmarks show that STKAN achieves competitive performance and performs better than the evaluated MLP-based variant in the tested settings. These results suggest that the design of nonlinear function approximators can serve as a useful complement to architectural design in spatio-temporal forecasting.

Global Station Weather Forecasting (GSWF) is pivotal for localized and extreme weather prediction over key regions. Despite efforts to exploit look-back windows, existing methods show limited accuracy gains and struggle with extreme events and error accumulation. These limitations stem from overreliance on short-term patterns, which are insufficient to capture chaotic weather dynamics, especially under partial observations. To address this problem, we propose a novel Triaxial State Space Model (TSSM) with a history-enhanced Temporal-VariableHistorical paradigm, which incorporates period-aligned historical weather data to compensate for long-term, large-scale periodic, and full-window weather patterns beyond the temporal lookback window. Specifically, TSSM stacks historical samples into period-aligned batches, where forecasting is causally supported by historical and current observations. Temporal, variable, and historical scanning are designed to capture axial temporal dependencies, variable correlations, and historical evolution. This structure is hierarchically shared to model seasonal to extreme events while alleviating misalignment across historical patterns. TSSM achieves SOTA performance on Weather-5K, the largest station weather dataset to date, with 10% and 61% gains in accuracy and extreme event metrics, and obtains 95% best or second-best results on human-involved datasets. Its advantages are more pronounced in long-horizon and iterative forecasting, reaching a 37.5% gain at 240h and up to 103.5% under a 48h times 5 iterative setting. Moreover, TSSM retains > 90% performance under up to 80% missing observations, compared with < 43% for baselines, demonstrating robustness and practical potential for reliable GSWF in global in-situ observation networks.

Reliable forecasting of several interrelated environmental variables - such as regional precipitation and temperature, or other correlated geophysical fields - across many locations calls for accurate predictions accompanied by trustworthy statements of their uncertainty. Modern deep-learning models forecast such variables accurately but usually report no uncertainty, and forcing them to output uncertainty through maximum likelihood tends to degrade their accuracy, especially when the variables are strongly correlated. Motivated by this tension, we develop TSCoNet, a two-stage convolutional-recurrent model coupled with a Gaussian copula that jointly forecasts multiple variables over space and time while quantifying predictive uncertainty. The method first learns accurate mean forecasts and then, holding the mean fixed, refines a shared representation to estimate the predictive variance, yielding calibrated prediction intervals after a standard recalibration, so that uncertainty is added without sacrificing point accuracy. We study the approach on simulated non-stationary spatial fields on the sphere and on a real dataset of monthly precipitation and temperature for fifty cities over 2000-2020. The model matches the accuracy of a strong deterministic forecaster while supplying calibrated prediction intervals that the deterministic model cannot, giving a single tool that provides both accurate point forecasts and reliable uncertainty for multivariate spatio-temporal data.

Accurate energy demand forecasting is essential for the reliable operation and planning of modern sustainable energy systems. Spatial-temporal graph neural networks (STGNNs) have recently achieved strong performance in point forecasting by jointly modeling temporal dynamics and relational dependencies across interconnected energy nodes. However, in real-world energy systems, accurate point forecasts alone are insufficient, as operators also require reliable uncertainty estimates to support risk-aware decision-making, grid stability, and operational planning under uncertainty. Conformal prediction provides a principled and model-agnostic framework for uncertainty quantification with statistical coverage guarantees, making it particularly attractive for safety-critical energy applications. However, existing conformal prediction approaches often fail to fully capture the complex spatial-temporal structure of energy systems. To address these limitations, we propose STOIC (Spatial-Temporal Graph Conformal Prediction with In-Context Learning), a novel framework that integrates graph-based forecasting with the zero-shot calibration capabilities of tabular foundation models. STOIC first generates point forecasts using an STGNN and subsequently reformulates spatial-temporal residuals into a tabular representation suitable for in-context learning. Leveraging a tabular foundation model, STOIC calibrates prediction intervals without task-specific retraining, effectively capturing both sequential and relational dependencies. We evaluate STOIC on five diverse benchmarks, including synthetic simulations as well as real-world electricity and district heating networks. Across all datasets, STOIC consistently outperforms existing conformal prediction baselines, delivering more reliable and robust uncertainty estimates for complex graph-structured energy time series.

In precipitation forecasting, not only accuracy but also temporal resolution is critical. However, increasing temporal resolution is constrained by observational limitations and the computational cost of dense discrete modeling. To overcome this limitation, we reformulate precipitation forecasting as a continuous-time dynamical system and propose RainODE, a framework that models precipitation evolution in latent space using a Neural ODE. This formulation enables derivative-consistent temporal dynamics and captures the dominant large-scale advective motion of precipitation systems. Nevertheless, a purely deterministic ODE struggles to represent non-advective intensity changes such as localized growth, decay, and sub-grid variability, often leading to over-smoothed predictions. To address this issue, we introduce a stochastic source modeling module based on a Brownian Bridge formulation, which refines residual intensity variations and restores fine-grained structures while preserving advective consistency. By combining deterministic continuous dynamics with stochastic refinement, RainODE enables arbitrary-time inference while maintaining sharp predictions. Experiments on SEVIR and the newly introduced Radar-based Precipitation Integrated Dataset (RAPID) demonstrate consistent improvements across multiple temporal intervals and precipitation regimes. The code is available at https://github.com/SeongYE/RainODE.

State-of-the-art medium-range AI weather models can outperform traditional Numerical Weather Prediction (NWP) but require massive training budgets. This restricts usage for under-resourced groups and severely limits fast model iteration. Here we develop Otter Weather, a highly efficient spatiotemporal forecasting model designed to democratise high-performance weather prediction with AI. Evaluated on ERA5 reanalysis data at 1.5° resolution using standard WeatherBench protocols, the Otter family significantly advances the skill-compute Pareto frontier. The deterministic version outperforms the best NWP baseline by 9.6% at a 24-hour lead time while requiring fewer than 3.5 A100-days for training. It provides a 2x efficiency gain over lightweight AI models and a 100-fold reduction in compute compared to resource-intensive frontier architectures. We extend these efficiency gains into probabilistic forecasting by training via the Continuous Ranked Probability Score (CRPS). Scaling to a larger architecture, Otter-XL achieves a 9.7% CRPS improvement over the IFS ENS baseline. This yields an almost two-fold increase in predictive skill over comparable lightweight models at similar compute budgets. Otter-XL also outperforms frontier architectures like GenCast by over 2%, while using an order of magnitude less compute. Finally, Otter is applied out-of-the-box to a complex acoustic scattering PDE task where it outperforms a state-of-the-art foundation modelling approach, suggesting that the advances made here might apply across a range of scientific domains.

Spatiotemporal systems comprise a collection of spatially distributed yet interdependent entities each generating unique dynamic signals. Highly sophisticated methods have been proposed in recent years delivering state-of-the-art (SOTA) forecasts but few have focused on interpretability. To address this, we propose the Future Decomposition Network (FDN), a novel forecast model capable of (a) providing interpretable predictions through classification (b) revealing latent activity patterns in the target time-series and (c) delivering forecasts competitive with SOTA methods at a fraction of their memory and runtime cost. We conduct comprehensive analyses on FDN for multiple datasets from hydrologic, traffic, and energy systems, demonstrating its improved accuracy and interpretability.

Accurate short-term PM$_{2.5}$ forecasting is important for public health protection, air-quality early warning, and urban environmental management. However, PM$_{2.5}$ variation is driven by multiple coupled factors, including stable periodic changes induced by human activities and meteorological regularity, station-specific short-term concentration evolution, and meteorology-driven pollutant dispersion among monitoring stations. Existing spatio-temporal forecasting methods may capture station relationships to some extent, but distance-only, correlation-based, or purely adaptive graphs are often insufficient to comprehensively represent these heterogeneous factors, especially wind-direction-dependent pollutant transport. To address this problem, we propose a Multi-View Geo-Wind Guided KAN model for PM$_{2.5}$ forecasting, named \textbf{MVG-KAN}, which models station-level PM$_{2.5}$ evolution from three complementary views: local periodic regularity, station-wise residual temporal dynamics, and meteorological-environment-guided spatial dispersion. Specifically, the periodic-residual forecasting backbone first separates stable daily and weekly patterns from non-periodic residual variations. A Geo-Wind Graph is constructed by combining geographic distance decay with wind-direction- and wind-speed-aware transport, providing a lightweight physically motivated directed spatial prior for residual propagation among stations. In addition, a temporal Kolmogorov-Arnold network (TKAN) residual head is then introduced to learn station-wise nonlinear autoregressive correction from de-periodized PM$_{2.5}$ residuals and historical multi-pollutant sequences, thereby enhancing the modeling of local residual inertia and pollutant co-variation.

Epidemic forecasting models typically rely on surveillance data reported over administrative regions, treating them as atomic units, thereby obscuring sub-regional spatial structure that shapes disease dynamics. We introduce a spatially structured multimodal epidemic forecasting setting that integrates region-level temporal surveillance data with spatially localized auxiliary signals that are misaligned in resolution and structure, reflecting realistic public health reporting constraints. Building on this formulation, we propose M-SPICE (Multimodal SPatIal Context for Epidemic Forecasting), a structure-aware spatiotemporal forecasting framework that performs joint reasoning over temporal disease dynamics and spatial context via attention-based multimodal fusion, allowing spatial signals to selectively condition temporal representations across forecast horizons. We evaluate our approach on real-world COVID-19, influenza, and influenza-like illness (ILI) forecasting tasks under realistic real-time evaluation protocols. Across all forecasting settings, our method consistently outperforms state-of-the-art multivariate time-series, multimodal, and epidemiological forecasting baselines while maintaining strong probabilistic forecasting performance. Finally, interpretability analyses reveal when, where, and how spatial signals are leveraged, highlighting settings in which purely temporal, region-aggregated models are most likely to fail.

Molecular dynamics (MD) simulation is computationally demanding, particularly for large-scale systems requiring long-term analysis. Accurate forecast of the outcomes of a MD simulation is not only an attractive scientific challenge but also has substantial practical value. In this work, we developed a data-driven framework, termed ASTEROID (Advanced Spatiotemporal TransformER fOr Inferring Dynamics), that can directly predict multi-step atomic coordinates, avoiding conventional iterative integration. For this purpose, our ASTEROID reformulates MD trajectories as high-dimensional spatiotemporal sequences and integrates the Spatiotemporal Information (STI) Transformation equation into a Transformer architecture. The core innovation of ASTEROID lies in its ability to model multiscale spatiotemporal dependencies. In particular, for spatial dependencies, a local-global self-attention mechanism captures both short- and long-range interactions. For temporal dependencies, an encoder-decoder structure integrates global context with autoregressive forecasting. ASTEROID was evaluated on several quantum-mechanics derived molecular datasets. Our results indicate that ASTEROID achieved not only a higher level of accuracy in multi-step prediction than existing methods on various benchmarks, but also significantly reduced computational cost of conventional MD simulation. Moreover, the model supports iterative multi-step forecasting over an extended time scale. This work establishes a robust and generalizable data-driven paradigm for accelerating MD simulations.

Forecasting particulate matter (PM10) requires both station-scale accuracy and continuous spatial fields, especially during severe dust storms. Chemical transport models (CTMs) provide gridded forecasts but retain local biases, whereas graph neural networks (GNNs) track monitoring sites well at short lead times but do not produce gridded outputs. Here we present OmniPM-Net, a Convolutional Conditional Neural Process (ConvCNP)-based fusion model that reconciles these two forecast types within a shared spatial representation. A terrain-aware Gaussian set convolution lifts irregular GNN station forecasts onto a regular grid, where a multi-scale Spatial Source Attention (SSA) module blends them with Copernicus Atmosphere Monitoring Service (CAMS) forecasts; a shared omni-query readout then decodes this representation into consistent PM10 predictions at either stations or grid cells over a 108 h horizon. Evaluated across 1,618 air-quality monitoring stations throughout China over the full year of 2024, OmniPM-Net matches the station-level accuracy of the stronger GNN baseline (mean absolute error 21.14 versus 22.00 ug/m3) and reduces the CAMS mean absolute error by 30%, while simultaneously delivering the gridded fields that the discrete GNN cannot. Its clearest gains are in the high-concentration tail, where the 90th-percentile MAE falls by 9% relative to the GNN and 25% relative to CAMS, and during dust episodes, where it improves categorical detection skill while tracking the evolving spatial trajectory.

Real-world spatio-temporal forecasting must handle irregular time points, spatially sparse observations, and the need for uncertainty quantification. This setting is often further compounded by nonlocal interactions (long-range spatial coupling). Modeling continuous-space, continuous-time nonlocal dynamics naturally leads to infinite-dimensional integro-differential equations (IDEs), making principled Bayesian inference intractable. We propose the NonLocal Bayesian Spatio-Temporal model (NLBST), a hierarchical Bayesian framework for continuous spatio-temporal fields that learns explicit nonlocal coupling while retaining tractable inference. NLBST represents the latent field via a coordinate-based spatial basis expansion and models the coefficient process with a continuous-time ODE whose learnable linear operator corresponds to a Galerkin reduction of a nonlocal IDE; a Neural ODE residual captures additional nonlinear dynamics. A linear-Gaussian observation model enables Kalman-style sequential updates under missing and irregular observations, while the spatial basis representation enables inductive prediction at unmeasured locations without retraining. Global parameters are learned via variational inference, and uncertainty is handled through a Bayesian hierarchy. Experiments on synthetic and real-world datasets demonstrate strong forecasting and spatial generalization with well-calibrated uncertainty, yielding substantial gains over baselines in strongly nonlocal and partially observed regimes.

Spatio-Temporal forecasting is crucial in diverse fields, such as transportation, climate, and energy. Urban spatio-temporal data exhibits temporal mirage: similar short-window inputs have divergent future trends, and vice versa. Existing spatio-temporal graph neural networks (STGNNs) cannot effectively identify such mirages. We argue that the core reason lies in the short-window inputs that have incomplete period observation, heterogeneous global spatial correlation, and cross-period superposition causality. To bridge this gap, we develop a novel Multi- Period Pattern Pre-training (MP3), a plug-and-play pre-training plugin for distinguishing temporal mirages. MP3 presents two core innovations: (1) The multi-period pattern learning is designed to learn multi-period patterns from long time series. Specifically, multi-period temporal modeling leverages edge convolution to identify different multi-period patterns. Multi-period spatial modeling uses a bottleneck project and a global memory bank to capture heterogeneous global spatial relations efficiently. Cross-period pattern interaction employs a causality-enhanced Transformer to capture dependencies across different period patterns. (2) This plugin can seamlessly integrate into existing STGNN backbones to strengthen their forecasting performance. The experiment on five STGNN baselines across five real-world datasets (including a large-scale dataset CA) verify the effectiveness, superior scalability and strong adaptability of MP3, which brings consistent and robust performance improvements across all evaluated baselines. On average, MP3 reduces the MAE 4.7% and the RMSE 5.0%. The code can be available at https://github.com/YAN-outlook/MP3.

Accurate oceanic forecasting is critical for climate monitoring and disaster early warning. However, ocean spatiotemporal forecasting encounters the double challenges of modeling complex dynamical systems and ensuring computational efficiency. We present Koopman Fourier Time-Differentiable (KFTD) Network, a time continuous twostage paradigm that decouples interpolation from prediction to achieve efficient and scalable spatiotemporal modeling. We map complex nonlinear dynamics into the Koopman linear space and exploit Fourier analysis to enable continuous time interpolation at arbitrary sub-steps. A lightweight residual network consumes the high fidelity intermediate states to yield the final forecast. Unlike diffusion models, KFTD eliminates multi step noise sampling and directly evolves the system in continuous time, yielding a 4 computational speedup. We further introduce a DPP Loss that supports arbitrary PDE constraints in an endtoend manner, breaking the physical consistency bottleneck of pure data-driven approaches. Empirical results on four ocean datasets confirm that our continuous time framework reduces MSE by an average of 5.6% (up to 12.7% for SST) and improves efficiency over MCVD by 76.25%.

Multi-Modality Spatio-Temporal Forecasting (MoSTF) extends traditional spatio-temporal forecasting by incorporating diverse traffic modalities. Despite significant recent strides in spatio-temporal modeling, existing approaches often fail to explicitly model the coupling relationships between different modality variables. Accurate MoSTF is challenging, as it requires modeling (1) temporal dynamic heterogeneity under exogenous influences and (2) heterogeneous spatial dependencies alongside complex cross-variable couplings. To address these challenges, we propose the Dual-Domain Spectral Filtering Network (DSFNet). Our framework employs dual-domain spectral filtering to capture heterogeneous spatial patterns and explicitly model the relationships between variables. Unlike graph-based message passing or dense attention over node-modality pairs, DSFNet factorizes space-modality interactions into feature-domain and spatial-domain spectral operators, enabling scalable modeling of nonlocal dependencies and cross-modality couplings. Furthermore, we introduce an external gating mechanism to adaptively regulate temporal dynamics under external influences. We validate our method through extensive experiments on five representative real-world traffic datasets. Compared with the second-best baselines, DSFNet reduces MAE by 3.21%-10.16% across these datasets. The results demonstrate that DSFNet significantly outperforms existing state-of-the-art baselines in accuracy while exhibiting efficiency and robustness.

Spatio-temporal graph-based models have typically been used to forecast new cases of infectious diseases such as COVID-19 and chickenpox outbreaks. However, the use of stochastic modelling into their learning process has been surprisingly under-investigated and rarely considered entire data sets of large countries. As a result, it is unknown whether these models would provide accurate forecasts in real-world disease spread scenarios. In this work, we propose a spatio-temporal stochastic graph-based architecture that integrates a stochastic formulation and uncertainty approximation process to forecast new infectious disease cases. We find that our approach can adapt to encode large and small population geographical networks within a single model architecture. Using two real-world data sets, COVID-19 in the US and chickenpox in Hungary, we report an enhanced effect of the proposed architecture across predictions of the 2022 first wave for COVID-19 in the US and comparative results of chickenpox waves during 2012-2014 in Hungary. By benchmarking with four spatio-temporal graph-based models, quantitative results show competitive overall weekly performance of the proposed approach on forecasting new cases for all 3,218 US counties and all 20 Hungary counties. The proposed approach can represent overall epidemic progression relative to baselines, though with a one-step delay; while exhibiting a reduced sensitivity to high-frequency and low-amplitude variability.

Recent physics foundation models claim general spatiotemporal forecasting ability, yet their evaluations often collapse performance into a single average score under a fixed training distribution. This makes it difficult to determine whether a model has learned generalizable physical dynamics or only performs well under particular settings. We construct a benchmark with 8 physical dynamics, 3 training-data mixtures, and 25 test regimes induced by dynamic-scale and initial-condition complexity shifts, covering in-distribution, distribution-shift, and out-of-distribution settings. We evaluate five physics foundation model architectures and four model variants per architecture (scratch and three pretrained sizes), resulting in 60,000 measurements. Our results show that current physics foundation models behave as conditional rather than universal generalists: their generality depends on the physical regime, temporal scale, initial-condition setting, pretraining, model size, and architecture. Improving the training data distribution only partially mitigates this limitation. Pretraining and scaling are also unable to reliably remove their ability biases. We argue that improving physics foundation models requires moving beyond scaling models or expanding data, toward learning mechanisms that better capture transferable physical knowledge across regimes, temporal scales, and distribution shifts.

As a core task in intelligent transportation systems, traffic forecasting plays a critical role in urban traffic management. Accurate traffic forecasting relies on modeling complex spatiotemporal dependencies, which is inherently challenging due to spatial heterogeneity in traffic systems.Despite significant progress, most existing methods are still limited to pairwise spatial dependency modeling, making it difficult to capture dynamic high-order interactions among nodes with similar traffic patterns. To address this issue, we propose PHGNet, a novel spatiotemporal forecasting framework based on prototype-guided hypergraph construction. At the core of PHGNet, a prototype learning mechanism is designed to adaptively assign pattern-similar nodes to hyperedges, thereby capturing high-order interactions with time-varying structures. To improve the reliability of dynamic hypergraph construction, we further develop a global-local node representation module to extract time-consistent features. For forecasting, iterative residual refinement and Temporal Query Attention are introduced to improve forecasting accuracy while supporting efficient parallel decoding. Extensive experiments on multiple real-world datasets demonstrate that PHGNet achieves superior predictive performance compared with state-of-the-art methods.

This work explores a dynamics-informed Temporal Fusion Transformer (TFT) as a data-driven surrogate for computationally intensive Earth system simulations. Focusing on multivariate time series describing global ocean transport, we demonstrate the surrogate's ability to forecast tip events across thousands of time steps. The data involve up to 21 non-stationary time series in addition to static covariates describing free parameters and initial conditions. Modifications to the architecture and objective function yield a surrogate that anticipates the timing of Atlantic and Pacific collapses to high fidelity and captures the stochastic uncertainty in transition timing across ensemble predictions. The learned surrogate achieves a 465x computational speedup over the numerical simulator while maintaining differentiability with respect to parameters and initial conditions.

Forecasting urban delivery demand becomes substantially more challenging when newly added service regions lack historical records. Existing spatiotemporal forecasters effectively model spatial dependence once sufficient node histories are available. Still, they remain parametric and therefore struggle to recover short-term operational dynamics in cold-start regions. Geospatial embeddings help identify where a region is and what function it serves, yet they do not directly reveal how a similar region behaves under a comparable temporal context. We propose Bridge, a retrieval-augmented spatiotemporal graph framework that combines an inductive contextual graph backbone with a time-aware memory of region-time windows. For each target region, Bridge retrieves future demand patterns from the memory using both regional context and recent dynamics, and refines the backbone forecast through a gated fusion mechanism. To align retrieval with forecasting utility, we further train the retriever with a future-aware objective that favors entries whose future trajectories best match the target. Experiments on four real-world delivery datasets show that Bridge consistently improves over competitive spatiotemporal baselines in both within-city cold-start and cross-city transfer with partial observations. The results show that retrieval augmentation provides a useful operational memory for cold-start urban demand forecasting when parametric graph generalization alone is insufficient.

Real-world time series come with text: metadata, descriptions, news, reports. Yet time series foundation models process numerical sequences in isolation, and the multimodal text-and-time-series models that attempt to bridge the two all adapt a pretrained language model post hoc, inheriting representations shaped without ever seeing temporal data. These models are also evaluated almost exclusively against other multimodal baselines, not against the strongest unimodal foundation models in either domain, leaving open whether joint training is needed at all. We present Chronicle, a compact 324M-parameter decoder-only transformer trained from scratch on natural language and time series within a single unified architecture. Both modalities share the same transformer blocks, attention mechanism, and residual stream; the bulk of pretraining uses unimodal batches so cross-modal capability emerges purely from shared parameters, with a short alignment stage that interleaves the two. To our knowledge, Chronicle is the first model jointly pretrained on text and time series from scratch, and the first multimodal model evaluated against dedicated foundation models in both domains. It matches Gemma-3-270M-PT on 19 NLU tasks, sets a new bar for frozen-embedding time series classification on 24 UCR/UEA datasets, and produces multimodal forecasts on Time-MMD that beat every supervised fusion baseline, all from a single backbone.

Spatiotemporal forecasting is critical for real-world applications like traffic management, yet capturing reliable interactions remains challenging under noisy and non-stationary conditions. Existing methods primarily rely on historical spatial priors, often failing to account for evolving temporal correlations and suffering from systematic errors. In this work, we propose a nested forecasting framework that couples future macro-level regional trends with micro-level historical observations, enabling top-down guidance from abstract future representations for fine-grained forecasting. Specifically, we employ a spectral clustering-based approach to construct semantically coherent regions, providing both theoretical and empirical evidence that this representation effectively filters systematic noise while preserving essential trends. Building on this, we develop a progressive coarse-to-fine predictor to integrate these representative features into the inference process. This enables the model to leverage trend predictions to anticipate dynamic anomalies, such as periodic offsets, in advance. Furthermore, extensive experiments on multiple high-dimensional datasets demonstrate that our method consistently outperforms state-of-the-art baselines, validating the effectiveness of future macro-guided nested forecasting.

Coupled spatiotemporal forecasting is important for predicting the future evolution of multiple interacting dynamical systems, such as in climate models. However, existing methods are severely constrained by the persistent bottleneck of compounding errors. In coupled systems, errors from each subsystem simulator propagate and amplify one another, a phenomenon we term Reciprocal Error Amplification, leading to a rapid collapse of long-range predictions. To address this challenge, we propose a universal framework called PnP-Corrector (Plug-and-Play Corrector). The core idea of our framework is to decouple the physical simulation from the error correction process: it freezes pre-trained physics simulation engines and exclusively trains a correction agent to proactively counteract the systematic biases emerging from the coupled system. Furthermore, we design an efficient predictive model architecture, DSLCast, to serve as the backbone of this framework. Extensive experiments demonstrate that our method significantly enhances the long-term stability and accuracy of coupled forecasting systems. For instance, in the challenging task of a 300-day global ocean-atmosphere coupled forecast, our PnP-Corrector framework reduces the prediction error of the baseline model by 28% and surpasses state-of-the-art models on several key metrics.

Scientific foundation models are expected to reuse representations under changes in dataset, acquisition protocol, and deployment domain, yet many sequence backbones treat scientific temporal structure as an unconstrained pattern to be fitted. We argue that this misses a central property of natural dynamical systems: neural and atmospheric time series are organized by interacting processes across multiple physical timescales, and failure to preserve this multiscale structure contributes to brittleness under distribution shift. We formalize this failure mode as temporal kernel mismatch, where a model fits in-distribution dynamics with an effective memory policy that is not anchored to the signal's physical timescales, leading to representation drift and degraded transfer. We propose Physics-Informed Multi-Scale Mamba (PIMSM), a state-space architecture that maps spectrum-estimated transition points between frequency regimes (knee frequencies) to scale-specific discretization parameters and anchors them to acquisition time units. On Human Connectome Project fMRI, PIMSM improves robustness and representation stability under severe temporal-context truncation, extreme low-resource transfer, and resting-state-to-task-state generalization. Without modality-specific adaptation, the same architecture also attains the lowest variable-wise MAE across all reported horizons and variables on Weather-5K held-out-station spatial out-of-distribution forecasting. These results support temporal-scale alignment as a practical inductive bias for scientific foundation models that must preserve structure, not only fit correlations, under deployment shift.

Subseasonal-to-seasonal (S2S) temperature forecasts, spanning several weeks to a few months, are critically needed in agriculture practice, energy planning, and extreme-weather induced risk management, yet their reliability varies substantially across seasons and regions. Forecast skill is often attributed primarily to lead time, but this perspective does not fully explain the spatiotemporal patterns of predictability. Here we show that S2S predictability is organized across interacting temporal components, spatial heterogeneity, and large-scale pattern coherence, and that this structure can be explicitly characterized and exploited. We develop a dual-scale learning framework that separates calendar-aligned historical climate context from lead-time matched recent weather evolution, combining them through spatially adaptive fusion to enable stable temperature forecasts across the 30 to 90-day window. The learned fusion weights reveal that the balance between these two temporal scales shifts systematically with season and geography: during winter, interannual context dominates over high latitudes and complex terrain where forecast is the most difficult, while summer predictions reflect a more balanced temporal contribution across the domain. This spatially explicit reorganization of predictability, rather than simple lead-time decay, emerges as the primary determinant of forecast skill within the subseasonal window. Topology-aware structural constraints further improve spatial coherence of predicted temperature fields, stabilizing large-scale pattern organization particularly over complex terrain. These results reframe S2S predictability as a structured, multi-scale phenomenon, providing a more interpretable foundation for improving forecast systems and informing their use in practice.

Accurate epidemic forecasting is crucial for public health response, resource allocation, and outbreak intervention, but remains difficult with sparse, noisy, and highly non-stationary data. Because epidemics unfold across interacting regions, spatiotemporal methods are natural candidates for improving forecasts. Despite growing interest in spatial information, no standardized benchmark exists, and current evaluations often use simple chronological train-test splits that do not reflect real-time forecasting practice. We address this gap with SpatialEpiBench, a challenging benchmark for spatiotemporal epidemic forecasting in realistic public-health settings. SpatialEpiBench includes 11 epidemic datasets with standardized rolling evaluations and outbreak-specific metrics. We evaluate adjacency-informed forecasting models with widely used epidemic priors that adapt general models to epidemiology, but find that most methods underperform a simple last-value baseline from 1 day to 1 month ahead, even during outbreaks and with these priors. We identify three major failure modes: (1) poor outbreak anticipation, (2) difficulty handling sparsity and noise, and (3) limited utility of common geographic adjacency for epidemiological spatial information. We release benchmark data, code, and instructions at https://github.com/Rachel-Lyu/SpatialEpiBench to support development of operationally useful epidemic forecasting models.

Accurate cloud workload forecasting is pivotal for efficient resource management but remains challenging as workloads are highly volatile and prone to sudden bursts. Although wavelets preserve temporal locality, rigid fixed bases struggle with complex patterns and isolated processing neglects critical spatial dependencies. To address this, we propose SWIFT, a pure convolutional framework designed for high-efficiency workload forecasting. We introduce a Learnable Cascaded Wavelet Path that reformulates the traditional fixed wavelet bases into adaptive convolutional operators, enabling precise, data-driven feature peeling. Complementing this, our Multivariate Interaction Module sequentially models inter-variable spatial and intra-variable feature interactions to stabilize and refine noisy workload states. Extensive experiments demonstrate that SWIFT achieves SOTA accuracy with linear O(L) complexity, reducing prediction error by up to 31.04% while cutting latency by 79.74%.

Urban air quality forecasting is challenging because pollutant concentrations are nonlinear, nonstationary, spatiotemporally dependent, and often affected by anomalous observations caused by traffic congestion, industrial emissions, and seasonal meteorological variability. This study proposes a Graph Convolutional Support Vector Regression (GraphSVR) framework for robust spatiotemporal forecasting of urban air pollution. The model combines graph convolutional learning to capture inter-station spatial dependence with support vector regression to model nonlinear temporal dynamics while reducing sensitivity to outlier observations. The proposed framework is evaluated using air quality records from 37 monitoring stations in Delhi and 18 stations in Mumbai, representing inland and coastal metropolitan environments in India. Forecasting performance is assessed across multiple horizons and compared with established temporal and spatiotemporal benchmarks. The results show that GraphSVR consistently improves predictive accuracy and maintains stable performance across seasons and outlier-prone pollution episodes. Statistical test further confirms the reliability of the proposed approach across the datasets. Furthermore, the conformal prediction approach is integrated with GraphSVR to generate calibrated prediction intervals, enhancing its practical value for uncertainty-aware air quality monitoring and public health decision-making.

Spatiotemporal forecasting in physical systems, such as large-scale traffic networks, requires modeling a dual dynamic: continuous macroscopic rhythms and discrete, unpredictable microscopic shocks. While Neural Ordinary Differential Equations (ODEs) excel at capturing smooth evolution, their inherent Lipschitz continuity constraints inevitably cause severe over-smoothing when confronting abrupt anomalies. Recent physics-informed methods attempt to bypass this by penalizing numerical integration errors to enforce manifold smoothness. However, we mathematically reveal that such rigid regularization inherently triggers gradient conflicts and ``attention collapse,'' stripping the model of its sensitivity to anomalies. To resolve this continuity-shock dilemma, we propose Local Truncation Error-Guided Neural ODEs (LTE-ODE). Rather than treating numerical error as a nuisance to be eliminated, we innovatively repurpose the Local Truncation Error (LTE) as an unsupervised forward inductive bias. By mapping the LTE into a dynamic spatial attention mask, our architecture gracefully preserves high-precision continuous ODE evolution in stable regions, while adaptively triggering a discrete compensation branch exclusively at shock points. Trained purely end-to-end without manifold penalties, LTE-ODE achieves state-of-the-art performance on multiple large-scale benchmarks, exhibiting exceptional robustness against highly non-linear fluctuations. Furthermore, our ablation on integration steps demonstrates high deployment flexibility, allowing the model to seamlessly adapt to varying hardware memory constraints in real-world applications.

Storm surge forecasting remains a critical challenge in mitigating the impacts of tropical cyclones on coastal regions, particularly given recent trends of rapid intensification and increasing nearshore storm activity. Traditional high fidelity numerical models such as ADCIRC, while robust, are often hindered by inevitable uncertainties arising from various sources. To address these challenges, this study introduces StormNet, a spatio-temporal graph neural network (GNN) designed for bias correction of storm surge forecasts. StormNet integrates graph convolutional (GCN) and graph attention (GAT) mechanisms with long short-term memory (LSTM) components to capture complex spatial and temporal dependencies among water-level gauge stations. The model was trained using historical hurricane data from the U.S. Gulf Coast and evaluated on Hurricane Idalia (2023). Results demonstrate that StormNet can effectively reduce the root mean square error (RMSE) in water-level predictions by more than 70% for 48-hour forecasts and above 50% for 72-hour forecasts, as well as outperform a sequential LSTM baseline, particularly for longer prediction horizons. The model also exhibits low training time, enhancing its applicability in real-time operational forecasting systems. Overall, StormNet provides a computationally efficient and physically meaningful framework for improving storm surge prediction accuracy and reliability during extreme weather events.

Distribution shift severely degrades the performance of deep forecasting models. While this issue is well-studied for individual time series, it remains a significant challenge in the spatio-temporal domain. Effective solutions like instance normalization and its variants can mitigate temporal shifts by standardizing statistics. However, distribution shift on a graph is far more complex, involving not only the drift of individual node series but also heterogeneity across the spatial network where different nodes exhibit distinct statistical properties. To tackle this problem, we propose Reversible Residual Normalization (RRN), a novel framework that performs spatially-aware invertible transformations to address distribution shift in both spatial and temporal dimensions. Our approach integrates graph convolutional operations within invertible residual blocks, enabling adaptive normalization that respects the underlying graph structure while maintaining reversibility. By combining Center Normalization with spectral-constrained graph neural networks, our method captures and normalizes complex Spatio-Temporal relationships in a data-driven manner. The bidirectional nature of our framework allows models to learn in a normalized latent space and recover original distributional properties through inverse transformation, offering a robust and model-agnostic solution for forecasting on dynamic spatio-temporal systems.

We present a theory-guided generalized Bayesian methodology for spatio-temporal raster data, which we use to train an ensemble of stochastic feed-forward neural networks with Gaussian-distributed weights. The methodology incorporates the dependence and causal structure of a spatio-temporal Ornstein-Uhlenbeck process into training and inference by enforcing constraints on the design of the data embedding and the related optimization routine. In inference mode, the networks are employed to generate causal ensemble forecasts by applying different initial conditions at different horizons. We call this workflow MMAF-guided learning. Experiments conducted on both synthetic and real data demonstrate that our forecasts remain calibrated across multiple time horizons. Moreover, we show that on such data, shallow feed-forward architectures can achieve performance comparable to, and in some cases better than, convolutional or diffusion deep learning architectures used in probabilistic forecasting tasks.

Accurate and reliable forecasting of epidemic incidences is critical for public health preparedness, yet it remains a challenging task due to complex nonlinear temporal dependencies and heterogeneous spatial interactions. Often, point forecasts generated by spatiotemporal models are unreliable in assigning uncertainty to future epidemic events. Probabilistic forecasting of epidemics is therefore crucial for providing the best or worst-case scenarios rather than a simple, often inaccurate, point estimate. We present deep spatiotemporal engression methods to generate accurate and reliable probabilistic forecasts on low-frequency epidemic datasets. The proposed methods act as distributional lenses, and out-of-sample probabilistic forecasts are generated by sampling from the trained models. Our frameworks encapsulate lightweight deep generative architectures, wherein uncertainty is quantified endogenously, driven by a pre-additive noise component during model construction. We establish geometric ergodicity and asymptotic stationarity of the spatiotemporal engression processes under mild assumptions on the network weights and pre-additive noise process. Comprehensive evaluations across six epidemiological datasets over three forecast horizons demonstrate that the proposal consistently outperforms several temporal and spatiotemporal benchmarks in both point and probabilistic forecasting. Additionally, we explore the explainability of the proposal to enhance the models' practical application for informed, timely public health interventions.

Epidemiological forecasting from surveillance data is a hard problem and hybridizing mechanistic compartmental models with neural models is a natural direction. The mechanistic structure helps keep trajectories epidemiologically plausible, while neural components can capture non-stationary, data-adaptive effects. In practice, however, many seemingly straightforward couplings fail under partial observability and continually shifting transmission dynamics driven by behavior, waning immunity, seasonality, and interventions. We catalog these failure modes and show that robust performance requires making non-stationarity explicit: we extract and extrapolate multi-scale structure from the observed infection series and use it as an interpretable control signal for a controlled neural ODE coupled to an epidemiological model. Concretely, we decompose infections into trend, seasonal, and residual components and use these signals to drive continuous-time latent dynamics while jointly forecasting and inferring time-varying transmission, recovery, and immunity-loss rates. Across early outbreak and multi-wave regimes, our approach attains the lowest RMSE on all five datasets (27-70% reduction over the strongest baseline), achieves the best peak detection accuracy, and recovers time-varying epidemiological rates within ground-truth ranges, without relying on auxiliary covariates.

Short-term forecasting of vegetation dynamics is a key enabler for data-driven decision support in precision agriculture. Normalized Difference Vegetation Index (NDVI) forecasting from satellite observations, however, remains challenging due to sparse and irregular sampling caused by cloud masking, as well as the heterogeneous climatic conditions under which crops evolve. In this work, we propose a probabilistic forecasting framework for field-level NDVI prediction under sparse, irregular clear-sky acquisitions. The architecture separates the encoding of historical NDVI and meteorological observations from future exogenous covariates, fusing both representations for multi-step quantile prediction. To address irregular revisit patterns and horizon-dependent uncertainty, we introduce a temporal-distance weighted quantile loss that aligns the training objective with the effective forecasting horizon. In addition, we incorporate cumulative and extreme-weather feature engineering to capture delayed meteorological effects relevant to vegetation response. Experiments on European satellite data show that the proposed approach outperforms statistical, deep learning, and time-series baselines on both pointwise and probabilistic evaluation metrics. Ablation studies confirm that target history is the primary driver of performance, with meteorological covariates providing additional gains in the full multimodal setting. The code is available at https://github.com/arco-group/ndvi-forecasting.