Weather Forecasting

Advanced deep learning-based approaches have been actively applied to forecast the spatiotemporal physical dynamics governed by partial differential equations (PDEs), which acts as a critical procedure in tackling many science and engineering problems. As real-world physical environments like PDE system parameters are always capricious, how to generalize across unseen out-of-distribution (OOD) forecasting scenarios using limited training data is of great importance. To bridge this barrier, existing methods focus on discovering domain-generalizable representations across various PDE dynamics trajectories. However, their zero-shot OOD generalization capability remains deficient, since extra test-time samples for domain-specific adaptation are still required. This is because the fundamental physical invariance in PDE dynamical systems are yet to be investigated or integrated. To this end, we first explicitly define a two-fold PDE invariance principle, which points out that ingredient operators and their composition relationships remain invariant across different domains and PDE system evolution. Next, to capture this two-fold PDE invariance, we propose a physics-guided invariant learning method termed iMOOE, featuring an Invariance-aligned Mixture Of Operator Expert architecture and a frequency-enriched invariant learning objective. Extensive experiments across simulated benchmarks and real-world applications validate iMOOE's superior in-distribution performance and zero-shot generalization capabilities on diverse OOD forecasting scenarios.

Time series forecasting has attracted significant attention in the field of AI. Previous works have revealed that the Channel-Independent (CI) strategy improves forecasting performance by modeling each channel individually, but it often suffers from poor generalization and overlooks meaningful inter-channel interactions. Conversely, Channel-Dependent (CD) strategies aggregate all channels, which may introduce irrelevant information and lead to oversmoothing. Despite recent progress, few existing methods offer the flexibility to adaptively balance CI and CD strategies in response to varying channel dependencies. To address this, we propose a generic plugin xCPD, that can adaptively model the channel-patch dependencies from the perspective of graph spectral decomposition. Specifically, xCPD first projects multivariate signals into the frequency domain using a shared graph Fourier basis, and groups patches into low-, mid-, and high-frequency bands based on their spectral energy responses. xCPD then applies a channel-adaptive routing mechanism that dynamically adjusts the degree of inter-channel interaction for each patch, enabling selective activation of frequency-specific experts. This facilitates fine-grained, input-aware modeling of smooth trends, local fluctuations, and abrupt transitions. xCPD can be seamlessly integrated on top of existing CI and CD forecasting models, consistently enhancing both accuracy and generalization across benchmarks.

Current methods for multivariate time series forecasting can be classified into channel-dependent and channel-independent models. Channel-dependent models learn cross-channel features but often overfit the channel ordering, which hampers adaptation when channels are added or reordered. Channel-independent models treat each channel in isolation to increase flexibility, yet this neglects inter-channel dependencies and limits performance. To address these limitations, we propose CPiRi, a channel permutation invariant (CPI) framework that infers cross-channel structure from data rather than memorizing a fixed ordering, enabling deployment in settings with structural and distributional co-drift without retraining. CPiRi couples spatio-temporal decoupling architecture with permutation-invariant regularization training strategy: a frozen pretrained temporal encoder extracts high-quality temporal features, a lightweight spatial module learns content-driven inter-channel relations, while a channel shuffling strategy enforces CPI during training. We further ground CPiRi in theory by analyzing permutation equivariance in multivariate time series forecasting. Experiments on multiple benchmarks show state-of-the-art results. CPiRi remains stable when channel orders are shuffled and exhibits strong inductive generalization to unseen channels even when trained on only half of the channels, while maintaining practical efficiency on large-scale datasets. The source code is released at https://github.com/JasonStraka/CPiRi.

We present a deep learning model for high-resolution probabilistic precipitation forecasting over an 8-hour horizon in Europe, overcoming the limitations of radar-only deep learning models with short forecast lead times. Our model efficiently integrates multiple data sources - including radar, satellite, and physics-based numerical weather prediction (NWP) - while capturing long-range interactions, resulting in accurate forecasts with robust uncertainty quantification through consistent probabilistic maps. Featuring a compact architecture, it enables more efficient training and faster inference than existing models. Extensive experiments demonstrate that our model surpasses current operational NWP systems, extrapolation-based methods, and deep-learning nowcasting models, setting a new standard for high-resolution precipitation forecasting in Europe, ensuring a balance between accuracy, interpretability, and computational efficiency.

Time series forecasting has long been dominated by advances in model architecture, with recent progress driven by deep learning and hybrid statistical techniques. However, as forecasting models approach diminishing returns in accuracy, a critical yet underexplored opportunity emerges: the strategic use of post-processing. In this paper, we address the last-mile gap in time-series forecasting, which is to improve accuracy and uncertainty without retraining or modifying a deployed backbone. We propose $\delta$-Adapter, a lightweight, architecture-agnostic way to boost deployed time series forecasters without retraining. $\delta$-Adapter learns tiny, bounded modules at two interfaces: input nudging (soft edits to covariates) and output residual correction. We provide local descent guarantees, $O(\delta)$ drift bounds, and compositional stability for combined adapters. Meanwhile, it can act as a feature selector by learning a sparse, horizon-aware mask over inputs to select important features, thereby improving interpretability. In addition, it can also be used as a distribution calibrator to measure uncertainty. Thus, we introduce a Quantile Calibrator and a Conformal Corrector that together deliver calibrated, personalized intervals with finite-sample coverage. Our experiments across diverse backbones and datasets show that $\delta$-Adapter improves accuracy and calibration with negligible compute and no interface changes.

Long-term time series forecasting (LTSF) plays a crucial role in fields such as energy management, finance, and traffic prediction. Transformer-based models have adopted patch-based strategies to capture long-range dependencies, but accurately modeling shape similarities across patches and variables remains challenging due to scale differences. To address this, we introduce patch-mean decoupling (PMD), which separates the trend and residual shape information by subtracting the mean of each patch, preserving the original structure and ensuring that the attention mechanism captures true shape similarities. Futhermore, to more effectively model long-range dependencies and capture cross-variable relationships, we propose Trend Restoration Attention (TRA) and Proximal Variable Attention (PVA). The former module reintegrates the decoupled trend from PMD while calculating attention output. And the latter focuses cross-variable attention on the most relevant, recent time segments to avoid overfitting on outdated correlations. Combining these components, we propose PMDformer, a model designed to effectively capture shape similarity in long-term forecasting scenarios. Extensive experiments indicate that PMDformer outperforms existing state-of-the-art methods in stability and accuracy across multiple LTSF benchmarks.

Score-based generative modeling through differential equations has driven breakthroughs in high-fidelity image synthesis, offering modular model design and efficient sampling. However, this success has not been widely translated to timeseries forecasting yet. This gap stems from the sequential nature of time series, in contrast to the unordered structure of images. Here, we extend the theoretical formulation used for images to explicitly address sequential structures. We propose a diffusion-based forecasting framework (TEDM) that adapts score estimation to temporal settings and elucidates its design space. Such a design allows empirical computation of noise and signal scaling directly from data, avoiding external schedules. Notably, this reduces sampling complexity to linear in the forecast horizon. Without elaborate preprocessing, TEDM sets new state-of-the-art results on multiple forecasting benchmarks. These results illustrate the growing potential of diffusion models beyond vision. TEDM generates low-latency forecasts using a lightweight architecture, making it ideal for real-time deployment.

Modeling the relationships among variables has become increasingly important, particularly in high-dimensional multivariate time series forecasting tasks. However, most existing methods primarily focus on capturing coarse-grained correlations between variables, overlooking a finer and more dynamic aspect: the variable interactions often manifest differently as time progresses. To address this limitation, we propose FACT, an Fine-grained Across-variable Convolution architecture for multivariate Time series forecasting that explicitly models fine-grained variable interactions from both the time and frequency domains. Technically, we introduce a depth-wise convolution block DConvBlock, which leverages a depth-wise convolution architecture with channel-specific kernels to model dynamic variable interactions at each granularity. To further enhance efficiency, we reconfigure the original one-dimensional variables into a two-dimensional space, reducing the variable distance and the required model layers. Then DConvBlock incorporates multi-dilated 2D convolutions with progressively increasing dilation rates, enabling the model to capture fine-grained and dynamic variable interactions while efficiently attaining a global reception field. Extensive experiments on twelve benchmark datasets demonstrate that FACT not only achieves state-of-the-art forecasting accuracy but also delivers substantial efficiency gains, significantly reducing both training time and memory consumption compared to attention mechanism. The code is available at https://anonymous.4open.science/r/FACT-MTSF.

Optical flow estimation is a fundamental computer vision task that predicts per-pixel displacements from consecutive images. Recent works attempt to exploit temporal cues to improve the estimation performance. However, their temporal modeling is restricted to short video sequences due to the unaffordable computational burden, thereby suffering from restricted temporal receptive fields. Moreover, their group-wise paradigm in one forward pass undermines inter-group information exchange, leading to modest performance improvement. To address these problems, we propose a novel multi-frame optical flow network based on an auto-regressive paradigm, named ARFlow. Unlike previous multi-frame methods, our method can be scalable to arbitrary-length videos with marginal computational overhead. Specifically, we design an Auto-regressive Flow Initialization (AFI) module and an Auto-regressive Multi-stride Flow Refinement (AMFR) module to forecast the next-frame flow based on multi-stride history observations. Our ARFlow achieves state-of-the-art performance, ranking 1st on both KITTI-2015 and Spring official benchmarks and 2nd on the MPI-Sintel (Final) benchmark among all open-sourced methods. Furthermore, due to the auto-regressive nature, our method can generalize to arbitrary video length with a constant GPU memory usage of 2.1GB.

We give a comprehensive theoretical analysis of transformers as time series pre- diction models, with a focus on MOIRAI (Woo et al., 2024). We study its ap- proximation and generalization capabilities. First, we demonstrate that there exist transformers that fit an autoregressive model on input univariate time series via gradient descent. We then analyze MOIRAI, one of the state-of-the-art multivariate time series prediction models capable of modeling arbitrary number of covariates. We prove that MOIRAI is capable of automatically fitting autoregressive models with an arbitrary number of covariates, offering insights into its design and em- pirical success. For generalization, we establish learning bounds for pretraining when the data satisfies Dobrushin’s condition. Experiments support our theoretical findings, highlighting the efficacy of using transformers for time series forecasting.

Flow Matching (FM) has recently emerged as a powerful approach for high-quality visual generation. However, their prohibitively slow inference due to a large number of denoising steps limits their potential use in real-time or interactive applications. Existing acceleration methods, like distillation, truncation, or consistency training, either degrade quality, incur costly retraining, or lack generalization. We propose FlowCast, a training-free speculative generation framework that accelerates inference by exploiting the fact that FM models are trained to preserve constant velocity. FlowCast speculates future velocity by extrapolating current velocity without incurring additional cost, and accepts it if it is within a mean-squared error threshold. This constant-velocity forecasting allows redundant steps in stable regions to be aggressively skipped while retaining precision in complex ones. FlowCast is a plug-and-play framework that integrates seamlessly with any FM model and requires no auxiliary networks. We also present a theoretical analysis and bound the worst-case deviation between speculative and full FM trajectories. Empirical evaluations demonstrate that FlowCast achieves $>2.5\times$ speedup in image generation, video generation, and editing tasks, outperforming existing baselines with no quality loss as compared to standard full generation.

Accurate forecasting of extreme weather events such as heavy rainfall or storms is critical for risk management and disaster mitigation. Although high-resolution radar observations have spurred extensive research on nowcasting models, precipitation nowcasting remains particularly challenging due to pronounced spatial locality, intricate fine-scale rainfall structures, and variability in forecasting horizons. While recent diffusion-based generative ensembles show promising results, they are computationally expensive and unsuitable for real-time applications. In contrast, deterministic models are computationally efficient but remain biased toward normal rainfall. Furthermore, the benchmark datasets commonly used in prior studies are themselves skewed--either dominated by ordinary rainfall events or restricted to extreme rainfall episodes--thereby hindering general applicability in real-world settings. In this paper, we propose exPreCast, an efficient deterministic framework for generating finely detailed radar forecasts, and introduce a newly constructed balanced radar dataset from the Korea Meteorological Administration (KMA), which encompasses both ordinary precipitation and extreme events. Our model integrates local spatiotemporal attention, a texture-preserving cubic dual upsampling decoder, and a temporal extractor to flexibly adjust forecasting horizons. Experiments on established benchmarks (SEVIR and MeteoNet) as well as on the balanced KMA dataset demonstrate that our approach achieves state-of-the-art performance, delivering accurate and reliable nowcasts across both normal and extreme rainfall regimes.

Time-series forecasting finds broad applications in real-world scenarios. Due to the dynamic nature of time series data, it is important for time-series forecasting models to handle potential distribution shifts over time. In this paper, we initially identify two types of distribution shifts in time series: concept drift and temporal shift. We acknowledge that while existing studies primarily focus on addressing temporal shift issues in time series forecasting, designing proper concept drift methods for time series forecasting has received comparatively less attention. Motivated by the need to address potential concept drift, while conventional concept drift methods via invariant learning face certain challenges in time-series forecasting, we propose a soft attention mechanism that finds invariant patterns from both lookback and horizon time series. Additionally, we emphasize the critical importance of mitigating temporal shifts as a preliminary to addressing concept drift. In this context, we introduce ShifTS, a method-agnostic framework designed to tackle temporal shift first and then concept drift within a unified approach. Extensive experiments demonstrate the efficacy of ShifTS in consistently enhancing the forecasting accuracy of agnostic models across multiple datasets, and outperforming existing concept drift, temporal shift, and combined baselines.

While many advances in time series models focus exclusively on numerical data, research on multimodal time series, particularly those involving contextual textual information, remains in its infancy. With recent progress in large language models and time series learning, we revisit the integration of paired texts with time series through the Platonic Representation Hypothesis, which posits that representations of different modalities converge to shared spaces. In this context, we identify that time-series-paired texts may naturally exhibit periodic properties that closely mirror those of the original time series. Building on this insight, we propose a novel framework, Texts as Time Series (TaTS), which considers the time-series-paired texts to be auxiliary variables of the time series. TaTS can be plugged into any existing numerical-only time series models and effectively enable them to handle time series data with paired texts. Through extensive experiments on both multimodal time series forecasting and imputation tasks across benchmark datasets with various existing time series models, we demonstrate that TaTS can enhance multimodal predictive performance without modifying model architectures.

Zero-shot time-series forecasting holds great promise, but is still in its infancy, hindered by limited and biased data corpora, leakage-prone evaluation, and privacy and licensing constraints. We propose the first practical univariate time-series simulation pipeline, which is simultaneously fast enough for on-the-fly data generation and enables notable zero-shot forecasting performance on M-Series and GiftEval benchmarks that capture trend/seasonality/intermittency patterns, typical of industrial forecasting applications across a variety of domains. Our simulator is based off of a seasonal autoregressive integrated moving average (SARIMA) as its core data source. Due to instability in the autoregressive component, naive SARIMA parameter sampling often leads to unusable paths. Instead, our simulator follows a three-step procedure: (1) we sample well-behaved trajectories from the system's characteristic polynomial stability region; (2) we introduce a superposition scheme that combines multiple paths into rich multi-seasonality traces; and (3) we add rate-based heavy-tailed noise models to capture burstiness and intermittency alongside seasonalities and trends. Orders of magnitude faster than kernel-based generators, our simulator enables training on circa 1B unique purely simulated series generated on the fly, after which well-established neural backbones exhibit strong zero-shot generalization, surpassing strong statistical forecasters and recent foundation baselines, while operating under strict zero-shot protocol. Notably, on GiftEval we observe a "student-beats-teacher" effect: models trained on our simulations exceed the forecasting accuracy of the generating processes (i.e. AutoARIMA), suggesting emergent generalization beyond the simulator's components.

Conformal prediction offers a powerful framework for building distribution-free prediction intervals for exchangeable data. Existing methods that extend conformal prediction to sequential data rely on fitting a relatively complex model to capture temporal dependencies. However, these methods can fail if the sample size is small and often require expensive retraining when the underlying data distribution changes. To overcome these limitations, we propose Reservoir Conformal Prediction (ResCP), a novel training-free conformal prediction method for time series. Our approach leverages the efficiency and representation learning capabilities of reservoir computing to dynamically reweight conformity scores. In particular, we compute similarity scores among reservoir states and use them to adaptively reweight the observed residuals at each step. With this approach, ResCP enables us to account for local temporal dynamics when modeling the error distribution without compromising computational scalability. We prove that, under reasonable assumptions, ResCP achieves asymptotic conditional coverage, and we empirically demonstrate its effectiveness across diverse forecasting tasks.

Training time-series forecast models requires aligning the conditional distribution of model forecasts with that of the label sequence. The standard direct forecast (DF) approach seeks to minimize the conditional negative log-likelihood of the label sequence, typically estimated using the mean squared error. However, this estimation proves to be biased in the presence of label autocorrelation. In this paper, we propose DistDF, which achieves alignment by alternatively minimizing a discrepancy between the conditional forecast and label distributions. Because conditional discrepancies are difficult to estimate from finite time-series observations, we introduce a newly proposed joint-distribution Wasserstein discrepancy for time-series forecasting, which provably upper bounds the conditional discrepancy of interest. This discrepancy admits tractable, differentiable estimation from empirical samples and integrates seamlessly with gradient-based training. Extensive experiments show that DistDF improves the performance diverse forecast models and achieves the state-of-the-art forecasting performance. Code is available at https://anonymous.4open.science/r/DistDF-F66B.

Most state-of-the-art probabilistic time series forecasting models rely on sampling to represent future uncertainty. However, this paradigm suffers from inherent limitations, such as lacking explicit probabilities, inadequate coverage, and high computational costs. In this work, we introduce **Probabilistic Scenarios**, an alternative paradigm designed to address the limitations of sampling. It operates by directly producing a finite set of {Scenario, Probability} pairs, thus avoiding Monte Carlo-like approximation. To validate this paradigm, we propose **TimePrism**, a simple model composed of only three parallel linear layers. Surprisingly, TimePrism achieves 9 out of 10 state-of-the-art results across five benchmark datasets on two metrics. The effectiveness of our paradigm comes from a fundamental reframing of the learning objective. Instead of modeling an entire continuous probability space, the model learns to represent a set of plausible scenarios and corresponding probabilities. Our work demonstrates the potential of the Probabilistic Scenarios paradigm, opening a promising research direction in forecasting beyond sampling.

Weather forecasting is a fundamental task in spatiotemporal data analysis, with broad applications across a wide range of domains. Existing data-driven forecasting methods typically model atmospheric dynamics over a fixed short time interval, e.g., 6 hours, and rely on naive autoregression-based rollout for long-term forecastsing, e.g., 5 days. However, this paradigm suffers from two key limitations: (1) it often inadequately models the spatial and multi-scale temporal dependencies inherent in global weather systems, and (2) the rollout strategy struggles to balance error accumulation with the capture of fine-grained atmospheric variations. In this study, we propose ARROW, an Adaptive-Rollout Multi-scale temporal Routing method for Global Weather Forecasting. To contend with the first limitation, we construct a multi-interval forecasting model that forecasts weather across different time intervals. Within the model, the Shared-Private Mixture-of-Experts captures both shared patterns and specific characteristics of atmospheric dynamics across different time scales, while Ring Positional Encoding accurately encodes the circular latitude structure of the Earth when representing spatial information. For the second limitation, we develop an adaptive rollout scheduler based on reinforcement learning, which selects the most suitable time interval to forecast according to the current weather state. Experimental results demonstrate that ARROW achieves state-of-the-art performance in global weather forecasting, establishing a promising paradigm in this field.

Recently, there has been a growing interest in Long-term Time Series Forecasting (LTSF), which involves predicting long-term future values by analyzing a large amount of historical time-series data to identify patterns and trends. Significant challenges exist in LTSF due to its complex temporal dependencies and high computational demands. Although Transformer-based models offer high forecasting accuracy, they are often too compute-intensive to be deployed on devices with hardware constraints. In this paper, we propose MixLinear, which synergistically combines orthogonal segment-based trend extraction in the time domain with adaptive low-rank spectral filtering in the frequency domain. Our approach exploits the complementary structural sparsity of time series: local temporal patterns are efficiently captured through mathematically linear transformations that separate intra-segment and inter-segment correlations, while global trends are compressed into an ultra-low-dimensional frequency latent space through learnable rank-constrained filters. By reducing the parameter scale of a downsampled $n$-length input/output one-layer linear model from $O(n^2)$ to $O(n)$, MixLinear achieves efficient computation without sacrificing accuracy. Extensive evaluations show that MixLinear achieves forecasting performance comparable to, or surpasses, state-of-the-art models with significantly fewer parameters ($0.1K$), which makes it well suited for deployment on devices with limited computational capacity.