Time series forecasting is critical for decision making across dynamic domains such as energy, finance, transportation, and cloud computing. However, real-world time series often exhibit non-stationarity, including temporal distribution shifts and spectral variability, which poses significant challenges for existing long-term time series forecasting methods. In this paper, we propose DTAF, a dual-branch framework that addresses non-stationarity in both the temporal and frequency domains. For the temporal domain, the Temporal Stabilizing Fusion (TFS) module employs a non-stationary mix of experts (MOE) filter to disentangle and suppress temporal non-stationary patterns while preserving long-term dependencies. For the frequency domain, the Frequency Wave Modeling (FWM) module applies frequency differencing to dynamically highlight components with significant spectral shifts. By fusing the complementary outputs of TFS and FWM, DTAF generates robust forecasts that adapt to both temporal and frequency domain non-stationarity. Extensive experiments on multiple real-world benchmarks demonstrate that DTAF outperforms state-of-the-art baselines, yielding significant improvements in forecasting accuracy under non-stationary conditions.

Time series classification (TSC) is an important task in time series analysis. Existing TSC methods mainly train on each single domain separately, suffering from a degradation in accuracy when the samples for training are insufficient in certain domains. The pre-training and fine-tuning paradigm provides a promising direction for solving this problem. However, time series from different domains are substantially divergent, which challenges the effective pre-training on multi-source data and the generalization ability of pre-trained models. To handle this issue, we introduce Augmented Series and Image Contrastive Learning for Time Series Classification (AimTS), a pre-training framework that learns generalizable representations from multi-source time series data. We propose a two-level prototype-based contrastive learning method to effectively utilize various augmentations in multi-source pre-training, which learns representations for TSC that can be generalized to different domains. In addition, considering augmentations within the single time series modality are insufficient to fully address classification problems with distribution shift, we introduce the image modality to supplement structural information and establish a series-image contrastive learning to improve the generalization of the learned representations for TSC tasks. Extensive experiments show that after multi-source pre-training, AimTS achieves good generalization performance, enabling efficient learning and even few-shot learning on various downstream TSC datasets.

Air pollution significantly threatens human health and ecosystems, necessitating effective air quality prediction to inform public policy. Traditional approaches are generally categorized into physics-based and data-driven models. Physics-based models usually struggle with high computational demands and closed-system assumptions, while data-driven models may overlook essential physical dynamics, confusing the capturing of spatiotemporal correlations. Although some physics-guided approaches combine the strengths of both models, they often face a mismatch between explicit physical equations and implicit learned representations. To address these challenges, we propose Air-DualODE, a novel physics-guided approach that integrates dual branches of Neural ODEs for air quality prediction. The first branch applies open-system physical equations to capture spatiotemporal dependencies for learning physics dynamics, while the second branch identifies the dependencies not addressed by the first in a fully data-driven way. These dual representations are temporally aligned and fused to enhance prediction accuracy. Our experimental results demonstrate that Air-DualODE achieves state-of-the-art performance in predicting pollutant concentrations across various spatial scales, thereby offering a promising solution for real-world air quality challenges.

With the growing availability of multi-domain time series data, there is an increasing demand for general forecasting models pre-trained on multi-source datasets to support diverse downstream prediction scenarios. Existing time series foundation models primarily focus on scaling up pre-training datasets and model sizes to enhance generalization performance. In this paper, we take a different approach by addressing two critical aspects of general forecasting models: (1) how to derive unified representations from heterogeneous multi-domain time series data, and (2) how to effectively capture domain-specific features to enable adaptive transfer across various downstream scenarios. To address the first aspect, we propose Decomposed Frequency Learning as the pre-training task, which leverages frequency-based masking and reconstruction to decompose coupled semantic information in time series, resulting in unified representations across domains. For the second aspect, we introduce the Time Series Register, which captures domain-specific representations during pre-training and enhances adaptive transferability to downstream tasks. Our model achieves the state-of-the-art forecasting performance on seven real-world benchmarks, demonstrating remarkable few-shot and zero-shot capabilities.

Existing works on general time series forecasting build foundation models with heavy model parameters through large-scale multi-source pretraining. These models achieve superior generalization ability across various datasets at the cost of significant computational burdens and limitations in resource-constrained scenarios. This paper introduces LightGTS, a lightweight general time series forecasting model designed from the perspective of consistent periodical modeling. To handle diverse scales and intrinsic periods in multi-source pre-training, we introduce Periodical Tokenization, which extracts consistent periodic patterns across different datasets with varying scales. To better utilize the periodicity in the decoding process, we further introduce Periodical Parallel Decoding, which leverage historical tokens to improve forecasting. Based on the two techniques above which fully leverage the inductive bias of periods inherent in time series, LightGTS uses a lightweight model to achieve outstanding performance on general time series forecasting. It achieves state-of-the-art forecasting performance on 9 real-world benchmarks in both zero-shot and full-shot setting with much better efficiency compared with existing time series foundation models

Time Series Forecasting (TSF) is key functionality in numerous fields, such as financial investment, weather services, and energy management. Although increasingly capable TSF methods occur, many of them require domain-specific data collection and model training and do not generalize well when applied in other domains. Time Series Foundation Models (TSFMs) that are pre-trained on massive heterogeneous time series data aim to overcome these limitations. The prospects for generalizability have spurred the development of a new generation of TSFMs. This study proposes a benchmark, TSFM-Bench, to facilitate comprehensive and unified evaluation of TSFMs. TSFM-Bench covers a wide range of TSFMs, including those based on large language models and those pre-trained on time series data. TSFM-Bench supports multiple forecasting scenarios, including zero-shot, few-shot, and full-shot, enabling assessment across the full range of adaptation strategies. TSFM-Bench also provides a standardized experimental protocols for critical evaluation processes such as dataset splitting, loading, normalization, and few-shot sampling, facilitating consistency and fairness. We report on an extensive evaluation of TSFMs across a diverse range of datasets spanning multiple domains and exhibiting varied statistical characteristics. Specifically, we identify pros and cons and inherent limitations of existing TSFMs, and we propose potential directions for new model designs.

Time Series forecasting is critical in diverse domains such as weather forecasting, financial investment, and traffic management. While traditional numerical metrics like mean squared error (MSE) can quantify point-wise accuracy, they fail to evaluate the geometric structure of time series data, which is essential to understand temporal dynamics. To address this issue, we propose the time series Geometric Structure Index (TGSI), a novel evaluation metric that transforms time series into images to leverage their inherent two-dimensional geometric representations. However, since the image transformation process is non-differentiable, TGSI cannot be directly integrated as a training loss. We further introduce the Shape-Aware Temporal Loss (SATL), a multi-component loss function operating in the time series modality to bridge this gap and enhance structure modeling during training. SATL combines three components: a first-order difference loss that measures structural consistency through the MSE between first-order differences, a frequency domain loss that captures essential periodic patterns using the Fast Fourier Transform while minimizing noise, and a perceptual feature loss that measures geometric structure difference in time-series by aligning temporal features with geometric structure features through a pre-trained temporal feature extractor and time-series image autoencoder. Experiments across multiple datasets demonstrate that models trained with SATL achieve superior performance in both MSE and the proposed TGSI metrics compared to baseline methods, without additional computational cost during inference.

Transformers for time series forecasting mainly model time series from limited or fixed scales, making it challenging to capture different characteristics spanning various scales. We propose Pathformer, a multi-scale Transformer with adaptive pathways. It integrates both temporal resolution and temporal distance for multi-scale modeling. Multi-scale division divides the time series into different temporal resolutions using patches of various sizes. Based on the division of each scale, dual attention is performed over these patches to capture global correlations and local details as temporal dependencies. We further enrich the multi-scale Transformer with adaptive pathways, which adaptively adjust the multi-scale modeling process based on the varying temporal dynamics of the input, improving the accuracy and generalization of Pathformer. Extensive experiments on eleven real-world datasets demonstrate that Pathformer not only achieves state-of-the-art performance by surpassing all current models but also exhibits stronger generalization abilities under various transfer scenarios. The code is made available at https://github.com/decisionintelligence/pathformer.

Robust multivariate time series forecasting is crucial in many cyberphysical and Internet of Things applications. Existing state-of-the-art robust forecasting models decompose time series into independent functions covering trends and periodicities. However, these independent functions fail to capture correlations among multiple time series, thereby reducing prediction accuracy. Moreover, existing robust forecasting models treat certain abrupt but normal changes, e.g., caused by holidays, as outliers because they occur infrequently and have data distributions that resemble those of outliers. This exacerbates model bias and reduces prediction accuracy. This paper aims to capture correlations across multiple time series and abrupt but normal changes, thereby improving prediction accuracy. We employ weak labels to partition the dataset into source and target domains. Then, we propose the Domain Adversarial Robust Forecaster (DARF). This forecasting model is based on adversarial domain adaptation and includes two novel modules: Correlated Robust Forecaster (CORF) and Domain Critic. Specifically, CORF constitutes an encoder-decoder framework proficient at robust multivariate time series forecasting, and Domain Critic works to reduce data bias. Extensive experiments and discussions show that DARF is capable of state-of-the-art forecasting accuracy.

Predictive autoscaling is a key enabler for optimizing cloud resource allocation in Alibaba Cloud's computing platforms, which dynamically adjust the Elastic Compute Service (ECS) instances based on predicted user demands to ensure Quality of Service (QoS). However, user demands in the cloud are often highly complex, with high uncertainty and scale-sensitive temporal dependencies, thus posing great challenges for accurate prediction of future demands. These in turn make autoscaling challenging---autoscaling needs to properly account for demand uncertainty while maintaining a reasonable trade-off between two contradictory factors, i.e., low instance running costs vs. low QoS violation risks. To address the above challenges, we propose a novel predictive autoscaling framework MagicScaler , consisting of a Multi-scale attentive Gaussian process based predictor and an uncertainty-aware scaler. First, the predictor carefully bridges the best of two successful prediction methodologies---multi-scale attention mechanisms, which are good at capturing complex, multi-scale features, and stochastic process regression, which can quantify prediction uncertainty, thus achieving accurate demand prediction with quantified uncertainty. Second, the scaler takes the quantified future demand uncertainty into a judiciously designed loss function with stochastic constraints, enabling flexible trade-off between running costs and QoS violation risks. Extensive experiments on three clusters of Alibaba Cloud in different Chinese cities demonstrate the effectiveness and efficiency of MagicScaler , which outperforms other commonly adopted scalers, thus justifying our design choices.