With the proliferation of Internet of Things (IoT) applications, advanced time series forecasting techniques have become increasingly critical for managing and responding to complex temporal dynamics. However, traditional RNN-based methods have faced challenges in the Long-term Time Series Forecasting (LTSF) domain when dealing with excessively long look-back windows and forecast horizons. Consequently, the dominance in this domain has shifted towards Transformer, MLP, and CNN approaches. The substantial number of recurrent iterations are the fundamental reasons behind the limitations of RNNs in LTSF. To address these issues, we propose two novel strategies to reduce the number of iterations in RNNs for LTSF tasks: Segment-wise Iterations and Parallel Multi-step Forecasting (PMF). RNNs that combine these strategies, called SegRNN, significantly reduce the required recurrent iterations for LTSF, resulting in notable improvements in forecast accuracy and inference speed. Extensive experiments demonstrate that SegRNN not only outperforms state-of-the-art Transformer-based models but also reduces runtime and memory usage by more than 78%, making it highly suitable for resource-constrained IoT scenarios. These achievements provide strong evidence that RNNs continue to excel in LTSF tasks and encourage further exploration of this domain with more RNN-based approaches. The code is available at: https://github.com/lss-1138/SegRNN.

This paper introduces SparseTSF, a novel and extremely lightweight method for Long-term Time Series Forecasting (LTSF), designed to address the challenges of modeling complex temporal dependencies over extended horizons with minimal computational resources. At the heart of SparseTSF lies the Cross-Period Sparse Forecasting technique, which simplifies the forecasting task by downsampling the original sequences to focus on cross-period trend prediction. This technique not only significantly reduces model complexity and the number of parameters but also serves as an implicit regularization mechanism that enhances the model's robustness, achieving an optimal balance between performance and efficiency. Based on this technique, SparseTSF uses fewer than 1,000 parameters to achieve competitive performance compared to state-of-the-art methods, with evident advantages under longer look-back windows (e.g., 720) that allow the model to better exploit inherent periodicity and trend information. Furthermore, SparseTSF showcases remarkable generalization capabilities, making it well-suited for scenarios with limited computational resources, small samples, or low-quality data.

Accurately forecasting power consumption in data center servers requires addressing the temporal distribution shift caused by dynamic resource demands. However, existing methods rely on global normalization, which cannot capture short-term localized shift, leading to unsatisfactory performance when forecasting non-stationary time series. To address this challenge, we propose a novel bi-level optimization framework for forecasting non-stationary long-term power consumption, namedNoSPF. The framework employs hierarchical optimization to separately model the stationary and local non-stationary components of power consumption time series, offering a flexible, model-agnostic paradigm for time-series forecasting. Using Discrete Wavelet Transform (DWT) for multi-scale time–frequency analysis,NoSPFdecomposes the series into non-stationary components driven by short-term fluctuations and stationary components that capture long-term trends. Furthermore,NoSPFintegrates a lightweight Multi-Layer Perceptron (MLP) to predict the local non-stationary components, enhancing the framework’s forecasting accuracy by providing more precise approximations of the future power distribution. Extensive experiments on real-world server datasets demonstrate the superior performance and effectiveness ofNoSPF.

Sufficiently modeling the correlations among variables (aka channels) is crucial for achieving accurate multivariate time series forecasting (MTSF). In this paper, we propose a novel technique called Temporal Query (TQ) to more effectively capture multivariate correlations, thereby improving model performance in MTSF tasks. Technically, the TQ technique employs periodically shifted learnable vectors as queries in the attention mechanism to capture global inter-variable patterns, while the keys and values are derived from the raw input data to encode local, sample-level correlations. Building upon the TQ technique, we develop a simple yet efficient model named Temporal Query Network (TQNet), which employs only a single-layer attention mechanism and a lightweight multi-layer perceptron (MLP). Extensive experiments demonstrate that TQNet learns more robust multivariate correlations, achieving state-of-the-art forecasting accuracy across 12 challenging real-world datasets. Furthermore, TQNet achieves high efficiency comparable to linear-based methods even on high-dimensional datasets, balancing performance and computational cost. The code is available at: https://github.com/ACAT-SCUT/TQNet.

Accurate workload prediction is crucial for resource allocation and management in large-scale cloud data centers. While many approaches have been proposed, most existing methods are based on Recurrent Neural Networks (RNNs) or their variants, focusing on short-term cloud workload prediction without considering or identifying the long-term changes and different periodic patterns of cloud workloads. Due to variations in user demands or workload dynamics, cloud workloads that appear stable in the short term often exhibit distinct patterns in the long term. This can lead to a significant decline in prediction accuracy for existing methods when applied to long-term cloud workload forecasting. To address these challenges and overcome the limitations of current approaches, we propose a Multi-Scale Network with Convolutions (MSCNet) for accurate long-term cloud workload prediction. MSCNet employs multi-scale modeling of the original cloud workload to effectively extract multi-scale features and different periodic patterns, learning the long-term dependencies among the cloud workload. Our core component, the Multi-Scale Block, combines the Multi-Scale Patch Block, Transformer Encoder, and Multi-Scale Convolutions Block for comprehensive multi-scale learning. This enables MSCNet to adaptively learn both short-term and long-term features and patterns of cloud workloads, resulting in accurate long-term cloud workload predictions. Extensive experiments are conducted using real-world cloud workload data from Alibaba, Google, and Azure to validate the effectiveness of MSCNet. The experimental results demonstrate that MSCNet achieves accurate long-term cloud workload prediction with a computational complexity of$O(L^{2}d)$, outperforming existing state-of-the-art methods.

Accurate prediction of cloud workload is crucial for effective resource allocation in cloud computing. However, due to the complexity and high dimensionality of workloads in the cloud environment, achieving precise workload prediction is a complex and challenging problem. Current approaches to cloud workload prediction mainly rely on deep learning methods based on the Recurrent Neural Network (RNN), which struggle to capture the long-term dependencies inherent in workloads effectively. To tackle these challenges and overcome the limitations of existing methods, we propose an effective approach Time-Frequency Enhanced Gated Recurrent Unit with Attention (TFEGRU) for cloud workload prediction. First, we design a Time-Frequency Enhanced Block (TFEB) to capture complex workload patterns and extract features from both the frequency and temporal domains. Next, we integrate channel independent strategy and channel embedding into the model to adapt to high-dimensional workloads and enhance predictive performance. Finally, we apply a Gated Recurrent Unit (GRU) in conjunction with a multi-head self-attention mechanism to achieve accurate workload prediction. To validate the effectiveness of TFEGRU, comprehensive experiments are conducted using real-world traces from Google and Alibaba cloud data centers. The experimental results demonstrate that TFEGRU achieves accurate and efficient predictions across diverse cloud workloads, outperforming existing state-of-the-art methods.

This paper introduces SparseTSF, a novel, extremely lightweight model for Long-term Time Series Forecasting (LTSF), designed to address the challenges of modeling complex temporal dependencies over extended horizons with minimal computational resources. At the heart of SparseTSF lies the Cross-Period Sparse Forecasting technique, which simplifies the forecasting task by decoupling the periodicity and trend in time series data. This technique involves downsampling the original sequences to focus on cross-period trend prediction, effectively extracting periodic features while minimizing the model’s complexity and parameter count. Based on this technique, the SparseTSF model uses fewer than 1k parameters to achieve competitive or superior performance compared to state-of-the-art models. Furthermore, SparseTSF showcases remarkable generalization capabilities, making it well-suited for scenarios with limited computational resources, small samples, or low-quality data. The code is publicly available at this repository: https://github.com/lss-1138/SparseTSF.

The stable periodic patterns present in time series data serve as the foundation for conducting long-horizon forecasts. In this paper, we pioneer the exploration of explicitly modeling this periodicity to enhance the performance of models in long-term time series forecasting (LTSF) tasks. Specifically, we introduce the Residual Cycle Forecasting (RCF) technique, which utilizes learnable recurrent cycles to model the inherent periodic patterns within sequences, and then performs predictions on the residual components of the modeled cycles. Combining RCF with a Linear layer or a shallow MLP forms the simple yet powerful method proposed in this paper, called CycleNet. CycleNet achieves state-of-the-art prediction accuracy in multiple domains including electricity, weather, and energy, while offering significant efficiency advantages by reducing over 90% of the required parameter quantity. Furthermore, as a novel plug-and-play technique, the RCF can also significantly improve the prediction accuracy of existing models, including PatchTST and iTransformer. The source code is available at: https://github.com/ACAT-SCUT/CycleNet.