Spatio-temporal reasoning in time series involves the explicit synthesis of temporal dynamics, spatial dependencies, and textual context.This capability is vital for high-stakes decision-making in systems such as traffic networks, power grids, and disease propagation.However, the field remains underdeveloped because most existing works prioritize predictive accuracy over reasoning.To address the gap, we introduce ST-Bench, a benchmark consisting of four core tasks, including etiological reasoning, entity identification, correlation reasoning, and in-context forecasting, developed via a network SDE-based multi-agent data synthesis pipeline.We then propose STReasoner, which empowers LLM to integrate time series, graph structure, and text for explicit reasoning.To promote spatially grounded logic, we introduce S-GRPO, a reinforcement learning algorithm that rewards performance gains specifically attributable to spatial information.Experiments show that STReasoner achieves average accuracy gains between 17% and 135% at only 0.004× the cost of proprietary models and generalizes robustly to real-world data.Our code is available at https://github.com/LingFengGold/STReasoner.

Transformer-based and CNN-based methods demonstrate strong performance in long-term time series forecasting. However, their high computational and storage requirements can hinder large-scale deployment. To address this limitation, we propose integrating lightweight MLP with advanced architectures using knowledge distillation (KD). Our preliminary study reveals different models can capture complementary patterns, particularly multi-scale and multi-period patterns in the temporal and frequency domains. Based on this observation, we introduce TimeDistill, a cross-architecture KD framework that transfers these patterns from teacher models (e.g., Transformers, CNNs) to MLP. Additionally, we provide a theoretical analysis, demonstrating that our KD approach can be interpreted as a specialized form of mixup data augmentation. TimeDistill improves MLP performance by up to 18.6%, surpassing teacher models on eight datasets. It also achieves up to 7X faster inference and requires 130X fewer parameters. Furthermore, we conduct extensive evaluations to highlight the versatility and effectiveness of TimeDistill. The code is available at Github Code Repo.

Spatial-Temporal Graph (STG) forecasting on large-scale networks has garnered significant attention. However, existing models predominantly focus on short-horizon predictions and suffer from notorious computational costs and memory consumption when scaling to long-horizon predictions and large graphs. Targeting the above challenges, we present FaST, an effective and efficient framework based on heterogeneity-aware Mixture-of-Experts (MoEs) for long-horizon and large-scale STG forecasting, which unlocks one-week-ahead (672 steps at a 15-minute granularity) prediction with thousands of nodes. FaST is underpinned by two key innovations. First, an adaptive graph agent attention mechanism is proposed to alleviate the computational burden inherent in conventional graph convolution and self-attention modules when applied to large-scale graphs. Second, we propose a new parallel MoE module that replaces traditional feed-forward networks with Gated Linear Units (GLUs), enabling an efficient and scalable parallel structure. Extensive experiments on real-world datasets demonstrate that FaST not only delivers superior long-horizon predictive accuracy but also achieves remarkable computational efficiency compared to state-of-the-art baselines. Our source code is available at: https://github.com/yijizhao/FaST.

Source-free domain adaptation (SFDA) is a challenging, yet valuable task within unsupervised domain adaptation (UDA), which adapts pretrained models to diverse unlabeled target domains while safeguarding the data security of the source domain. However, existing SFDA methods primarily focus on computer vision applications, often overlooking the unique characteristics of time series, such as temporal dependencies and sequential nature. Moreover, the fine-tuning paradigm of current SFDA methods is typically limited to posterior adaptation, focusing solely on constraining the statistical properties of model outputs. We argue that this black-box paradigm lacks semantic interpretability and risks aligning with spurious contextual noise, leading to negative transfer. This necessitates a paradigm evolution from blind statistical adaptation to interpretable adaptation. To this end, we introduce model salience as a quantifiable proxy of semantic interpretability, representing the importance weights a trained model assigns to specific temporal fragments. Accordingly, we propose a novel fine-tuning paradigm for time-series SFDA, termed PrEPoA, which integrates Prior Evaluation of model salience with Posterior Adaptation. In the prior evaluation stage, a key pattern reconstruction (KPR) module based on a sensitive masking mechanism is designed to quantify the model salience, while a novel interpattern triplet loss is introduced to calibrate it. In the posterior adaptation stage, robust prototype clustering (RPC) generates trustworthy reference labels as pseudo-ground truth for adaptation. Comprehensive experiments on the wireless sensor data mining (WISDM), human activity recognition (HAR), heterogeneity HAR (HHAR), machine fault diagnosis (MFD), and sleep stage classification (SSC) datasets demonstrate the superiority of our PrEPoA framework compared to nine UDA and seven SFDA methods. Furthermore, we experimentally validate that PrEPoA serves as a plug-and-play module that effectively incorporated into other SFDA methods.

Yaxuan Kong, Yiyuan Yang, Yoontae Hwang, Wenjie Du, Stefan Zohren, Zhangyang Wang, Ming Jin, Qingsong Wen. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2025.

Ocean salinity plays a vital role in circulation, climate, and marine ecosystems, yet its measurement is often sparse, irregular, and noisy, especially in drifter-based datasets. Traditional approaches, such as remote sensing and optimal interpolation, rely on linearity and stationarity, and are limited by cloud cover, sensor drift, and low satellite revisit rates. While machine learning models offer flexibility, they often fail under severe sparsity and lack principled ways to incorporate physical covariates without specialized sensors. In this paper, we introduce the OceAn Salinity Imputation System, a novel diffusion adversarial framework designed to address these challenges by: (1) employing a transformer-based global dependency capturing module to learn long-range spatio-temporal correlations from sparse trajectories; (2) constructing a generative imputation model that conditions on easily observed tidal covariates to progressively refine imputed salinity fields; and (3) using a scheduler diffusion method to enhance the model's robustness. This unified architecture exploits the periodic nature of tidal signals as a proxy for unmeasured physical drivers, without the need for additional equipment. We evaluate OASIS on four benchmark datasets, including one real-world measurement from Fort Pierce Inlet and three simulated Gulf of Mexico trajectories. Results show consistent improvements over both traditional and neural baselines, achieving up to 52.5% reduction in MAE compared to Kriging. We also develop a lightweight, web-based deployment system that enables salinity imputation through interactive and batch interfaces, available at: https://github.com/yfeng77/OASIS.

Dynamic graph neural networks (DGNNs) have emerged as a leading paradigm for learning from dynamic graphs, which are commonly used to model real-world systems and applications. However, due to the evolving nature of dynamic graph data distributions over time, well-trained DGNNs often face significant performance uncertainty when inferring on unseen and unlabeled test graphs in practical deployment. In this case, evaluating the performance of deployed DGNNs at test time is crucial to determine whether a well-trained DGNN is suited for inference on an unseen dynamic test graph. In this work, we introduce a new research problem: DGNN model evaluation, which aims to assess the performance of a specific DGNN model trained on observed dynamic graphs by estimating its performance on unseen dynamic graphs during test time. Specifically, we propose a Dynamic Graph neural network Evaluator, dubbed DYGEvAL, toaddress this new problem. The proposed DyGEvAL involves a two-stage framework: (1) test-time dynamic graph simulation, which captures the training-test distributional differences as supervision signals and trains an evaluator; and (2) DyGEvAL development and training, which accurately estimates the performance of the well-trained DGNN model on the test-time dynamic graphs. Extensive experiments demonstrate that the proposed DyGEvAL serves as an effective evaluator for assessing various DGNN backbones across different dynamic graphs under distribution shifts.

Time series analysis plays a critical role in numerous applications, supporting tasks such as forecasting, classification, anomaly detection, and imputation. In this work, we present the time series pattern machine (TSPM), a model designed to excel in a broad range of time series tasks through powerful representation and pattern extraction capabilities. Traditional time series models often struggle to capture universal patterns, limiting their effectiveness across diverse tasks. To address this, we define multiple scales in the time domain and various resolutions in the frequency domain, employing various mixing strategies to extract intricate, task-adaptive time series patterns. Specifically, we introduce TimeMixer++, a general-purpose TSPM that processes multi-scale time series using (1) multi-resolution time imaging (MRTI), (2) time image decomposition (TID), (3) multi-scale mixing (MCM), and (4) multi-resolution mixing (MRM) to extract comprehensive temporal patterns. MRTI transforms multi-scale time series into multi-resolution time images, capturing patterns across both temporal and frequency domains. TID leverages dual-axis attention to extract seasonal and trend patterns, while MCM hierarchically aggregates these patterns across scales. MRM adaptively integrates all representations across resolutions. TimeMixer++ achieves state-of-the-art performance across 8 time series analytical tasks, consistently surpassing both general-purpose and task-specific models. Our work marks a promising step toward the next generation of TSPMs, paving the way for further advancements in time series analysis.

Scaling laws offer valuable insights into the design of time series foundation models (TSFMs). However, previous research has largely focused on the scaling laws of TSFMs for in-distribution (ID) data, leaving their out-of-distribution (OOD) scaling behavior and the influence of model architectures less explored. In this work, we examine two common TSFM architectures—encoder-only and decoder-only Transformers—and investigate their scaling behavior on both ID and OOD data. These models are trained and evaluated across varying parameter counts, compute budgets, and dataset sizes. Our experiments reveal that the log-likelihood loss of TSFMs exhibits similar scaling behavior in both OOD and ID settings. We further compare the scaling properties across different architectures, incorporating two state-of-the-art TSFMs as case studies, showing that model architecture plays a significant role in scaling. The encoder-only Transformers demonstrate better scalability than the decoder-only Transformers, while the architectural enhancements in the two advanced TSFMs primarily improve ID performance but reduce OOD scalability. While scaling up TSFMs is expected to drive performance breakthroughs, the lack of a comprehensive understanding of TSFM scaling laws has hindered the development of a robust framework to guide model scaling. We fill this gap in this work by synthesizing our findings and providing practical guidelines for designing and scaling larger TSFMs with enhanced model capabilities.

Recent advancements in time series forecasting have explored augmenting models with text or vision modalities to improve accuracy. While text provides contextual understanding, it often lacks fine-grained temporal details. Conversely, vision captures intricate temporal patterns but lacks semantic context, limiting the complementary potential of these modalities. To address this, we propose Time-VLM, a novel multimodal framework that leverages pre-trained Vision-Language Models (VLMs) to bridge temporal, visual, and textual modalities for enhanced forecasting. Our framework comprises three key components: (1) a Retrieval-Augmented Learner, which extracts enriched temporal features through memory bank interactions; (2) a Vision-Augmented Learner, which encodes time series as informative images; and (3) a Text-Augmented Learner, which generates contextual textual descriptions. These components collaborate with frozen pre-trained VLMs to produce multimodal embeddings, which are then fused with temporal features for final prediction. Extensive experiments demonstrate that Time-VLM achieves superior performance, particularly in few-shot and zero-shot scenarios, thereby establishing a new direction for multimodal time series forecasting. Code is available at https://github.com/CityMind-Lab/ICML25-TimeVLM.

Text-to-Time Series generation holds significant potential to address challenges such as data sparsity, imbalance, and limited availability of multimodal time series data across domains. While diffusion models have achieved remarkable success in Text-to-X (e.g., vision and audio data) generation, their use in time series generation remains limit. Existing approaches face two critical limitations: (1) reliance on domain-specific captions that generalize poorly, and (2) inability to generate time series of arbitrary length, limiting real-world use. In this work, we first introduce a new multimodal dataset containing over 600,000 high-resolution text-time series pairs. Second, we propose Text-to-Series (T2S), a diffusion-based framework that bridges the gap between natural language and time series in a domain-agnostic manner. It employs a length-adaptive VAE to encode time series of varying lengths into consistent latent embeddings. On top of that, T2S effectively aligns textual representations with latent embeddings by utilizing Flow Matching and employing DiT as the denoiser. We train T2S in an interleaved paradigm across multiple lengths, allowing it to generate sequences of arbitrary lengths. Extensive evaluations demonstrate that T2S achieves state-of-the-art performance across 13 datasets spanning 12 domains.

Many real-world applications contain data in the form of multivariate time series (TS) with the hierarchical structure, where classic methods forecasting each TS independently are inadequate for coherency (i.e., satisfying the hierarchical aggregation constraints).Furthermore, the discrepancies between statistical properties of different levels can be huge, exacerbated by non-Gaussian distributions and non-linear correlations.In this paper, we propose a novel end-to-end hierarchical TS forecasting model, i.e., a Flow-based Reconcile Transformer (FRT).FRT employs a conditional normalizing flow-based autoregressive transformer, to represent complex data distribution, while simultaneously reconciling the forecasts to ensure coherency.Go beyond other state-of-the-art methods, FRT accomplishes forecasting and reconciliation simultaneously, while avoiding any post-processing steps.Moreover, FRT is a deep model that does not rely on any strong assumptions such as unbiased estimates or Gaussian distribution.Our experiments are conducted on four real-world hierarchical datasets from different industrial domains (three public ones and a dataset from the application servers of our company's data center) and the results demonstrate the efficacy of our proposed method.Our method has been implemented extensively within the production environments of a prominent global payment company.It has emerged as a cornerstone for workload forecasting within their data center and plays a critical role in the optimization of cloud computing resource allocation across * Both authors contributed equally to this research.

Spatio-Temporal (ST) data science, which includes sensing, managing, and mining large-scale data across space and time, is fundamental to understanding complex systems in domains such as urban computing, climate science, and intelligent transportation. Traditional deep learning approaches have significantly advanced this field, particularly in the stage of ST data mining. However, these models remain task-specific and often require extensive labeled data. Inspired by the success of Foundation Models (FM), especially large language models, researchers have begun exploring the concept of Spatio-Temporal Foundation Models (STFMs) to enhance adaptability and generalization across diverse ST tasks. Unlike prior architectures, STFMs empower the entire workflow of ST data science, ranging from data sensing, management, to mining, thereby offering a more holistic and scalable approach. Despite rapid progress, a systematic study of STFMs for ST data science remains lacking. This survey aims to provide a comprehensive review of STFMs, categorizing existing methodologies and identifying key research directions to advance ST general intelligence.

Explaining time series classification models is crucial, particularly in high-stakes applications such as healthcare and finance, where transparency and trust play a critical role. Although numerous time series classification methods have identified key subsequences, known as shapelets, as core features for achieving state-of-the-art performance and validating their pivotal role in classification outcomes, existing post-hoc time series explanation (PHTSE) methods primarily focus on timestep-level feature attribution. These explanation methods overlook the fundamental prior that classification outcomes are predominantly driven by key shapelets. To bridge this gap, we present ShapeX, an innovative framework that segments time series into meaningful shapelet-driven segments and employs Shapley values to assess their saliency. At the core of ShapeX lies the Shapelet Describe-and-Detect (SDD) framework, which effectively learns a diverse set of shapelets essential for classification. We further demonstrate that ShapeX produces explanations which reveal causal relationships instead of just correlations, owing to the atomicity properties of shapelets. Experimental results on both synthetic and real-world datasets demonstrate that ShapeX outperforms existing methods in identifying the most relevant subsequences, enhancing both the precision and causal fidelity of time series explanations.

Dynamic graph modeling aims to uncover evolutionary patterns in real-world systems, enabling accurate social recommendation and early detection of cancer cells. Inspired by the success of recent state space models in efficiently capturing long-term dependencies, we propose DyG-Mamba by translating dynamic graph modeling into a long-term sequence modeling problem. Specifically, inspired by Ebbinghaus' forgetting curve, we treat the irregular timespans between events as control signals, allowing DyG-Mamba to dynamically adjust the forgetting of historical information. This mechanism ensures effective usage of irregular timespans, thereby improving both model effectiveness and inductive capability. In addition, inspired by Ebbinghaus' review cycle, we redefine core parameters to ensure that DyG-Mamba selectively reviews historical information and filters out noisy inputs, further enhancing the model’s robustness. Through exhaustive experiments on 12 datasets covering dynamic link prediction and node classification tasks, we show that DyG-Mamba achieves state-of-the-art performance on most datasets, while demonstrating significantly improved computational and memory efficiency. Our code is available at https://github.com/Clearloveyuan/DyG-Mamba.

Time series foundation models (TSFMs) demonstrate impressive zero-shot performance for time series forecasting. However, an important yet underexplored challenge is how to effectively finetune TSFMs on specific downstream tasks. While naive finetuning can yield performance gains, we argue that it falls short of fully leveraging TSFMs' capabilities, often resulting in overfitting and suboptimal performance. Given the diverse temporal patterns across sampling scales and the inherent multi-scale forecasting capabilities of TSFMs, we adopt a causal perspective to analyze finetuning process, through which we highlight the critical importance of explicitly modeling multiple scales and reveal the shortcomings of naive approaches. Focusing on encoder-based TSFMs, we propose Multiscale finetuning (MSFT), a simple yet general framework that explicitly integrates multi-scale modeling into the finetuning process. Experimental results on three different backbones (Moirai, Moment and Units) demonstrate that TSFMs finetuned with MSFT not only outperform naive and typical parameter efficient finetuning methods but also surpass state-of-the-art deep learning methods. Codes are available at https://github.com/zqiao11/MSFT.

Self-correction of large language models (LLMs) emerges as a critical component for enhancing their reasoning performance. Although various self-correction methods have been proposed, a comprehensive evaluation of these methods remains largely unexplored, and the question of whether LLMs can truly correct themselves is a matter of significant interest and concern. In this study, we introduce CorrectBench, a benchmark developed to evaluate the effectiveness of self-correction strategies, including intrinsic, external, and fine-tuned approaches, across three tasks: commonsense reasoning, mathematical reasoning, and code generation. Our findings reveal that: 1) Self-correction methods can improve accuracy, especially for complex reasoning tasks; 2) Mixing different self-correction strategies yields further improvements, though it reduces efficiency; 3) Reasoning LLMs (e.g., DeepSeek-V3) have limited optimization under additional self-correction methods and have high time costs. Interestingly, a comparatively simple chain-of-thought (CoT) baseline demonstrates competitive accuracy and efficiency. These results underscore the potential of self-correction to enhance LLM's reasoning performance while highlighting the ongoing challenge of improving their efficiency. Consequently, we advocate for further research focused on optimizing the balance between reasoning capabilities and operational efficiency.

Time series forecasting has remained a focal point due to its vital applications in sectors such as energy management and transportation planning. Spectral-temporal graph neural network is a promising abstraction underlying most time series forecasting models that are based on graph neural networks (GNNs). However, more is needed to know about the underpinnings of this branch of methods. In this paper, we establish a theoretical framework that unravels the expressive power of spectral-temporal GNNs. Our results show that linear spectral-temporal GNNs are universal under mild assumptions, and their expressive power is bounded by our extended first-order Weisfeiler-Leman algorithm on discrete-time dynamic graphs. To make our findings useful in practice on valid instantiations, we discuss related constraints in detail and outline a theoretical blueprint for designing spatial and temporal modules in spectral domains. Building on these insights and to demonstrate how powerful spectral-temporal GNNs are based on our framework, we propose a simple instantiation named Temporal Graph Gegenbauer Convolution (TGGC), which significantly outperforms most existing models with only linear components and shows better model efficiency.

Time series forecasting is a critical and challenging task in practical application. Recent advancements in pre-trained foundation models for time series forecasting have gained significant interest. However, current methods often overlook the multi-scale nature of time series, which is essential for accurate forecasting. To address this, we propose HiMTM, a hierarchical multi-scale masked time series modeling with self-distillation for long-term forecasting. HiMTM integrates four key components: (1) hierarchical multi-scale transformer (HMT) to capture temporal information at different scales; (2) decoupled encoder-decoder (DED) that directs the encoder towards feature extraction while the decoder focuses on pretext tasks; (3) hierarchical self-distillation (HSD) for multi-stage feature-level supervision signals during pre-training; and (4) cross-scale attention fine-tuning (CSA-FT) to capture dependencies between different scales for downstream tasks. These components collectively enhance multi-scale feature extraction in masked time series modeling, improving forecasting accuracy. Extensive experiments on seven mainstream datasets show that HiMTM surpasses state-of-the-art self-supervised and end-to-end learning methods by a considerable margin of 3.16-68.54%. Additionally, HiMTM outperforms the latest robust self-supervised learning method, PatchTST, in cross-domain forecasting by a significant margin of 2.3%. The effectiveness of HiMTM is further demonstrated through its application in natural gas demand forecasting.

Time series forecasting holds significant importance in many real-world dynamic systems and has been extensively studied. Unlike natural language process (NLP) and computer vision (CV), where a single large model can tackle multiple tasks, models for time series forecasting are often specialized, necessitating distinct designs for different tasks and applications. While pre-trained foundation models have made impressive strides in NLP and CV, their development in time series domains has been constrained by data sparsity. Recent studies have revealed that large language models (LLMs) possess robust pattern recognition and reasoning abilities over complex sequences of tokens. However, the challenge remains in effectively aligning the modalities of time series data and natural language to leverage these capabilities. In this work, we present Time-LLM, a reprogramming framework to repurpose LLMs for general time series forecasting with the backbone language models kept intact. We begin by reprogramming the input time series with text prototypes before feeding it into the frozen LLM to align the two modalities. To augment the LLM's ability to reason with time series data, we propose Prompt-as-Prefix (PaP), which enriches the input context and directs the transformation of reprogrammed input patches. The transformed time series patches from the LLM are finally projected to obtain the forecasts. Our comprehensive evaluations demonstrate that \method is a powerful time series learner that outperforms state-of-the-art, specialized forecasting models. Moreover, Time-LLM excels in both few-shot and zero-shot learning scenarios. The code is made available at https://github.com/KimMeen/Time-LLM.

Time series analysis is essential for comprehending the complexities inherent in various real-world systems and applications. Although large language models (LLMs) have recently made significant strides, the development of artificial general intelligence (AGI) equipped with time series analysis capabilities remains in its nascent phase. Most existing time series models heavily rely on domain knowledge and extensive model tuning, predominantly focusing on prediction tasks. In this paper, we argue that current LLMs have the potential to revolutionize time series analysis, thereby promoting efficient decision-making and advancing towards a more universal form of time series analytical intelligence. Such advancement could unlock a wide range of possibilities, including time series modality switching and question answering. We encourage researchers and practitioners to recognize the potential of LLMs in advancing time series analysis and emphasize the need for trust in these related efforts. Furthermore, we detail the seamless integration of time series analysis with existing LLM technologies and outline promising avenues for future research.

Time series analysis stands as a focal point within the data mining community, serving as a cornerstone for extracting valuable insights crucial to a myriad of real-world applications. Recent advances in Foundation Models (FMs) have fundamentally reshaped the paradigm of model design for time series analysis, boosting various downstream tasks in practice. These innovative approaches often leverage pre-trained or fine-tuned FMs to harness generalized knowledge tailored for time series analysis. This survey aims to furnish a comprehensive and up-to-date overview of FMs for time series analysis. While prior surveys have predominantly focused on either application or pipeline aspects of FMs in time series analysis, they have often lacked an in-depth understanding of the underlying mechanisms that elucidate why and how FMs benefit time series analysis. To address this gap, our survey adopts a methodology-centric classification, delineating various pivotal elements of time-series FMs, including model architectures, pre-training techniques, adaptation methods, and data modalities. Overall, this survey serves to consolidate the latest advancements in FMs pertinent to time series analysis, accentuating their theoretical underpinnings, recent strides in development, and avenues for future exploration.

In long-term time series forecasting (LTSF) tasks, an increasing number of works have acknowledged that discrete time series originate from continuous dynamic systems and have attempted to model their underlying dynamics. Recognizing the chaotic nature of real-world data, our model, Attraos, incorporates chaos theory into LTSF, perceiving real-world time series as low-dimensional observations from unknown high-dimensional chaotic dynamical systems. Under the concept of attractor invariance, Attraos utilizes non-parametric Phase Space Reconstruction embedding along with a novel multi-resolution dynamic memory unit to memorize historical dynamical structures, and evolves by a frequency-enhanced local evolution strategy. Detailed theoretical analysis and abundant empirical evidence consistently show that Attraos outperforms various LTSF methods on mainstream LTSF datasets and chaotic datasets with only one-twelfth of the parameters compared to PatchTST.

The great learning ability of deep learning facilitates us to comprehend the real physical world, making learning to simulate complicated particle systems a promising endeavour both in academia and industry. However, the complex laws of the physical world pose significant challenges to the learning based simulations, such as the varying spatial dependencies between interacting particles and varying temporal dependencies between particle system states in different time stamps, which dominate particles' interacting behavior and the physical systems' evolution patterns. Existing learning based methods fail to fully account for the complexities, making them unable to yield satisfactory simulations. To better comprehend the complex physical laws, we propose a novel model - Graph Networks with Spatial-Temporal neural Ordinary Differential Equations (GNSTODE) - that characterizes the varying spatial and temporal dependencies in particle systems using a united end-to-end framework. Through training with real-world particle-particle interaction observations, GNSTODE can simulate any possible particle systems with high precisions. We empirically evaluate GNSTODE's simulation performance on two real-world particle systems, Gravity and Coulomb, with varying levels of spatial and temporal dependencies. The results show that GNSTODE yields better simulations than state-of-the-art methods, showing that GNSTODE can serve as an effective tool for particle simulation in real-world applications. Our code is made available at https://github.com/Guangsi-Shi/AI-for-physics-GNSTODE.

Time series are the primary data type used to record dynamic system measurements and generated in great volume by both physical sensors and online processes (virtual sensors). Time series analytics is therefore crucial to unlocking the wealth of information implicit in available data. With the recent advancements in graph neural networks (GNNs), there has been a surge in GNN-based approaches for time series analysis. These approaches can explicitly model inter-temporal and inter-variable relationships, which traditional and other deep neural network-based methods struggle to do. In this survey, we provide a comprehensive review of graph neural networks for time series analysis (GNN4TS), encompassing four fundamental dimensions: forecasting, classification, anomaly detection, and imputation. Our aim is to guide designers and practitioners to understand, build applications, and advance research of GNN4TS. At first, we provide a comprehensive task-oriented taxonomy of GNN4TS. Then, we present and discuss representative research works and introduce mainstream applications of GNN4TS. A comprehensive discussion of potential future research directions completes the survey. This survey, for the first time, brings together a vast array of knowledge on GNN-based time series research, highlighting foundations, practical applications, and opportunities of graph neural networks for time series analysis.

Self-supervised learning (SSL) has recently achieved impressive performance on various time series tasks. The most prominent advantage of SSL is that it reduces the dependence on labeled data. Based on the pre-training and fine-tuning strategy, even a small amount of labeled data can achieve high performance. Compared with many published self-supervised surveys on computer vision and natural language processing, a comprehensive survey for time series SSL is still missing. To fill this gap, we review current state-of-the-art SSL methods for time series data in this article. To this end, we first comprehensively review existing surveys related to SSL and time series, and then provide a new taxonomy of existing time series SSL methods by summarizing them from three perspectives: generative-based, contrastive-based, and adversarial-based. These methods are further divided into ten subcategories with detailed reviews and discussions about their key intuitions, main frameworks, advantages and disadvantages. To facilitate the experiments and validation of time series SSL methods, we also summarize datasets commonly used in time series forecasting, classification, anomaly detection, and clustering tasks. Finally, we present the future directions of SSL for time series analysis.

Graph representation learning (GRL) is critical for graph-structured data analysis. However, most of the existing graph neural networks (GNNs) heavily rely on labeling information, which is normally expensive to obtain in the real world. Although some existing works aim to effectively learn graph representations in an unsupervised manner, they suffer from certain limitations, such as the heavy reliance on monotone contrastiveness and limited scalability. To overcome the aforementioned problems, in light of the recent advancements in graph contrastive learning, we introduce a novel self-supervised GRL algorithm via graph contrastive adjusted zooming, namely, G-Zoom, to learn node representations by leveraging the proposed adjusted zooming scheme. Specifically, this mechanism enables G-Zoom to explore and extract self-supervision signals from a graph from multiple scales: micro (i.e., node level), meso (i.e., neighborhood level), and macro (i.e., subgraph level). First, we generate two augmented views of the input graph via two different graph augmentations. Then, we establish three different contrastiveness on the above three scales progressively, from node, neighboring, to subgraph level, where we maximize the agreement between graph representations across scales. While we can extract valuable clues from a given graph on the micro and macro perspectives, the neighboring-level contrastiveness offers G-Zoom the capability of a customizable option based on our adjusted zooming scheme to manually choose an optimal viewpoint that lies between the micro and macro perspectives to better understand the graph data. In addition, to make our model scalable to large graphs, we use a parallel graph diffusion approach to decouple model training from the graph size. We have conducted extensive experiments on real-world datasets, and the results demonstrate that our proposed model outperforms the state-of-the-art methods consistently.

Multivariate time-series anomaly detection is critically important in many applications, including retail, transportation, power grid, and water treatment plants. Existing approaches for this problem mostly employ either statistical models which cannot capture the nonlinear relations well or conventional deep learning (DL) models e.g., convolutional neural network (CNN) and long short-term memory (LSTM) that do not explicitly learn the pairwise correlations among variables. To overcome these limitations, we propose a novel method, correlation-aware spatial-temporal graph learning (termed ), for time-series anomaly detection. explicitly captures the pairwise correlations via a correlation learning (MTCL) module based on which a spatial-temporal graph neural network (STGNN) can be developed. Then, by employing a graph convolution network (GCN) that exploits one-and multihop neighbor information, our STGNN component can encode rich spatial information from complex pairwise dependencies between variables. With a temporal module that consists of dilated convolutional functions, the STGNN can further capture long-range dependence over time. A novel anomaly scoring component is further integrated into to estimate the degree of an anomaly in a purely unsupervised manner. Experimental results demonstrate that can detect and diagnose anomalies effectively in general settings as well as enable early detection across different time delays. Our code is available at https://github.com/huankoh/CST-GL.

Multivariate time series forecasting has long received significant attention in real-world applications, such as energy consumption and traffic prediction. While recent methods demonstrate good forecasting abilities, they have three fundamental limitations. (i).Discrete neural architectures:Interlacing individually parameterized spatial and temporal blocks to encode rich underlying patterns leads to discontinuous latent state trajectories and higher forecasting numerical errors. (ii).High complexity:Discrete approaches complicate models with dedicated designs and redundant parameters, leading to higher computational and memory overheads. (iii).Reliance on graph priors:Relying on predefined static graph structures limits their effectiveness and practicability in real-world applications. In this paper, we address all the above limitations by proposing a continuous model to forecastMultivariateTime series with dynamicGraph neuralOrdinaryDifferentialEquations (MTGODE). Specifically, we first abstract multivariate time series into dynamic graphs with time-evolving node features and unknown graph structures. Then, we design and solve a neural ODE to complement missing graph topologies and unify both spatial and temporal message passing, allowing deeper graph propagation and fine-grained temporal information aggregation to characterize stable and precise latent spatial-temporal dynamics. Our experiments demonstrate the superiorities ofMTGODEfrom various perspectives on five time series benchmark datasets.

Deep learning on graphs has attracted significant interests recently. However, most of the works have focused on (semi-) supervised learning, resulting in shortcomings including heavy label reliance, poor generalization, and weak robustness. To address these issues, self-supervised learning (SSL), which extracts informative knowledge through well-designed pretext tasks without relying on manual labels, has become a promising and trending learning paradigm for graph data. Different from SSL on other domains like computer vision and natural language processing, SSL on graphs has an exclusive background, design ideas, and taxonomies. Under the umbrella of graph self-supervised learning, we present a timely and comprehensive review of the existing approaches which employ SSL techniques for graph data. We construct a unified framework that mathematically formalizes the paradigm of graph SSL. According to the objectives of pretext tasks, we divide these approaches into four categories: generation-based, auxiliary property-based, contrast-based, and hybrid approaches. We further describe the applications of graph SSL across various research fields and summarize the commonly used datasets, evaluation benchmark, performance comparison and open-source codes of graph SSL. Finally, we discuss the remaining challenges and potential future directions in this research field.

Anomaly detection from graph data has drawn much attention due to its practical significance in many critical applications including cybersecurity, finance, and social networks. Existing data mining and machine learning methods are either shallow methods that could not effectively capture the complex interdependency of graph data or graph autoencoder methods that could not fully exploit the contextual information as supervision signals for effective anomaly detection. To overcome these challenges, in this paper, we propose a novel method, Self-Supervised Learning for Graph Anomaly Detection (SL-GAD). Our method constructs different contextual subgraphs (views) based on a target node and employs two modules,generative attribute regressionandmulti-view contrastive learningfor anomaly detection. While thegenerative attribute regressionmodule allows us to capture the anomalies in the attribute space, themulti-view contrastive learningmodule can exploit richer structure information from multiple subgraphs, thus abling to capture the anomalies in the structure space, mixing of structure, and attribute information. We conduct extensive experiments on six benchmark datasets and the results demonstrate that our method outperforms state-of-the-art methods by a large margin.

Continuous-time dynamic graphs naturally abstract many real-world systems, such as social and transactional networks. While the research on continuous-time dynamic graph representation learning has made significant advances recently, neither graph topological properties nor temporal dependencies have been well-considered and explicitly modeled in capturing dynamic patterns. In this paper, we introduce a new approach, Neural Temporal Walks (NeurTWs), for representation learning on continuous-time dynamic graphs. By considering not only time constraints but also structural and tree traversal properties, our method conducts spatiotemporal-biased random walks to retrieve a set of representative motifs, enabling temporal nodes to be characterized effectively. With a component based on neural ordinary differential equations, the extracted motifs allow for irregularly-sampled temporal nodes to be embedded explicitly over multiple different interaction time intervals, enabling the effective capture of the underlying spatiotemporal dynamics. To enrich supervision signals, we further design a harder contrastive pretext task for model optimization. Our method demonstrates overwhelming superiority under both transductive and inductive settings on six real-world datasets.

Anomaly detection on graphs plays a significant role in various domains, including cybersecurity, e-commerce, and financial fraud detection. However, existing methods on graph anomaly detection usually consider the view in a single scale of graphs, which results in their limited capability to capture the anomalous patterns from different perspectives. Towards this end, we introduce a novel graph anomaly detection framework, namely ANEMONE, to simultaneously identify the anomalies in multiple graph scales. Concretely, ANEMONE first leverages a graph neural network backbone encoder with multi-scale contrastive learning objectives to capture the pattern distribution of graph data by learning the agreements between instances at the patch and context levels concurrently. Then, our method employs a statistical anomaly estimator to evaluate the abnormality of each node according to the degree of agreement from multiple perspectives. Experiments on three benchmark datasets demonstrate the superiority of our method.

Graph representation learning plays a vital role in processing graph-structured data. However, prior arts on graph representation learning heavily rely on labeling information. To overcome this problem, inspired by the recent success of graph contrastive learning and Siamese networks in visual representation learning, we propose a novel self-supervised approach in this paper to learn node representations by enhancing Siamese self-distillation with multi-scale contrastive learning. Specifically, we first generate two augmented views from the input graph based on local and global perspectives. Then, we employ two objectives called cross-view and cross-network contrastiveness to maximize the agreement between node representations across different views and networks. To demonstrate the effectiveness of our approach, we perform empirical experiments on five real-world datasets. Our method not only achieves new state-of-the-art results but also surpasses some semi-supervised counterparts by large margins. Code is made available at https://github.com/GRAND-Lab/MERIT