We present ST-FLIP, a spatiotemporal extension of the Fluid-Implicit Particle (FLIP) method for incompressible free-surface and two-phase liquid simulation. ST-FLIP enables time steps up to an order of magnitude larger than those typically used in CFL-constrained solvers, while preserving detailed flow structures and visual fidelity. It addresses a common failure mode of large time steps in hybrid particle-grid liquid solvers: temporal under-sampling of particle motion produces aliasing-driven free-surface artifacts after projection. Our key idea is to interpret particles as samples in four-dimensional space-time: in addition to standard spatial jittering, we randomize particle positions along the time axis as well and perform particle-to-grid deposition using a separable 4D kernel. This yields a Monte Carlo estimator of perstep time-slab-integrated particle quantities. Although particles are treated as samples in 4D space-time, our approach works as a lightweight plugin by collapsing to slab-integrated 3D grid fields for projection. Building on recent particle-based phase-field work, we reuse the particle-to-grid weight accumulators as a conceptual space-time phase field, providing variable-coefficient projection weights and eliminating the need for per-step surface reconstruction. The method can be easily integrated into existing FLIP/PIC or APIC solvers with negligible additional computational cost per time step. The effectiveness of our approach is demonstrated through a series of comparisons with state-of-the-art solvers, yielding several-fold speedups for multi-billion-particle simulations at high effective 3D resolutions on a single workstation.
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Major social media platforms increasingly adopt community-based fact-checking to address misinformation on their platforms. While previous research has largely focused on its effect on engagement (e. g., reposts), an understanding of how fact-checks affect a user's follower base is missing. In this study, we employ quasi-experimental methods to causally assess whether users lose followers after their posts are corrected via community fact-checks. Based on time-series data on follower counts for N = 4391 community fact-checked posts from X, we find that community fact-checks do not lead to meaningful declines in the follower counts of users who post misleading content. This suggests that followers of spreaders of misleading posts tend to remain loyal and do not view community fact-checks as a sufficient reason to disengage. Our findings underscore the need for complementary interventions to more effectively disincentivize the production of misinformation on social media.
Community-based fact-checking systems, such as Community Notes on X (formerly Twitter), aim to mitigate online misinformation by surfacing annotations judged helpful by contributors with diverse viewpoints. While prior work has shown that the platform's bridging-based algorithm effectively selects helpful notes at the time of display, little is known about how evaluations change after notes become visible. Using a large-scale dataset of 437,396 community notes and 35 million ratings from over 580,000 contributors, we examine the stability of helpful notes and the rating dynamics that follow their initial display. We find that 30.2% of displayed notes later lose their helpful status and disappear. Using interrupted time series models, we further show that note display triggers a sharp increase in rating volume and a significant shift in rating leaning, but these effects differ across rater groups. Contributors with viewpoints similar to note authors tend to increase supportive ratings, while dissimilar contributors increase negative ratings, producing systematic post-display polarization. Counterfactual analyses suggest that this post-display polarization, particularly from dissimilar raters, plays a substantial role in note disappearance. These findings highlight the vulnerability of consensus-based fact-checking systems to polarized rating behavior and suggest pathways for improving their resilience.
Accurate rainfall forecasting is essential for climate and disaster management, but precipitation exhibits extreme zero inflation that modern time-series Foundation Models (TSFMs) fundamentally cannot represent due to their continuous regression outputs. This structural mismatch causes pervasive drizzle-like false alarms, miscalibrated nonzero intensities, and severely underdetected extremes, while retraining large TSFMs is computationally prohibitive and environmentally unsustainable for most regions. We present a training-free wrapper that corrects zero inflation for frozen TSFMs without updating any parameters. Our method restores discrete zero mass using empirical occurrence statistics, aligns positive-value distributions via probability-integral transforms, and applies Generalized Pareto tail mapping for extreme-value consistency. Experiments on South Australian rainfall show substantial gains with negligible overhead (<5,ms per forecast, compared to hundreds of GPU-hours for retraining). The proposed wrapper enables carbon-neutral, globally deployable climate services and directly advances the goals of UN SDG~13 (Climate Action).
Online Time Series Forecasting (OTSF) requires models to continuously adapt to concept drift. However, existing methods often treat concept drift as a monolithic phenomenon. To address this limitation, we first redefine concept drift by categorizing it into two distinct types: Recurring Drift, where previously seen patterns reappear, and Emergent Drift, where entirely new patterns emerge. We then propose DynaME (Dynamic Multi-period Experts), a novel hybrid framework designed to effectively address this dual nature of drift. For Recurring Drift, DynaME employs a committee of specialized experts that are dynamically fitted to the most relevant historical periodic patterns at each time step. For Emergent Drift, the framework detects high-uncertainty scenarios and shifts reliance to a stable, general expert. Extensive experiments on several benchmark datasets and backbones demonstrate that DynaME effectively adapts to both concept drifts and significantly outperforms existing baselines. Our source code is available at https://github.com/shhong97/DynaME.
Time series forecasting underpins many real-world services. Recent trends have focused on foundation models inspired by the paradigm of large language models, which rely on large volumes of centralized time-series data across diverse domains. However, such approaches raise significant concerns regarding data privacy. Federated learning (FL) has emerged as a promising paradigm for training unified time-series models using isolated datasets distributed across multiple clients. Nevertheless, existing FL methods face two critical challenges: heterogeneous variables and heterogeneous temporal correlations. To address these issues, we propose FedRMamba, a personalized federated forecasting framework built entirely from Mamba state-space blocks. Each client adopts a residual-coupled architecture, where a global frequency-aware Mamba module captures the common low-frequency structures shared across different variables, while a local patch-wise Mamba module learns personalized high-frequency patterns within the multivariate context. To clearly separate these responsibilities, we introduce a frequency-aware supervision that aligns the global path with low-frequency components and the local path with high-frequency residuals. Additionally, we design a gated fusion mechanism that dynamically combines the low-frequency and high-frequency components for improved prediction. We conduct extensive experiments to evaluate the performance of our proposed framework, demonstrating its effectiveness in handling heterogeneous data in federated settings.
Time series forecasting is crucial for the World Wide Web and represents a core technical challenge in ensuring the stable and efficient operation of modern web services, such as intelligent transportation and website throughput. However, we have found that existing methods typically employ a strategy of embedding each time step as an independent token. This paradigm introduces a fundamental information bottleneck when processing long sequences, the root cause of which is that independent token embedding destroys a crucial structure within the sequence—what we term as multi-offset temporal correlation. This refers to the fine-grained dependencies embedded within the sequence that span across different time steps, which is especially prevalent in regular Web data. To fundamentally address this issue, we propose a new perspective on time series embedding. We provide an upper bound on the approximate reconstruction performance of token embedding, which guides our design of a concise yet effective Multi-Offset Time Embedding (MOTE) method to mitigate the performance degradation caused by standard token embedding. Furthermore, our MOTE can be integrated into various existing models and serve as a universal building block. Based on this paradigm, we further design a novel forecasting architecture named Time-TK. This architecture first utilizes a Multi-Offset Interactive KAN (MI-KAN) to learn and represent specific temporal patterns among multiple offset sub-sequences. Subsequently, it employs an efficient Multi-Offset Temporal Interaction mechanism (MOTI) to effectively capture the complex dependencies between these sub-sequences, achieving global information integration. Extensive experiments on 14 real-world benchmark datasets, covering domains such as traffic flow and BTC/USDT throughput, demonstrate that Time-TK significantly outperforms all baseline models, achieving state-of-the-art forecasting accuracy.
With the rapid development of web services, large amounts of time series data are generated and accumulated across various domains such as finance, healthcare, and online platforms. As such data often co-evolves with multiple variables interacting with each other, estimating the time-varying dependencies between variables (i.e., the dynamic network structure) has become crucial for accurate modeling. However, real-world data is often represented as tensor time series with multiple modes, resulting in large, entangled networks that are hard to interpret and computationally intensive to estimate. In this paper, we propose Kronecker Time-Varying Graphical Lasso (KTVGL), a method designed for modeling tensor time series. Our approach estimates mode-specific dynamic networks in a Kronecker product form, thereby avoiding overly complex entangled structures and producing interpretable modeling results. Moreover, the partitioned network structure prevents the exponential growth of computational time with data dimension. In addition, our method can be extended to stream algorithms, making the computational time independent of the sequence length. Experiments on synthetic data show that the proposed method achieves higher edge estimation accuracy than existing methods while requiring less computation time. To further demonstrate its practical value, we also present a case study using real-world data. Our source code and datasets are available at https://github.com/Higashiguchi-Shingo/KTVGL.
Generative latent diffusion models (LDMs) have been extensively applied in various fields yet underperform in time-series prediction. Therefore, We propose the Re-Diffusion model, a latent diffusion approach that generates backbone residuals specifically tailored for time-series forecasting. The model comprises a variational autoencoder that compresses the residuals between the actual future values and the predictions from the backbone into latent space. It also includes a conditional diffusion generator to forecast the potential distribution of these residuals. Our findings reveal that this latent-space methodology particularly enhances existing backbone predictors, by effectively reducing prediction bias through an advanced estimation of complex error distributions. While previous diffusion-based models tend to struggle with long-term forecasting, Re-Diffusion integrates the strengths of diffusion methods, leading to improvements in long-term predictions. Our experimental results indicate that the Re-Diffusion model achieves a 10% promotion over state-of-art predictors, marking a significant advancement in the field of time-series forecasting.
As an important task in modern web technologies, multivariate time series forecasting drives many core functionalities. However, in realistic web-scale environments, sensor failures, privacy filtering, sampling, and instrumentation churn frequently yield missing variables, making training sets complete while test sets contain only a small subset of variables. The challenge lies in utilizing incomplete data for forecasting, which is known as Variable Subset Forecasting (VSF). Distribution shift is inherent to time series and remains in VSF, including inter-series shift as changes in cross-series correlations and intra-series shift as substantial distribution differences within the same series across different time windows. Existing VSF approaches typically impute missing variables and then forecast on the completed series, yet they overlook these shifts and thus underperform in realistic web-scale scenarios. To address these challenges, we propose Shift Resilient Diffusive Imputation (SRDI), a framework tailored to VSF and robust to distribution shift. Specifically, SRDI integrates a divide-conquer strategy with the denoising process, which decomposes the input into invariant patterns and variant patterns, representing the temporally stable parts of inter-series correlation and the highly fluctuating parts, respectively. By extracting spatiotemporal features from each part separately and then appropriately combining them, inter-series shift can be effectively mitigated. Then, we innovatively organize SRDI and the forecasting model into a meta-learning paradigm tailored for VSF scenarios. We address the intra-series shift by treating time windows as tasks during training and employing an adaptation process before testing, which naturally supports robust online forecasting in dynamic web environments. Extensive experiments on four datasets have demonstrated our superior performance compared with state-of-the-art methods. Our code is available at https://github.com/xhhmacau/SRDI.
The strategic planning and reliability of modern web services, from cloud infrastructures to e-commerce platforms, increasingly hinge on accurate long-term forecasting of high-dimensional time series. A fundamental challenge within this task is modeling the intricate point-to-point dependencies that span across both time and variable dimensions. However, many existing methods face restricted direction modeling and computational inefficiency due to their reliance on localized paradigms and Transformer architectures. To address these, we propose replacing Self-Attention with autocorrelation, achieving two key innovations: 1) We propose calculating autocorrelation across both variable and time dimensions, which is a global paradigm, to model point-to-point dependencies. 2) Our proposed Spectral Product Mechanism (SPM) optimizes traditional autocorrelation into a data-driven form suitable for deep learning. Moreover, SPM reformulates autocorrelation as spectral product and reduces the complexity from O(N2) to O(NlogN), while its Hadamard product-based correlation score matrix further reduces core computation to O(N) compared to Self-Attention's O(N2) matrix multiplication. We further propose a Generalized Spectral Product Mechanism (GSPM), which extends traditional autocorrelation by mapping input into distinct feature representations, enabling modeling of complex dependencies through cross-feature correlations. SPM and GSPM surpass current state-of-the-art (SOTA) methods on 14 authoritative benchmarks, collectively securing the top rank on 22 out of 28 metrics, while ranking 1st in time, 2nd in memory, and 2nd in parameter overhead. Source code is available at: https://github.com/lxy-PhD2022/SPM.
Time series anomaly detection aims to identify samples that deviate from a normal sample distribution in a time series, enabling various web-centric applications. Most existing approaches are static, targeting pre-defined types of anomalies. These methods thus fail to work well on streaming time series with changing data distributions and anomaly formats. To contend with such streaming time series and to accommodate memory constraints, we propose the first data-efficient streaming time series anomaly detection framework, called DESS. To accumulate historical knowledge, DESS includes a novel evolving proxy generation module to synthesize a small but informative proxy summarizing the historical data, facilitating data efficiency. Next, DESS employs an innovative heterogeneous temporal feature extraction module to explicitly capture correlations of multi-level time series semantics. Finally, DESS enables fast streaming anomaly detection by employing a parameter-efficient training scheme that only activates a subset of lightweight parameters while ensuring performance. Extensive experiments on real data offer insight into the effectiveness and efficiency of DESS, showing that it is able to outperform the best baselines by up to 17.53% while reducing the training time by up to 64.88%.
Transformer-based foundation models have achieved remarkable progress in tasks such as time-series forecasting and image segmentation. However, they frequently suffer from error accumulation in multivariate long-sequence prediction and exhibit vulnerability to out-of-distribution samples in image-related tasks. Furthermore, these challenges become particularly pronounced in large-scale Web data analysis tasks, which typically involve complex temporal patterns and multimodal features. This complexity substantially increases optimization difficulty, rendering models prone to stagnation at saddle points within high-dimensional parameter spaces. To address these issues, we propose a lightweight Transformer architecture in conjunction with a novel Escape-Explore Optimizer (EEO). The optimizer enhances both exploration and generalization while effectively avoiding sharp minima and saddle-point traps. Experimental results show that, in representative Web data scenarios, our method achieves performance on par with state-of-the-art models across 11 time-series benchmark datasets and the Synapse medical image segmentation task. Moreover, it demonstrates superior generalization and stability, thereby validating its potential as a versatile cross-task foundation model for Web-scale data mining and analysis.
Time series forecasting is crucial for the development of sophisticated web technologies, driving smarter, more responsive, and data-driven web applications. A key to accurate forecasting lies in effectively capturing the intricate dependencies among different variables (channels). While existing channel-dependent methods have shown strong performance by explicitly modeling inter-channel relationships, they face two critical challenges when applied to high-dimensional datasets with thousands of channels. First, the computational complexity of them grows quadratically with the number of channels, leading to significant scalability issues. Second, attention weights reveal that inter-channel dependencies exhibit both local clusters and global structures, yet current methods fail to disentangle these heterogeneous patterns, resulting in mutual interference and degraded forecasting accuracy. To address these challenges, we propose a novel Channel Reordering-Aligned group Fusion Transformer (CRAFT) for high-dimensional time series forecasting. Specifically, we design an energy-based channel reordering mechanism that reorganizes channels into a minimal-energy state, preserving inherent local-global structures. Building on reordered structure, we introduce a group fusion Transformer that explicitly separates local and global dependencies, significantly reducing computational complexity while enhancing representational clarity. Experiments on high-dimensional datasets demonstrate that CRAFT consistently outperforms baselines, achieving higher forecasting accuracy with lower computational overhead.
The World Wide Web needs reliable predictive capabilities to respond to changes in user behavior and usage patterns. Time series forecasting (TSF) is a key means to achieve this goal. In recent years, the large language models (LLMs) for TSF (LLM4TSF) have achieved good performance. However, there is a significant difference between pretraining corpora and time series data, making it hard to guarantee forecasting quality when directly applying LLMs to TSF; fine-tuning LLMs can mitigate this issue, but often incurs substantial computational overhead. Thus, LLM4TSF faces a dual challenge of prediction performance and compute overhead. To address this, we aim to explore a method for improving the forecasting performance of LLM4TSF while freezing all LLM parameters to reduce computational overhead. Inspired by in-context learning (ICL), we propose LVICL. LVICL uses our vector-injected ICL to inject example information into a frozen LLM, eliciting its in-context learning ability and thereby enhancing its performance on the example-related task (i.e., TSF). Specifically, we first use the LLM together with a learnable context vector adapter to extract a context vector from multiple examples adaptively. This vector contains compressed, example-related information. Subsequently, during the forward pass, we inject this vector into every layer of the LLM to improve forecasting performance. Compared with conventional ICL that adds examples into the prompt, our vector-injected ICL does not increase prompt length; moreover, adaptively deriving a context vector from examples suppresses components harmful to forecasting, thereby improving model performance. Extensive experiments demonstrate the effectiveness of our approach.
The World Wide Web thrives on intelligent services that rely on accurate time series classification, which has recently witnessed significant progress driven by advances in deep learning. However, existing studies face challenges in domain incremental learning. In this paper, we propose a lightweight and robust dual-causal disentanglement framework (DualCD) to enhance the robustness of models under domain incremental scenarios, which can be seamlessly integrated into time series classification models. Specifically, DualCD first introduces a temporal feature disentanglement module to capture class-causal features and spurious features. The causal features can offer sufficient predictive power to support the classifier in domain incremental learning settings. To accurately capture these causal features, we further design a dual-causal intervention mechanism to eliminate the influence of both intra-class and inter-class confounding features. This mechanism constructs variant samples by combining the current class's causal features with intra-class spurious features and with causal features from other classes. The causal intervention loss encourages the model to accurately predict the labels of these variant samples based solely on the causal features. Extensive experiments on multiple datasets and models demonstrate that DualCD effectively improves performance in domain incremental scenarios. We summarize our rich experiments into a comprehensive benchmark to facilitate research in domain incremental time series classification.
With the increasing relevance of web mining and content analysis in uncovering mobility patterns from large-scale online data, traffic flow prediction plays a crucial role in proactive urban planning and enhancing the responsiveness of intelligent transportation systems. However, existing traffic flow prediction methods often fail to explicitly capture correlations in continuous multivariate sequences that are naturally suited for trend and periodic pattern extraction by vision models and rely on fixed spatial graphs that neglect the cognitive advantages of granular-ball structures, which limits their ability to model interactions and strengthen spatiotemporal dependencies. To address these challenges, this paper proposes a Cross-domain Mamba framework that integrates Multi-scale Imaging and Granular-ball Computing for traffic flow prediction (MIGC-CMamba). First, a multi-scale sequence imaging method is presented, which converts the original time series into image modality and leverages MambaVision to capture both local and global dependencies. Second, a multi-granularity spatial graph is constructed via granular-ball clustering, which balances global trend representation and local detail preservation. Third, a cross-domain enhancement mechanism adaptively integrates temporal and spatial domains, strengthening spatiotemporal dependencies. Lastly, extensive experiments demonstrate superior performance over state-of-the-art baselines, highlighting how vision-based imaging, cognition-inspired granular-ball modeling, and content-aware mining jointly advance the modeling of spatiotemporal dependencies in traffic flow prediction.