TimeCF: A TimeMixer-Based Model with adaptive Convolution and Sharpness-Aware Minimization Frequency Domain Loss for long-term time seris forecasting

Recent studies have shown that by introducing prior knowledge, multi-scale analysis of complex and non-stationary time series in real environments can achieve good results in the field of long-term forecasting. However, affected by channel-independent methods, models based on multi-scale analysis may produce suboptimal prediction results due to the autocorrelation between time series labels, which in turn affects the generalization ability of the model. To address this challenge, we are inspired by the idea of sharpness-aware minimization and the recently proposed FreDF method and design a deep learning model TimeCF for long-term time series forecasting based on the TimeMixer, combined with our designed adaptive convolution information aggregation module and Sharpness-Aware Minimization Frequency Domain Loss (SAMFre). Specifically, TimeCF first decomposes the original time series into sequences of different scales. Next, the same-sized convolution modules are used to adaptively aggregate information of different scales on sequences of different scales. Then, decomposing each sequence into season and trend parts and the two parts are mixed at different scales through bottom-up and top-down methods respectively. Finally, different scales are aggregated through a Feed-Forward Network. What's more, extensive experimental results on different real-world datasets show that our proposed TimeCF has excellent performance in the field of long-term forecasting.

Non-Stationary Time Series Forecasting Based on Fourier Analysis and Cross Attention Mechanism

Time series forecasting has important applications in financial analysis, weather forecasting, and traffic management. However, existing deep learning models are limited in processing non-stationary time series data because they cannot effectively capture the statistical characteristics that change over time. To address this problem, this paper proposes a new framework, AEFIN, which enhances the information sharing ability between stable and unstable components by introducing a cross-attention mechanism, and combines Fourier analysis networks with MLP to deeply explore the seasonal patterns and trend characteristics in unstable components. In addition, we design a new loss function that combines time-domain stability constraints, time-domain instability constraints, and frequency-domain stability constraints to improve the accuracy and robustness of forecasting. Experimental results show that AEFIN outperforms the most common models in terms of mean square error and mean absolute error, especially under non-stationary data conditions, and shows excellent forecasting capabilities. This paper provides an innovative solution for the modeling and forecasting of non-stationary time series data, and contributes to the research of deep learning for complex time series.

Temporal cross-validation impacts multivariate time series subsequence anomaly detection evaluation

Evaluating anomaly detection in multivariate time series (MTS) requires careful consideration of temporal dependencies, particularly when detecting subsequence anomalies common in fault detection scenarios. While time series cross-validation (TSCV) techniques aim to preserve temporal ordering during model evaluation, their impact on classifier performance remains underexplored. This study systematically investigates the effect of TSCV strategy on the precision-recall characteristics of classifiers trained to detect fault-like anomalies in MTS datasets. We compare walk-forward (WF) and sliding window (SW) methods across a range of validation partition configurations and classifier types, including shallow learners and deep learning (DL) classifiers. Results show that SW consistently yields higher median AUC-PR scores and reduced fold-to-fold performance variance, particularly for deep architectures sensitive to localized temporal continuity. Furthermore, we find that classifier generalization is sensitive to the number and structure of temporal partitions, with overlapping windows preserving fault signatures more effectively at lower fold counts. A classifier-level stratified analysis reveals that certain algorithms, such as random forests (RF), maintain stable performance across validation schemes, whereas others exhibit marked sensitivity. This study demonstrates that TSCV design in benchmarking anomaly detection models on streaming time series and provide guidance for selecting evaluation strategies in temporally structured learning environments.

Almost-Optimal Local-Search Methods for Sparse Tensor PCA

Local-search methods are widely employed in statistical applications, yet interestingly, their theoretical foundations remain rather underexplored, compared to other classes of estimators such as low-degree polynomials and spectral methods. Of note, among the few existing results recent studies have revealed a significant "local-computational" gap in the context of a well-studied sparse tensor principal component analysis (PCA), where a broad class of local Markov chain methods exhibits a notable underperformance relative to other polynomial-time algorithms. In this work, we propose a series of local-search methods that provably "close" this gap to the best known polynomial-time procedures in multiple regimes of the model, including and going beyond the previously studied regimes in which the broad family of local Markov chain methods underperforms. Our framework includes: (1) standard greedy and randomized greedy algorithms applied to the (regularized) posterior of the model; and (2) novel random-threshold variants, in which the randomized greedy algorithm accepts a proposed transition if and only if the corresponding change in the Hamiltonian exceeds a random Gaussian threshold-rather that if and only if it is positive, as is customary. The introduction of the random thresholds enables a tight mathematical analysis of the randomized greedy algorithm's trajectory by crucially breaking the dependencies between the iterations, and could be of independent interest to the community.

FCPCA: Fuzzy clustering of high-dimensional time series based on common principal component analysis

Clustering multivariate time series data is a crucial task in many domains, as it enables the identification of meaningful patterns and groups in time-evolving data. Traditional approaches, such as crisp clustering, rely on the assumption that clusters are sufficiently separated with little overlap. However, real-world data often defy this assumption, exhibiting overlapping distributions or overlapping clouds of points and blurred boundaries between clusters. Fuzzy clustering offers a compelling alternative by allowing partial membership in multiple clusters, making it well-suited for these ambiguous scenarios. Despite its advantages, current fuzzy clustering methods primarily focus on univariate time series, and for multivariate cases, even datasets of moderate dimensionality become computationally prohibitive. This challenge is further exacerbated when dealing with time series of varying lengths, leaving a clear gap in addressing the complexities of modern datasets. This work introduces a novel fuzzy clustering approach based on common principal component analysis to address the aforementioned shortcomings. Our method has the advantage of efficiently handling high-dimensional multivariate time series by reducing dimensionality while preserving critical temporal features. Extensive numerical results show that our proposed clustering method outperforms several existing approaches in the literature. An interesting application involving brain signals from different drivers recorded from a simulated driving experiment illustrates the potential of the approach.

TIMING: Temporality-Aware Integrated Gradients for Time Series Explanation

Recent explainable artificial intelligence (XAI) methods for time series primarily estimate point-wise attribution magnitudes, while overlooking the directional impact on predictions, leading to suboptimal identification of significant points. Our analysis shows that conventional Integrated Gradients (IG) effectively capture critical points with both positive and negative impacts on predictions. However, current evaluation metrics fail to assess this capability, as they inadvertently cancel out opposing feature contributions. To address this limitation, we propose novel evaluation metrics-Cumulative Prediction Difference (CPD) and Cumulative Prediction Preservation (CPP)-to systematically assess whether attribution methods accurately identify significant positive and negative points in time series XAI. Under these metrics, conventional IG outperforms recent counterparts. However, directly applying IG to time series data may lead to suboptimal outcomes, as generated paths ignore temporal relationships and introduce out-of-distribution samples. To overcome these challenges, we introduce TIMING, which enhances IG by incorporating temporal awareness while maintaining its theoretical properties. Extensive experiments on synthetic and real-world time series benchmarks demonstrate that TIMING outperforms existing time series XAI baselines. Our code is available at https://github.com/drumpt/TIMING.

Pets: General Pattern Assisted Architecture For Time Series Analysis

Time series analysis has found widespread applications in areas such as weather forecasting, anomaly detection, and healthcare. However, real-world sequential data often exhibit a superimposed state of various fluctuation patterns, including hourly, daily, and monthly frequencies. Traditional decomposition techniques struggle to effectively disentangle these multiple fluctuation patterns from the seasonal components, making time series analysis challenging. Surpassing the existing multi-period decoupling paradigms, this paper introduces a novel perspective based on energy distribution within the temporal-spectrum space. By adaptively quantifying observed sequences into continuous frequency band intervals, the proposed approach reconstructs fluctuation patterns across diverse periods without relying on domain-specific prior knowledge. Building upon this innovative strategy, we propose Pets, an enhanced architecture that is adaptable to arbitrary model structures. Pets integrates a Fluctuation Pattern Assisted (FPA) module and a Context-Guided Mixture of Predictors (MoP). The FPA module facilitates information fusion among diverse fluctuation patterns by capturing their dependencies and progressively modeling these patterns as latent representations at each layer. Meanwhile, the MoP module leverages these compound pattern representations to guide and regulate the reconstruction of distinct fluctuations hierarchically. Pets achieves state-of-the-art performance across various tasks, including forecasting, imputation, anomaly detection, and classification, while demonstrating strong generalization and robustness.

A Kernel-Based Approach for Accurate Steady-State Detection in Performance Time Series

This paper addresses the challenge of accurately detecting the transition from the warmup phase to the steady state in performance metric time series, which is a critical step for effective benchmarking. The goal is to introduce a method that avoids premature or delayed detection, which can lead to inaccurate or inefficient performance analysis. The proposed approach adapts techniques from the chemical reactors domain, detecting steady states online through the combination of kernel-based step detection and statistical methods. By using a window-based approach, it provides detailed information and improves the accuracy of identifying phase transitions, even in noisy or irregular time series. Results show that the new approach reduces total error by 14.5% compared to the state-of-the-art method. It offers more reliable detection of the steady-state onset, delivering greater precision for benchmarking tasks. For users, the new approach enhances the accuracy and stability of performance benchmarking, efficiently handling diverse time series data. Its robustness and adaptability make it a valuable tool for real-world performance evaluation, ensuring consistent and reproducible results.

Multivariate Long-term Time Series Forecasting with Fourier Neural Filter

Multivariate long-term time series forecasting has been suffering from the challenge of capturing both temporal dependencies within variables and spatial correlations across variables simultaneously. Current approaches predominantly repurpose backbones from natural language processing or computer vision (e.g., Transformers), which fail to adequately address the unique properties of time series (e.g., periodicity). The research community lacks a dedicated backbone with temporal-specific inductive biases, instead relying on domain-agnostic backbones supplemented with auxiliary techniques (e.g., signal decomposition). We introduce FNF as the backbone and DBD as the architecture to provide excellent learning capabilities and optimal learning pathways for spatio-temporal modeling, respectively. Our theoretical analysis proves that FNF unifies local time-domain and global frequency-domain information processing within a single backbone that extends naturally to spatial modeling, while information bottleneck theory demonstrates that DBD provides superior gradient flow and representation capacity compared to existing unified or sequential architectures. Our empirical evaluation across 11 public benchmark datasets spanning five domains (energy, meteorology, transportation, environment, and nature) confirms state-of-the-art performance with consistent hyperparameter settings. Notably, our approach achieves these results without any auxiliary techniques, suggesting that properly designed neural architectures can capture the inherent properties of time series, potentially transforming time series modeling in scientific and industrial applications.

Towards an Introspective Dynamic Model of Globally Distributed Computing Infrastructures

Large-scale scientific collaborations like ATLAS, Belle II, CMS, DUNE, and others involve hundreds of research institutes and thousands of researchers spread across the globe. These experiments generate petabytes of data, with volumes soon expected to reach exabytes. Consequently, there is a growing need for computation, including structured data processing from raw data to consumer-ready derived data, extensive Monte Carlo simulation campaigns, and a wide range of end-user analysis. To manage these computational and storage demands, centralized workflow and data management systems are implemented. However, decisions regarding data placement and payload allocation are often made disjointly and via heuristic means. A significant obstacle in adopting more effective heuristic or AI-driven solutions is the absence of a quick and reliable introspective dynamic model to evaluate and refine alternative approaches. In this study, we aim to develop such an interactive system using real-world data. By examining job execution records from the PanDA workflow management system, we have pinpointed key performance indicators such as queuing time, error rate, and the extent of remote data access. The dataset includes five months of activity. Additionally, we are creating a generative AI model to simulate time series of payloads, which incorporate visible features like category, event count, and submitting group, as well as hidden features like the total computational load-derived from existing PanDA records and computing site capabilities. These hidden features, which are not visible to job allocators, whether heuristic or AI-driven, influence factors such as queuing times and data movement.