Time Series

Engineering Digital Twins and Prognostics and Health Management (PHM) systems rely on robust perception modules to extract actionable information from heterogeneous and non-stationary time-series data. However, most existing approaches remain task-specific, data-hungry, and difficult to integrate into scalable monitoring and decision-making pipelines. Moreover, purely data-driven models often lack robustness and transferability across varying operating conditions. To address these challenges, this paper proposes a modular foundation model for time-series perception based on a collection of pretrained representation encoders. The framework leverages self-supervised learning on heterogeneous datasets to learn transferable and task-agnostic representations, which can be reused across multiple PHM tasks. A gating mechanism is introduced to dynamically select relevant encoders for a given target dataset, enabling conditional computation and adaptive model composition. The selected representations are projected into a shared latent space and aggregated using a Transformer-based self-attention module that explicitly models cross-encoder interactions. The resulting architecture supports multiple downstream tasks, including imputation, long-term forecasting, and few-shot learning, through lightweight task-specific heads, while keeping pretrained encoders frozen during adaptation. Extensive ablation studies demonstrate the complementary roles of self-supervised pretraining, encoder selection, representation alignment, and adaptive aggregation. Experimental results on the ETT benchmark show competitive performance across tasks, while a real-world industrial case study on virtual sensing for hydro-generator rotor temperature highlights the practical relevance of the approach.

Time series forecasting remains challenging when the underlying data contain rare but critical extreme events. This issue is particularly important in hydrologic forecasting, where streamflow distributions are often highly skewed and extreme peaks can have substantial impacts on flood monitoring, water resource management, and early warning systems. Although Transformer-based forecasting models have achieved strong performance by modeling long-range temporal dependencies, they typically treat all time points uniformly and may therefore underrepresent rare extreme patterns. In this paper, we propose the Extreme-Adaptive Transformer (Exformer), a forecasting framework designed to explicitly model temporal dependencies involving both normal and extreme events. Exformer introduces an extreme-adaptive attention mechanism composed of three sparse components: Local, Stride, and Extreme. The Local and Stride components capture short-term and periodic temporal dependencies, respectively, while the Extreme component selectively models event-aware dependencies between normal and extreme streamflow patterns. Experiments on four real-world hydrologic streamflow datasets show that Exformer achieves superior 3-day forecasting performance compared with state-of-the-art baselines. Our findings demonstrate that explicitly incorporating extreme-aware attention improves the forecasting capacity of Transformer models on imbalanced time series with rare but consequential events.

Transformer architectures have shown strong potential in time series forecasting, where multi-head self-attention is widely used to capture temporal dependencies across historical timestamps. However, standard self-attention has quadratic time and memory complexity with respect to the look-back length. This cost may limit its use in resource-constrained or high-throughput forecasting systems, where fast and memory-efficient inference is important. Through qualitative and quantitative analyses, we observe that self-attention maps in time series forecasting often contain redundant patterns across different timestamps. This phenomenon can be related to the repeated temporal patterns and relatively stable temporal correlations in many real-world time series. Motivated by this observation, we propose Self-Gating Attention (SGA), a plug-and-play attention mechanism that represents the attention score with a shared learnable matrix and an input-dependent residual component. The shared matrix captures common attention patterns, while the residual component captures input-dependent variations. In this way, SGA avoids the query and key projections used in standard attention score computation, leading to linear time and score-matrix memory complexity with respect to the look-back length. We integrate SGA into several forecasting backbones and compare it with standard self-attention and lightweight attention variants on nine publicly available real-world datasets covering electricity, finance, weather, medical monitoring, human activity, and climate records. The results show that SGA improves inference efficiency on public benchmarks while maintaining competitive forecasting performance against state-of-the-art attention mechanisms. These benchmark results provide deployment-oriented evidence.

Time series foundation models (TSFMs) have shown strong zero-shot forecasting performance, but their generalization in covariate-driven, non-stationary settings is underexplored. Electricity price forecasting (EPF) presents a challenging testbed due to complex temporal dependencies, distributional shifts, and strong reliance on structural and contextual information. We propose a two-dataset-benchmarking framework for EPF to mitigate contamination risk and enable fair evaluation of TSFMs. We examine key aspects of EPF including point and probabilistic forecasting performance, tail behavior, price spikes, and comparisons against domain-specific methods. We find that TSFMs are highly competitive and often outperform general-purpose baselines. Yet, their performance depends critically on covariate support, and they do not consistently surpass domain-specific methods tailored to EPF. Interestingly, simple ensembles of TSFMs and domain-specific methods appear to have significant potential, suggesting that the two approaches capture complementary predictive information.

Anomaly detection is a critical and evolving field in Machine Learning, with applications targeting different domains such as cybersecurity, finance, healthcare, manufacturing and IoT (Internet of Things) systems. Traditionally, anomaly detection algorithms have been designed using both supervised and unsupervised learning paradigms. The fundamental challenge in real-world anomaly detection scenarios is related to the inherent class imbalance (anomalies are typically rare) and, for supervised methods, to the scarcity of labelled anomalous data. Indeed, labelling is both expensive and time-consuming. Conversely unsupervised methods do not require labelling, but may suffer from high false positive rates when deployed in safety-critical applications. In this work we introduce a novel unsupervised algorithm for anomaly detection in time series based on the Haar discrete wavelet and a suitably designed $t$-test. We establish the theoretical foundation of the proposed $t$-test and, through extensive experimentation across 343 datasets, demonstrate that our algorithm outperforms state-of-the-art unsupervised and self-supervised benchmarks.

Low-voltage load forecasting is an important component in current and future energy systems with a high degree of electrification and decentralized generation. However, current forecasting methods require significant manual effort, often lack uncertainty estimation and proper peak prediction, and they are often not adequately evaluated in terms of grid requirements. In the present study, we provide an extensive evaluation of short-term net load forecasts of 200 real-world low-voltage feeders with a focus on the rapidly evolving time series foundation models. Our study compares Chronos-Bolt, Chronos-2 and TabPFN-TS to six baseline models and demonstrates superior performance, in particular for Chronos-2. An ablation study, in which weather covariates are omitted, shows that time series foundation models adapt to increased uncertainty, despite the importance of weather information. A novel application-oriented metric links the model's forecasting capabilities in peak prediction to the trade-off in grid asset planning and operation between cost reduction and minimizing the risk of failure.

We propose a model agnostic methodology to measure lag relevance in machine learning forecasting models applied to univariate time series. Particularly, we are working in the context of time series using the frameworks of Ghost variables and Shapley values, together with additive importance measures, to introduce the auto-relevance and partial auto-relevance functions as the lag importance values. Additionally, we propose a novel method to replace absent features in coalition based methods with a one step forecast from the same model. We evaluate these proposals under different simulations and real data cases. This combined framework perspective is particularly suitable for time series. In addition, to show our discoveries we use a pull of models from the seasonal ARMA family and recurrent neural networks. We found that the calculated relevance measures successfully demonstrate the expected lag structure in almost all cases.

Time series are central to modern data mining applications, from industrial telemetry and server metrics to finance and physiology, yet time-series self-supervised learning often depends on view and augmentation choices that encode domain-specific invariances. We study how an SSL recipe behaves when its method-specific configuration is reused unchanged after the pretraining signal family changes, framing this as a fixed-recipe stress test rather than a comparison against optimally tuned methods. We introduce Latent Euclidean Next-Embedding Prediction Architecture (LeNEPA), a no-augmentation next-latent-token objective with a causal backbone. LeNEPA replaces the stop-gradient/EMA stabilization used by vanilla NEPA with SIGReg-based isotropy regularization and computes the predictive loss in a lightweight projected space that is discarded for evaluation. We compare LeNEPA with an ECG-tuned JEPA recipe under a fixed-horizon frozen-probe protocol on PTB-XL and Diag, a synthetic diagnostic corpus generated with Aionoscope. Both methods are retrained independently on each dataset while keeping their method-specific recipes unchanged. In this protocol, the ECG-tuned JEPA recipe is strong in-domain on PTB-XL but weaker when reused unchanged on Diag, whereas LeNEPA preserves useful frozen-probe gains on both datasets. Learning curves suggest faster early representation acquisition: LeNEPA reaches 80% of its final AUROC/AUPRC gain after 2--5k updates, compared with 5--10k updates for the faster JEPA readout. As a separate external frozen-encoder check, a CauKer-pretrained LeNEPA variant reaches 77.65% mean UCR-128 Random-Forest accuracy in a single-seed, best-checkpoint run, within 1.16 points of Mantis and within 0.24 points of MOMENT (77.89%). Overall, the results support no-augmentation latent prediction as a useful candidate recipe for low-retuning time-series SSL.

Time-series models are often evaluated by what they can forecast or classify, but those scores do not show whether their representations preserve the process state a user may want to inspect: event timing, phase, amplitude, frequency, or regime variables. We introduce Aionoscope, a generator-based diagnostic tool for debugging latent-state accessibility in frozen time-series representations. Aionoscope separates process generation from observation rendering, producing seeded synthetic streams with exact categorical and dense labels across mixture complexity and nuisance variation. We instantiate Aionoscope as Primitive Process Mixtures and evaluate 37 model-plus-adapter systems with a common pooled linear-probe protocol. The main result is a mismatch between coarse and fine-grained accessibility. Most systems make component presence easy to recover, but expose dense process state much less reliably: the highest observed dense-probe row reaches 0.689 mean masked $R^2$, while a dense-feature oracle reaches 0.999. This is the failure mode Aionoscope is designed to surface: a representation can look informative at the level of "what kind of signal is present" while hiding the timing, phase, amplitude, frequency, or regime variables needed for debugging.

Despite the increasing sophistication of industrial AI systems, the ability to reliably detect subtle and noisy anomalies in complex time series data remains a critical yet unresolved challenge. In large-scale industrial applications, labeling time series data is often prohibitively expensive and time-consuming, making unsupervised learning a practical and widely adopted approach. However, existing unsupervised methods frequently struggle to distinguish near-normal anomalies from normal patterns and are vulnerable to noise contamination within normal samples. To address these limitations, we propose a novel framework that leverages active learning to iteratively enhance the performance of unsupervised models. Our framework's core contributions are (1) a masked time-series reconstruction feedback strategy that forces the model to learn robust temporal dependencies, and (2) a minimax learning strategy that promotes robustness by differentially treating normal and abnormal samples. This process encourages the model to better capture the dynamics of subtle and noisy patterns. The proposed framework is evaluated across 28 test cases involving four multivariate time-series datasets and seven unsupervised backbone models. Experimental results demonstrate a 12.39% improvement in AUC compared to the original models, confirming that our method can be readily integrated into existing unsupervised reconstruction-based anomaly detection systems to significantly enhance their performance.

The generation of synthetic relational databases often involves modeling complex temporal dynamics, such as transaction logs or event sequences. A significant challenge in this domain is the handling of categorical time series (e.g., status codes), where standard encoding methods like one-hot encoding fail to capture intrinsic frequency-domain features such as seasonality and cyclicity. In this paper, we introduce Sequential RC-TGAN (Seq. RC-TGAN), a temporal extension of the RC-TGAN framework, equipped with a novel integrated loss function based on the \textit{Spectral Envelope Theory}. This differentiable loss allows the generator to directly optimize the preservation of latent periodic structures via backpropagation. While spectral envelope theory is inherently designed for categorical sequences, we extend this frequency-domain regularization to continuous time series by employing a Variational Gaussian Mixture Model (VGM) discretization strategy. To establish a mathematically rigorous evaluation standard, we simulate categorical time series governed by a parameter $α$, with exactly known theoretical spectral envelopes. Integrating these dynamic sequences into the child tables of a relational database yields a robust ground-truth benchmark for evaluating the frequency-domain fidelity of our generative framework. Furthermore, we address the lack of robust evaluation standards for relational time series by proposing two new metrics: Spectral Density Divergence and Spectral Envelope Divergence. Experimental results on real-world datasets, as well as our simulated benchmarks, demonstrate that our end-to-end approach significantly outperforms state-of-the-art systems in reproducing cyclic patterns and long-term seasonality across both categorical and continuous features.

Electroencephalography (EEG) foundation models aim to learn generalizable representations from large-scale brain recordings. However, the role of temporal feature extractors and whether pretrained time-series foundation models (TSFMs) can be effectively transferred to this setting remains underexplored. We conduct a controlled comparison of three temporal feature extraction strategies, including a linear baseline, a convolutional encoder, and a frozen pretrained TSFM (MOMENT), within a unified EEG foundation model. We evaluate their impact on representation quality using two downstream tasks: motor imagery and emotion recognition. Results reveal different trends across the evaluated benchmarks. On the motor imagery dataset, simple temporal representations perform competitively, whereas the emotion dataset benefits from richer temporal modeling. Although not specifically adapted to EEG, the pretrained TSFM serves as an effective temporal feature extractor, suggesting that general-purpose time-series representations can be transferred as frozen temporal feature extractors within EEG foundation models.

In many real-world applications, such as retail sales, energy usage, and supply chain planning, forecasting is performed across hierarchical structures. These structures often represent aggregations (e.g., products to categories to regions), where forecasts must not only be accurate but also coherent, meaning that lower-level predictions sum correctly to higher-level forecasts. Traditional statistical methods, such as Bottom-Up and MinT, enforce coherence through post-processing but fail to model complex nonlinear temporal dependencies and covariate interactions. We propose Hierarchical Temporal Fusion (HTF), a novel extension of the Temporal Fusion Transformer (TFT) that integrates structured hierarchical embeddings with a coherence-aware loss function to ensure consistent forecasts across all levels of a hierarchy. Rather than applying reconciliation after forecasting, HTF embeds coherence directly into the training objective. The coherence loss penalizes the difference between aggregated child forecasts and their corresponding parent forecasts during training, enabling the model to learn both temporal dynamics and structural consistency simultaneously. We evaluate HTF on two publicly available benchmark datasets: the M5 Walmart forecasting dataset and a publicly available hierarchical energy consumption dataset. Results demonstrate that HTF substantially reduces forecast incoherence while improving forecasting accuracy compared with classical reconciliation methods and deep learning baselines. In addition, attention visualization and embedding analysis provide insight into how temporal and structural information contribute to hierarchical forecasting performance.

Generative models have achieved remarkable success in data synthesis, though recent advances driven by increasing model scale have introduced challenges in computational cost and efficiency. Quantum machine learning offers a promising alternative, representing complex data distributions using compact, highly expressive models. Here, we propose QDiffusion-TS, the first quantum generative diffusion model for time series synthesis, and validate it on the IQM quantum processor. The framework extends a classical diffusion architecture by replacing feed-forward components within the denoising transformer with quantum neural networks, yielding a hybrid quantum transformer that reduces the number of trainable parameters in each replaced component by nearly three orders of magnitude. Evaluated on financial time series from Apple and Amazon, the model generates synthetic data that more accurately reproduces the real distributions, reducing Wasserstein distance by approximately 44% relative to its classical counterpart across both datasets. In a downstream forecasting task, augmentation with the generated data improves predictive performance by up to 71% in RMSE over a baseline trained solely on real data. These results show that quantum enhanced architectures can consistently match and frequently surpass classical performance with substantially fewer parameters, establishing a practical framework towards more efficient and scalable data-driven generative modelling.

Time-series forecasting research has been moving steadily toward larger architectures, from specialized transformers to general-purpose foundation models, on the assumption that capacity is what unlocks accuracy. We take the opposite position: most of the gap can be closed at far lower cost by tuning preprocessing rather than scaling models. We use Ridge regression as the testbed, since it has a closed-form solution and interpretable weights, which let the optimal hyperparameters be read off the search directly. We search over context length, local normalization, regularization, and augmentation on eight standard benchmarks and find three patterns. (1) Optimal lookback is strongly series-specific and often non-monotonic in forecast horizon, with fitted power-law exponents ranging from $+0.46$ on ETTm2 to $-0.19$ on Exchange and Traffic, challenging the convention that longer horizons need longer history. (2) Normalizing over a learned trailing fraction of the context, rather than its entirety, is almost universally preferred. (3) Series within the same dataset often disagree on hyperparameters; the optimal degree of cross-series sharing varies from fully shared to fully per-series. The resulting models beat prior linear forecasters on most dataset-horizon entries and exceed Transformer, MLP, and CNN baselines on six of eight benchmarks. The optimized hyperparameters also serve as a diagnostic on the data itself, revealing structures that larger models absorb silently into their learned parameters. We provide an accompanying interactive online demonstration and the code at https://sakanaai.github.io/SearchCast/.

We study the problem of model selection among probabilistic forecasting models evaluated on datasets of multiple time series. The performance of a model on a single time series is quantified by the average value (score) of a proper scoring rule over a test set, but extending model selection to data sets of time series requires aggregating these scores. Common approaches either rely on scaling scores and averaging them (mean scaled score) or avoid scaling by using alternative statistics such as mean ranks or win rates. However, these approaches can yield conflicting conclusions. We show that such discrepancies arise from the skewness of the distribution of the scores, which is particularly pronounced when test sets are short. The skewness can cause non-mean criteria (e.g., mean rank, median, win rate) to select misspecified models. In contrast, the mean score is immune from this problem. We further show that, as the size of the test sets increases, all aggregation criteria converge to the same model selection decision, mitigating these discrepancies. Our experiments on intermittent demand time series, including data from the M5 competition, highlight the importance of sufficiently large test sets; the mean scaled score appears to be the more reliable approach, also because empirically we found its decision to remain consistent when different scaling factors are adopted.

From climate teleconnections to gene regulation, modern time-series datasets encompass tens or hundreds of interacting variables, making causal discovery increasingly challenging. Constraint-based methods offer statistical rigor but their nonlinear CI tests are infeasible at scale, while score-based alternatives avoid CI testing but require arbitrary thresholds to binarize continuous edge scores. We propose GRACE ($\textbf{G}$ated $\textbf{R}$efinement for $\textbf{A}$ccurate $\textbf{C}$ausal $\textbf{E}$dge discovery), which refines constraint-based discovery using Hard Concrete gates with $L_0$ regularization: each candidate edge has an independent gate whose values concentrate near 0 or 1, yielding a clean bimodal separation that makes the binary decision robust, unlike the narrow, overlapping score distributions produced by $L_1$ and attention-based methods. A fast linear CI skeleton provides high-recall candidates; a single gated model then prunes false positives by learning which edges genuinely improve prediction, with automatic regularization adapted to problem dimensions and skeleton density. Systematic experiments on synthetic benchmarks, spanning diverse graph topologies (scale-free, Erdős-R'enyi, small-world) and dimensionalities up to $d=100$, show that GRACE substantially improves F1 over its base CI method while maintaining high precision, and outperforms attention-based and score-based alternatives. GRACE matches or exceeds expensive nonlinear CI tests at a fraction of the cost ($75\times$ faster). On a real-world river flow dataset, where rainfall confounders, variable propagation lags, and distributional shifts violate standard assumptions, a temporal bootstrap variant of GRACE recovers 9 of 11 causal edges along the Elbe River with only 1 false positive ($F_1 = 0.86$, AUROC${} = 0.99$), reducing the skeleton's 106 false positives by 99%.

Time series classification involves learning a mapping from a continuous, temporally ordered sequence of real-valued observations to a discrete response variable, like class labels. This task is fundamental in domains, including health monitoring, where the temporal structure of data is critical for accurate prediction. Dynamic Time Warping (DTW) is a standard technique for measuring similarity between sequences varying in time or speed. However, DTW is restricted to discrete point matching. To move beyond pairwise alignment, we propose a theoretical framework that learns mappings between real-valued functions. These mappings approximate the flow associated with the characteristic curves of a linear transport equation with a space-dependent velocity field, providing a diffeomorphic transformation between two time series. Using the method of characteristics, we transform this partial differential equation into ordinary differential equations (ODEs) modeling system dynamics. The objective function used to learn these ODEs derives from the fundamental theorem of calculus. To enable flexible, expressive representations of the velocity field, we utilize reproducing kernel Hilbert spaces and optimal control methods. Our method, Diffeomorphic Time Warping (DiffTW), provides a theoretically grounded dissimilarity measure. Using a 1-nearest neighbor classifier, DiffTW outperforms DTW on 60 of 86 datasets.

Deep learning methods have achieved state-of-the-art in time series forecasting, yet their accuracy varies considerably across samples, as some instances remain inherently difficult to predict. Reject option mechanisms, which allow models to abstain from high-risk predictions, are well established in classification and regression but underexplored in forecasting. Existing abstention strategies typically rely on proxies, such as the width of the prediction interval or learned confidence scores derived from forecasts. However, these approaches are inherently tied to the training domain, limiting their ability to generalize. We propose a selective forecasting framework that addresses this limitation by modeling the empirical percentile of forecasting errors, that is, a scale-invariant statistic, based on structural characteristics extracted from recent lags via metalearning. By decoupling the rejection decision from the forecast itself and grounding it in domain-agnostic features, the framework enables effective abstention transfer across heterogeneous time series. Experiments in both in-domain and transfer learning settings show that rejecting samples predicted as challenging consistently improves forecasting accuracy across coverage levels.

Epidemic forecasting models typically rely on surveillance data reported over administrative regions, treating them as atomic units, thereby obscuring sub-regional spatial structure that shapes disease dynamics. We introduce a spatially structured multimodal epidemic forecasting setting that integrates region-level temporal surveillance data with spatially localized auxiliary signals that are misaligned in resolution and structure, reflecting realistic public health reporting constraints. Building on this formulation, we propose M-SPICE (Multimodal SPatIal Context for Epidemic Forecasting), a structure-aware spatiotemporal forecasting framework that performs joint reasoning over temporal disease dynamics and spatial context via attention-based multimodal fusion, allowing spatial signals to selectively condition temporal representations across forecast horizons. We evaluate our approach on real-world COVID-19, influenza, and influenza-like illness (ILI) forecasting tasks under realistic real-time evaluation protocols. Across all forecasting settings, our method consistently outperforms state-of-the-art multivariate time-series, multimodal, and epidemiological forecasting baselines while maintaining strong probabilistic forecasting performance. Finally, interpretability analyses reveal when, where, and how spatial signals are leveraged, highlighting settings in which purely temporal, region-aggregated models are most likely to fail.

Time series analysis has recently been coupled with Large Language Models (LLMs) to leverage their reasoning and world knowledge capabilities, yet gains remain limited. We attribute this to a fundamental mismatch between existing task formulations and LLM strengths: most settings reduce time series understanding to curve-fitting systems, focusing on low-level prediction while ignoring the semantic, contextual, and reasoning-intensive nature of real-world temporal decision-making.To address these limitations, we introduce TSCognition, a multimodal benchmark for multi-dimensional time series reasoning. It collects real-world time series and textual information from 15 public sources and constructs approximately 41K QA samples around five cognitive reasoning tasks: Decoding, Grounding, Inferring, Extrapolating, and Acting. Building on this, we further propose TSAlign, a unified framework that encodes time series into compact patch-level representations and aligns them with semantic directions in the LLM embedding space via gated residual injection and multivariate fusion.Experiments show that TSAlign outperforms existing LLM, VLM, and time series QA baselines on TSCognition and the publicly available TimerBed benchmark while substantially reducing computational cost.Code is available at: https://github.com/EIT-NLP/CognitiveTSR

Supervised learning demands large quantities of labeled data, a bottleneck that is expensive and reliant on domain-specific expertise. Self-supervised learning, particularly contrastive learning, has emerged as a compelling alternative, enabling rich representation learning directly from unlabeled data. Yet its success hinges critically on the design of positive and negative sample pairs. Existing approaches for time series rely on hand-crafted augmentations and masking heuristics that embed strong domain assumptions, often limiting generalization across diverse temporal patterns and potentially introducing spurious correlations. In this work, we challenge this paradigm by demonstrating that explicitly encoding temporal shift invariance through a simple, deterministic view construction is sufficient to learn strong representations for time series classification. By exploiting temporal structure, our method, Shift Invariant Feature Training (ShiFT), achieves state-of-the-art performance on six diverse real-world time series benchmark datasets, as well as the UCR and UEA archives, while reducing training time. Beyond empirical performance, we present a systematic analysis of contrastive learning dynamics in time series settings, examining the effects of batch size and the number of negatives on downstream performance. Our findings provide practical insights for designing efficient contrastive learning frameworks for time series representation learning. The source code is publicly available at https://github.com/sfi-norwai/ShiFT.

We introduce RocketPFN, a training-free pipeline for time series classification that combines random convolutional feature extraction (Rocket) with in-context classification via a pretrained tabular foundation model (TabPFN v2.5). On 92 UCR datasets (30-resample protocol), RocketPFN matches HC2, the strongest published method on the archive, in mean accuracy (both 0.900, Wilcoxon p=0.50), with no training on the target data and a median inference time of 30 seconds per fold. It also significantly outperforms every individual classifier in the HC2 ensemble. On UEA (20 datasets) the difference is likewise not statistically significant. A separate comparison concerns TSC foundation models: when paired with the same downstream classifier, MOMENT, Mantis, and MantisV2 are all significantly outperformed by RocketPFN using fewer extracted features and no learned parameters (p<0.001 in each case). This holds even when the encoders were pretrained on corpora that include the UCR training samples. We propose this two-stage pipeline as a reference point for evaluating zero-shot TSC foundation models.

Real-time process monitoring requires methods that extract actionable information from high-dimensional time-series data. In this work, we present a new approach for process monitoring that combines tools of topological data analysis (TDA) and machine learning. In the proposed approach, we represent multivariate time-series data as manifolds and use topological descriptors to summarize the structure of such data; we then use a neural ordinary differential equation to learn the dynamic evolution of the topological structure of the system. Using real data from an industrial process, we show that this trajectory-based event detection approach is effective at detecting diverse types of events. We contrast this approach against reconstruction-based approaches such as principal component analysis and autoencoders and against a trajectory-based approach that uses Koopman autoencoders.

Time-series anomaly detection has significant practical value for industrial and medical monitoring, as well as other critical domains. Current Transformer- and large-model-based detection approaches incur excessive computational overhead, while existing lightweight alternatives are constrained by insufficient feature extraction and inadequate modeling of dependencies across multivariate variables. To mitigate the above drawbacks, this study develops a lightweight, efficient anomaly detection model, dubbed PaAno, within the patch-oriented representation learning paradigm. In the encoder module, a multiscale feature-extraction backbone is constructed using convolutional kernels with differentiated receptive fields to capture hierarchical temporal characteristics; subsequent cross-scale adaptive attention aggregation, combined with residual connection optimization, further stabilizes feature representation learning. A cross-variable fusion attention module is embedded to explicitly characterize inter-variable correlations, empowering the model to identify anomalous patterns amid intricate operational conditions. Moreover, a novel pretext task based on temporal patch-window sorting is customized to uncover intrinsic structural properties of time series, and triplet loss is leveraged to optimize the patch embedding space for enhanced feature discrimination. Extensive experiments on the TSB-AD benchmark demonstrate that the proposed PaAno achieves state-of-the-art detection accuracy on both univariate and multivariate tasks, yielding significant performance gains across evaluation metrics, including VUS-PR, relative to the original PaAno. Leveraging a compact network design, the presented model achieves favorable computational efficiency, enabling deployment on resource-limited terminals for real-time anomaly inference.

Current time series forecasting (TSF) research predominantly focuses on scale-homogeneous data, where different time series share similar numerical magnitude ranges. However, in real-world industrial scenarios such as financial product sales, different time series often differ by orders of magnitude (scale heterogeneity). Since these series share similar temporal patterns, joint modeling is desirable for better data utilization, yet existing scaling methods either compress low-scale signals (global normalization) or destroy semantic discriminability and amplify inverse-scaling errors (window-based scaling). This paper proposes a self-Adaptive Scale-handling (AS) module that learns adaptive scale factors tailored to each input, preserving semantic discriminability while reducing inverse-scaling errors. AS consists of Scale Calibrating (SC), which calibrates prior mean scaling factors through neural networks, and Scaling Selection (SS), which decides whether to apply calibration or retain the original factor, avoiding over-calibration. Experiments on real-world fund sales datasets from Ant Fortune and Alipay show that AS seamlessly integrates into popular TSF models and consistently improves their performance. The code and dataset are available at the link https://github.com/Meteor-Stars/ASTSF.

Seasonal influenza infects millions of people and causes substantial morbidity and mortality in the United States each year, making accurate short-term forecasting a core public-health need. Reliable forecasts of epidemic time series can inform vaccination timing, hospital staffing, and resource allocation, yet the comparative behavior of modern forecasting architectures on infectious-disease surveillance data remains insufficiently characterized. We address this gap through a systematic evaluation of regional influenza forecasting using influenza-like illness surveillance and influenza-associated hospitalization time series under both temporal and spatial generalization settings for 1-4-week-ahead prediction. We compare classical neural network architectures, numerical transformer-based models, pretrained time series foundation models, and LLM-based forecasting approaches. Across tasks, we demonstrate that a mixture-of-experts model that fuses multiple pretrained forecasters achieves the strongest overall performance, indicating that heterogeneous pretrained representations provide complementary predictive information. Our results further show that numerical transformer-based models produce reliable forecasts, while pretraining provides the largest gains at longer horizons, particularly when the pretraining domain is mechanistically aligned with influenza dynamics. In contrast, LLM-based time series methods underperform relative to numerical forecasters in this setting. Finally, we examine hospitalization information as both an auxiliary covariate and a pretraining source. Hospitalization signals provide complementary improvements in selected settings and clarify when additional surveillance streams enhance the robustness of multi-horizon forecasting. These findings provide actionable guidance on model selection, pretraining strategy, and auxiliary-signal use for influenza preparedness.

Time series anomaly detection plays a crucial role in a wide range of real-world applications. Reconstruction-based methods have become the mainstream paradigm, but they suffer from over-generalization and under-generalization problems, which are challenging to balance. To address this, we introduce multi-scale clustering to enhance reconstruction-based methods. At the representation level, we integrate the cluster center representations of normal patterns to constrain the model to target representative normal patterns for reconstruction, preventing dominance of powerful capacity and representation capability. At the anomaly criterion level, we derive anomaly confidence score based on cluster membership probability and combine it with reconstruction error, providing dual criteria for detection. Furthermore, the effectiveness of the cluster center representations and anomaly confidence score depends on the clustering performance. Accordingly, we extract neighborhood-centered representations for multi-view clustering to improve clustering performance. Extensive experiments on multiple real-world datasets from diverse application domains demonstrate the state-of-the-art performance of SCAN.

Accurate identification of Pinus sylvestris var. mongolica plantations is important for monitoring afforestation quality and ecological restoration in northern Shaanxi. This paper proposes ROSA-TFormer, a radar-optical sensor-aware temporal Transformer for P. sylvestris classification using Sentinel-1/2 time-series data generated on Google Earth Engine. The model integrates separate SAR and optical embedding branches, a sensor-aware gate, and temporal attention pooling to capture multi-source seasonal features. Experiments on monthly and half-month point-level datasets show that ROSA-TFormer achieves strong classification performance, with 99.67% overall accuracy, 99.56% macro F1, and 98.91% P. sylvestris F1 on the HalfMonth-dataBig dataset. Spatial block validation and ablation results further indicate the effectiveness of radar-optical temporal fusion and sensor-aware modeling. The results demonstrate the potential of ROSA-TFormer for point-level P. sylvestris plantation classification, while broader wall-to-wall validation remains necessary.

Multivariate time series anomaly detection (MTSAD) is critical for a wide range of application areas, such as industrial monitoring, cybersecurity, or healthcare. Real-world data is often sparse, irregularly sampled or partially observed, yet existing methods assume uniformly sampled time series. We propose a generative approach based on Latent SDEs that projects the observed time series on a continuous-time stochastic dynamical system, directly being able to handle missing observations and irregular sampling, while also naturally capturing possible cyclic behavior that many real-world use cases inherently possess. Experiments on six anomaly benchmark datasets show that our proposed method ranks first among state-of-the-art baselines. We further demonstrate that our method remains robust under severe data sparsity, while performance significantly degrades for the tested baseline methods. These results highlight latent SDEs as a natural inductive bias for anomaly detection in multivariate time series, especially in presence of real-world irregularities.

Data valuation quantifies the intrinsic quality of individual samples to enable principled data curation, quality control, and robust learning. For time series in critical domains such as healthcare, finance, and industrial monitoring, effective valuation methods are essential yet fundamentally lacking. Existing approaches are either model-dependent, limiting their generalizability, or designed for i.i.d. data and thus fail to capture temporal dependencies, multi-scale patterns, and non-stationary dynamics inherent to sequential data. We introduce TimeLAVA, a learning-agnostic framework that values temporal segments by their marginal contribution to minimizing distributional discrepancy between evaluated and reference data. At its core is a novel Selective Wavelet-based Wasserstein discrepancy combining multi-scale wavelet transforms for temporal localization with unbalanced optimal transport for robustness to distributional shifts. Segment values are efficiently computed via sensitivity analysis without requiring model training and aggregated into point-wise scores. We provide theoretical guarantees linking valuation to model-agnostic generalization and prove bounded sensitivity to outlier contamination. Extensive experiments across anomaly detection, data pruning, and label noise detection demonstrate that TimeLAVA produces significantly more informative value scores than existing methods on diverse real-world datasets.

Decision-making with deep learning-based time series forecasting requires not only accurate predictions but also actionable insights. However, current architectures do not inherently provide such information. Specifically, guidance is needed on how current conditions must be modified to shift from a predicted outcome to a desired future scenario. Counterfactual explanations provide a natural framework for this task, as they represent minimal input changes that alter the model's prediction, indicating when and how intervention is required. Existing approaches rely on instance-wise optimization, leading to inconsistency across instances, high computational costs, and limited applicability in real-time settings. To address these limitations, we reformulate counterfactual generation for time series forecasting as the problem of learning a globally consistent intervention strategy, allowing counterfactuals to be generated through a single shared function. We propose Counterfactual Time Series Explanations (ConTex), a model-agnostic, decomposed architecture comprising a temporal context encoder and a conditional encoder, followed by two heads that capture interventions in terms of temporal relevance and modification strength. This structure overcomes the instability and inconsistency of instance-based approaches by producing targeted, interpretable interventions across time and feature dimensions in a single forward pass, making it suitable for real-time applications. Across multiple forecasting architectures and benchmark datasets, ConTex achieves state-of-the-art validity while generating sparse counterfactuals that minimize the number of necessary interventions. Additionally, our approach reduces computational cost by at least 12-36x compared to instance-wise generation and supports real-time inference at approximately 0.007 seconds.

Cyclicity and trend are important components of time series data and many studies based on cyclicity and trend have achieved good results in long-term time series forecasting. However, we believe that current work neglects the influence of real-world inter-channel correlations in time series data which leads to suboptimal predictions. Furthermore, these models rely on complex designs to capture diverse information so that resulting in low computational efficiency. To address this challenge, we propose McWC, a long-term time series forecasting model that separately models the cyclicity, trend, and inter-channel correlations. Specifically, McWC first decouples cyclical information from data using a multi-layer cyclicity construction module. Then, it extracts inter-channel correlations using multi-layer perceptron. Next, it models and fuses the multi-layer high-frequency and low-frequency information from data using a multi-level wavelet decomposition module. Finally, it aggregates the results of different components to obtain the output. Simultaneously, we decouple intra-channel autocorrelations by calculating a loss function in the frequency domain. Experiments on six real-world datasets demonstrate that McWC achieves state-of-the-art performance, exhibiting excellent computational efficiency and historical information extraction capabilities.

Soil Moisture (SM) modelling constitutes a complex spatiotemporal learning problem characterised by nonlinear environmental interactions, heterogeneous data sources, and limited ground observations. Physics-based approaches, such as water balance models, rely on explicit hydrological equations and high-quality inputs, but their computational cost and scalability limitations restrict large-scale deployment. Data-driven artificial intelligence (AI) methods have emerged as flexible alternatives, enabling the extraction of empirical relationships between soil moisture and environmental variables with reduced modelling assumptions. This work presents a structured survey of AI-based models for soil moisture estimation and classification. Existing approaches are organized into five categories: (a) statistical time-series models, (b) geostatistical methods (c) classical machine learning (ML) models, (d) Deep Learning (DL) models and (e) Probabilistic/Bayesian methods. These models leverage historical soil moisture records, meteorological variables, vegetation indices, topography, soil characteristics, and geolocation data to perform regression or classification tasks.

Molecular dynamics (MD) simulation is computationally demanding, particularly for large-scale systems requiring long-term analysis. Accurate forecast of the outcomes of a MD simulation is not only an attractive scientific challenge but also has substantial practical value. In this work, we developed a data-driven framework, termed ASTEROID (Advanced Spatiotemporal TransformER fOr Inferring Dynamics), that can directly predict multi-step atomic coordinates, avoiding conventional iterative integration. For this purpose, our ASTEROID reformulates MD trajectories as high-dimensional spatiotemporal sequences and integrates the Spatiotemporal Information (STI) Transformation equation into a Transformer architecture. The core innovation of ASTEROID lies in its ability to model multiscale spatiotemporal dependencies. In particular, for spatial dependencies, a local-global self-attention mechanism captures both short- and long-range interactions. For temporal dependencies, an encoder-decoder structure integrates global context with autoregressive forecasting. ASTEROID was evaluated on several quantum-mechanics derived molecular datasets. Our results indicate that ASTEROID achieved not only a higher level of accuracy in multi-step prediction than existing methods on various benchmarks, but also significantly reduced computational cost of conventional MD simulation. Moreover, the model supports iterative multi-step forecasting over an extended time scale. This work establishes a robust and generalizable data-driven paradigm for accelerating MD simulations.

Joint prediction sets for multivariate time series should control a single event while adapting to cross-coordinate dependence. We study filtered conformal ellipsoids: a frozen state-space filter emits a one-step predictive mean and covariance, and split-conformal calibration is applied to the resulting Mahalanobis scores. The filter is used to choose the ellipsoid shape; conformal calibration chooses the scalar radius, so the construction benefits from a learned predictive covariance without relying on Gaussian tail probabilities for coverage. The main difficulty is that filtered scores are dependent and learned recurrent filters need not contract in their raw hidden state; we therefore analyse contraction in an observable predictive-law quotient that identifies hidden states producing the same future sequence of emitted Gaussian laws. Under a stable Bayes Gaussian-projection filter, covariance bounds, and a finite-horizon observability Fisher condition, small excess Gaussian negative log-likelihood implies contraction of the learned emitted laws. Combined with a threshold-autocovariance envelope this yields a Chebyshev-type approximate coverage bound for filtered split-conformal prediction under dependence; a sharper Bernstein-type bound requires an additional geometric-mixing concentration assumption. Under Gaussian oracle realisability we also obtain a near-oracle log-volume comparison within the class of conditionally valid Gaussian ellipsoid rules. We instantiate the framework with a GCN-GRU filter with diagonal-plus-low-rank covariance. On moderate-size graph-native traffic benchmarks (METRLA-$20$ and PEMSBAY-$50$), the learned filter gives sharper at-target ellipsoids than static-covariance and non-filter baselines; at full-graph scale and on non-graph-native datasets, factor and copula baselines can be stronger.

Large language models (LLMs) are increasingly being used for automated decision-making systems in finance, healthcare, or environmental monitoring. Time series data are ubiquitous in these fields, yet hard to process automatically. Can time series be analyzed by LLM agents? We examine three approaches: providing the agent with raw numerical data, using the LLM as a coding agent, or a combination of both. In the coding agent setup, the model iteratively queries the data using Python code. Using two time series understanding benchmarks, we show that agents with code access can outperform models processing raw data by up to 10%. However, even the best performing agent still answers about 22-34% of the questions incorrectly. To get insights into models' strategies and reasoning gaps, we analyze the model outputs with a strong LLM judge. Our analysis reveals that coding agents can select appropriate statistical tests, but often miss important nuances. Meanwhile, models with access to raw data can reach the right conclusions using back-of-the-envelope calculations.

High-quality time series forecasting is pivotal for real-world decision-making. However, traditional point-wise metrics often fail to reveal complex temporal patterns and align poorly with human intuitive preferences. While the ''LLM-as-a-Judge'' paradigm has revolutionized text evaluation by providing flexible, human-aligned judgment, its application to time series remains largely unexplored. In this paper, we leverage Vision-Language Models (VLMs) as judges for time series forecasting, harnessing their ability to comprehend time series plots grounded in textual information. Specifically, we propose a novel framework integrating micro- and macro-level judgments informed by contextual information to evaluate time series forecasting. To this end, we introduce TimeVista, a comprehensive VLM-as-a-Judge benchmark comprising 5563 time series samples paired with detailed evaluation rubrics. Extensive meta-evaluations demonstrate that VLMs are highly reliable judges, achieving significantly higher consistency with human preferences than conventional metrics. Building upon our benchmark, we comprehensively assess recent Time Series Foundation Models (TSFMs) under the VLM-as-a-Judge paradigm. Our results demonstrate that VLMs serve as robust and interpretable judges, providing a comprehensive, human-aligned standard for evaluating time series models.

We introduce biarchetype analysis for the first time in the context of univariate functional data. This unsupervised methodology extends archetype analysis by simultaneously identifying archetypal structures across both the cases (countries, in our application) and the temporal argument. Both cases and time points are expressed as mixtures of biarchetypes, yielding a concise and highly interpretable representation of complex functional observations. Although biarchetype analysis is not intended as a clustering technique, it offers superior interpretability compared with biclustering approaches, as it is based on extreme, representative patterns rather than average centroids, thereby enhancing human comprehension. We apply the proposed method to 10-year government bond yields of European countries over the period 2001-2025. The results identify three distinct time regimes (the pre-crisis period, the euro-area sovereign debt crisis, and the post-crisis period), and reveal Germany, Greece, and Hungary as country archetypes.

Rare events in time series are critical to model but hard to learn due to data scarcity. Current generative models struggle with extreme values. We observe that rare events leave distinct topological fingerprints - transitions in Betti numbers from point-cloud embeddings - that are more stable and discriminative than statistical moments. We introduce PHINN, a flow-matching framework using dynamic Betti curves as conditioning signals and a persistence landscape loss for homology consistency. It scales to multivariate data, includes a natural-language interface to set Betti targets, supports cross-domain meta-learning and few-shot generation, and provides certified adversarial robustness. On financial, epidemiological, and multi-modal benchmarks, PHINN outperforms statistical and diffusion baselines in topological fidelity (beta-RMSE down 41-63%, transition accuracy up 84%) and matches jump-diffusion models in tail coverage while exceeding them in shape fidelity. All results have 95% confidence intervals.

Synthesizing realistic time series with generative models has wide-ranging applications in real-world scenarios. Despite recent progress, most existing methods are trained under the assumption of abundant training data, which substantially limits their effectiveness in data-scarce settings. In this paper, we propose TimeMoDE, a novel framework that integrates Diffusion Transformers with Mixture-of-Experts to exploit both domain adaptability and diffusion-stage awareness for time series generation under data scarcity. It is pre-trained on a large-scale collection of multi-domain datasets to extract domain-agnostic temporal representations and domain-specific information benefiting generalization during fine-tuning. We propose Domain Prompts to condition expert assignment for indistinguishable noised tokens, mitigating the limitations of capturing inter-dataset relationships. Moreover, we incorporate diffusion timestep signals to equip the experts with awareness of time series degradation variations, facilitating adaptive calibrate to stage-dependent denoising requirements. Extensive experiments demonstrate that TimeMoDE outperforms existing methods under diverse low-data settings. It establishes an innovative paradigm for advanced time series few-shot generation.

Time series data in real-world deployments is overwhelmingly irregular. Observations are asynchronous, missing values are informative rather than random, and sampling frequencies vary across sensors and operational windows. However, existing Time Series Question Answering (TSQA) benchmarks mostly assume regularly sampled inputs, leaving a fundamental gap in understanding how large language models (LLMs) and AI agents perform under irregular conditions. To bridge this gap, we introduce IRTS-ToolBench, a benchmark of 1,700 questions spanning 10 task types across 13 domains. IRTS-ToolBench is designed to be used independently by any researcher working on LLM-based irregular time series analysis, providing standardized inputs and a reproducible evaluation protocol. Code can be found in https://github.com/SanhornC/IRTS-ToolBench.

Time series forecasting models often benefit from historical patterns. Inspired by Retrieval-Augmented Generation (RAG), recent research explored retrieving relevant historical time series segments to enhance forecasting. However, relying solely on time series similarity is often insufficient for retrieval under non-stationarity. To address this, we propose a multimodal approach: a \textbf{S}emantics-\textbf{E}nhanced \textbf{R}etrieval-\textbf{A}ugmented Time Series \textbf{F}orecasting framework, SERAF. Unlike mainstream approaches that depend only on time series similarity, SERAF conducts dual retrieval over the time series and their self-generated textual descriptions. It retrieves two complementary sets of historical patterns and corresponding futures, which are selectively and jointly used to guide future predictions. Experiments across seven real-world datasets demonstrate the effectiveness of SERAF in bridging numerical and semantic views of time series compared with state-of-the-art baselines.

Wearable devices and smartphones generate rich behavioural time series that can support proactive health interventions, yet systematic comparisons of modern forecasting architectures for these data are lacking. In particular, it remains unclear how models generalise across populations, how different architectures respond to participant-level fine-tuning and how forecasting accuracy degrades across multi-day horizons. We benchmark six deep learning architectures, two zero-shot Foundation Models (FM) and statistical baselines on three public datasets encompassing over 800 participants, reporting per-feature metrics for step counts, screen time and sleep duration across 1-8 day horizons. We further conduct a per-feature personalisation study across all six architectures and assess FM transferability across dataset sizes and temporal granularities. Our key findings are: (i) no single architecture dominates, PatchTST leads among trained models while the three runners-up (TCN, MLP, Transformer) show no meaningful performance difference; (ii) the FM TimesFM matches or exceeds trained models zero-shot, especially in low-data regimes and (iii) participant-level fine-tuning reduces per-feature RMSE by 16-60%, with sleep benefiting most and step counts least. These results provide practical guidance on architecture selection, FM applicability and personalisation strategies for mobile health forecasting. To the best of our knowledge, this is the first study to jointly evaluate modern deep learning, FMs and personalisation for multi-horizon behavioural forecasting from wearables.

Large language models (LLMs) have enabled time series (TS) analysis by jointly modeling numerical observations and textual context through a shared token interface. However, TS tokens and prompt tokens exhibit fundamentally different information structures, making uniform token processing inefficient. In this paper, we study token efficiency in TS language modeling from an asymmetric-token perspective. We show that TS tokens have highly uneven spectral contributions, where many tokens share redundant frequency patterns while a small subset preserves critical temporal evidence. We also observe that prompt-token influence attenuates with model depth, suggesting that full prompt retention across all layers is unnecessary. Based on these findings, we develop an adaptive token budgeting framework that compresses TS tokens via frequency-domain structure and progressively reduces prompt tokens across layers. Experiments across forecasting, classification, imputation, and anomaly detection demonstrate up to \textit{\textbf{7.68$\times$}} inference acceleration and performance gains in \textit{\textbf{78%}} of evaluated settings, showing the effectiveness of asymmetric token compression for scalable TS foundation models.

Cloud-computing relies on large-scale networks which are inherently complex systems. In this paper, we present a novel approach to root cause analysis (RCA) of cloud network incidents, leveraging graph-based causal discovery techniques. Our method addresses the limitations of rule-based automation by introducing a spatiotemporal grouping strategy and an automation ontology to reduce the dimensionality of the problem. We construct a causal graph from binary time series data using bivariate Granger causality and conditional independence tests. For inference, we introduce a probabilistic method that assigns edge-specific conditional probabilities as a function of time lag, allowing for interpretable, time-aware root cause scoring via causal graph traversal. We evaluated the system using a labeled dataset of 35 production incidents from a major cloud provider. The model successfully recalled the correct root cause in 85.7% of incidents and produced an exact match in 74.3%. In production, the deployed system has been used in over 800 real-world incidents, with positive qualitative feedback from network engineers. These results highlight the practicality of a data-driven, causal approach to RCA in dynamic and large-scale operational environments.

Time-series clustering remains challenging due to the inherent trade-off between clustering effectiveness and computational efficiency. Similarity-based methods often suffer from quadratic complexity caused by pairwise distance computations, while deep learning-based approaches typically rely on costly iterative training and a large number of trainable parameters. In this paper, we propose MSRGC-Net, an efficient time-series clustering framework that integrates multiscale reservoir computing, granular-ball-based anchoring graph construction, and consensus learning. MSRGC-Net adopts a training-free reservoir computing paradigm to extract multiscale temporal representations from raw time series without backpropagation, significantly reducing computational overhead. To capture the intrinsic structure of the resulting representations, granular-ball computing is employed to adaptively model data distributions via density-consistent regions, yielding compact and robust anchor graph representations. Furthermore, a consensus-based anchoring graph optimization strategy is introduced to effectively align multiscale reservoir representations and integrate complementary information across temporal scales. Extensive experiments on widely used univariate and multivariate benchmark datasets demonstrate that MSRGC-Net consistently outperforms state-of-the-art methods in clustering performance while maintaining superior computational efficiency.

Condition-based Predictive Maintenance (PdM) for truck fleets has gained momentum in recent years. This maintenance strategy aims to minimize unplanned downtimes and reduce costs by monitoring the health status of vehicles and taking proactive action based on their condition. However, the implementation of condition-based PdM systems is challenging due to the large volume of data generated by the trucks, the inherent complexity of detecting failures through sensor data and the difficulties in finding cost-effective trade-offs in the solution's implementation. In this paper, we define and validate a condition-based PdM methodology built on the assumption that the wear-and-tear state of the monitored component can be represented as a monotonically non-decreasing time series. It involves selecting only the most recent observations from the time series and transforming them into a tabular format for classification using machine learning (ML) models designed for tabular data. Our results indicate that the proposed methodology reduces costs on the Scania Component X dataset compared to current state-of-the-art (SOTA) approaches, while also simplifying the modeling process through AutoML.

Large language models (LLMs) have demonstrated strong reasoning and instruction-following capabilities, making them potentially powerful tools for time-series analysis. However, time series lie outside their native textual modality, raising a fundamental question: how should time series be represented so that LLMs can reason about them effectively? Existing work typically serializes raw numerical sequences or fine-tunes pre-trained LLMs on time-series data. These approaches place the burden of extracting temporal structure directly on the LLM, creating a modality mismatch that often degrades performance on long sequences and introduces substantial computational overhead. In this work, we introduce Time-Series-to-Structured-Program representation (T2SP), a deterministic, training-free method that represents a time series as a structured symbolic program. T2SP decomposes time series into trends, periods, and salient events, expressing them in a program-friendly format aligned with the textual and code-like modalities on which LLMs are natively trained. By shifting temporal-structure extraction from the model to the representation itself, T2SP enables off-the-shelf LLMs to leverage their existing reasoning capabilities for time-series understanding. We evaluate T2SP on three reasoning tasks -- editing, captioning, and question answering -- where it consistently improves performance, reduces reasoning time, and lowers failure rates compared with raw-string representations. Our results demonstrate that T2SP provides an effective interface between time series and LLMs.

The deployment of Time-Series Foundation Models (TSFMs) in physical sciences is hindered by a critical trade-off: while these models encode rich, universal temporal dynamics, they suffer from severe distributional misalignment when applied zero-shot to specific scientific domains, and their computational cost prohibits deployment in edge-computing sensor networks. We address a fundamental challenge: How can we extract latent structural knowledge from misaligned foundation models (FM) to train lightweight, specialized forecasters? We propose Gated Uncertainty-Aware Routing for Distillation (Guard), a novel framework that reframes multiteacher distillation as an instance-wise decision process with two adaptive mechanisms: (1) a Contextual Router that dynamically selects the most relevant teacher based on local input statistics, exploiting complementarity across diverse foundation models; and (2) an Uncertainty-Gated Temperature mechanism that acts as a "circuit-breaker," automatically attenuating distillation strength when teacher confidence diverges from domain reality. We evaluate our proposed lightweight framework on four climate-critical domains: meteorology, ecosystem carbon flux, soil moisture, and energy grids. Our method significantly reduces RMSE relative to a fixed-weight multi-teacher distillation baseline, successfully distilling knowledge from pretrained FMs (teachers) even when they exhibit suboptimal zero-shot accuracy due to distribution shift between the original and target data domains. We demonstrate that these domain-misaligned teachers can still serve as critical correctives, outperforming the globally superior FMs on 28.5% of the hardest instances. Ultimately, this enables high-precision scientific forecasting suitable for resource-constrained edge deployment. Code is available at https://github.com/RupasreeDey/GUARD-KDD2026.

Transformer-based models have emerged as leading paradigms in time-series forecasting in recent years, employing self-attention mechanisms to capture long-range dependencies. Despite their success, these single-stage forecasting architectures exhibit persistent systematic residual biases arising from structural discrepancies, unmodeled stochastic components, or inadequate multi-scale temporal representations. This limitation persists when residuals are treated as irreducible noise, precluding adaptive correction of structured error patterns. To address this limitation, we introduce a two-stage, model-agnostic framework that explicitly decouples forecasting and residual learning into distinct stages of representation learning. A base transformer first generates the initial predictions. Subsequently, a dedicated meta-corrector dynamically models structured error patterns across multivariate channels, preserves cross-variable dependencies, and iteratively refines the residual bias of the base transformer. By formalizing this pipeline as a hypothesis space expansion, our framework addresses approximation limitations inherent in single-stage architectures, removes reliance on restrictive assumptions, and enables end-to-end learning of complex error dynamics. Evaluated on eight popular benchmark datasets using established protocols, our approach achieves state-of-the-art performance, with significant improvements in standard metrics (MSE, MAE). The results demonstrate the framework's ability to mitigate systematic biases and enhance robustness to complex temporal dynamics, advancing the practical applicability of transformer-based forecasting models.

Understanding and forecasting lake dynamics is critical for monitoring water quality and ecosystem health across lakes and reservoirs. While machine learning methods have been recently applied to ecological time-series data, existing works assume regular sampling in time and depth, and struggle to generalize across lakes with heterogeneous variables, depths, and observation patterns. To address these limitations, we introduce \textsc{LakeFM}, a foundation model for aquatic systems, pre-trained on large-scale ecological datasets comprising both simulated and observed lakes. Through extensive empirical evaluation, we show that \textsc{LakeFM} learns meaningful representations spanning broader lake-level characteristics, and achieves competitive or often superior-forecasting performance compared to existing time-series foundation and non-foundation models, while producing physically plausible predictions consistent with real-world lake dynamics.

Matrix-valued time series arise in a wide range of applications, such as spatio-temporal data from medical imaging and geophysics. Existing methods are mainly designed for static settings and lack adaptability to streaming and time-varying environments. Adaptive filtering techniques have also been largely limited to data with scalar or vector values, leaving adaptive forecasting for matrix-valued time series inadequately understood. To bridge these gaps, we develop an adaptive tensor regression framework that includes Matrix-on-Matrix (MoM) and Tensor-on-Matrix (ToM) formulations for streaming matrix-valued prediction. The two formulations differ in whether to directly model matrix-valued outputs or to exploit temporal structure via higher-order tensor representations. For the proposed tensor regression framework, we develop stochastic gradient descent (SGD) algorithms for online learning. We show that stacking multiple responses across time into higher-order tensors improves performance; in particular, the ToM achieves lower steady-state error and stronger denoising capability than MoM, motivating our focus on the ToM model. We further characterize the tracking behavior of SGD under time-varying dynamics. From a statistical perspective, we establish fixed-time recovery guarantees for ToM under general low-dimensional structures, including sparsity, low-rankness, and their joint sparselow-rank models.

The Cloud-Edge Continuum (CEC) enables latency-critical applications by distributing resources to the far edge, but its extreme volatility makes proactive Zero Touch Management via time-series forecasting essential. However, orchestrators face a severe "cold start" problem: newly discovered nodes lack the historical data required to train localized predictive models, while generalized models fail to capture unique hardware and microservice behaviors. To solve this, we propose a fully automated time-series prediction architecture driven by a novel data-mixing methodology. At the infrastructure level, we introduce a lightweight, technology-agnostic Resource Exposer (RE) that dynamically discovers nodes and continuously collects customizable telemetry (e.g., compute, network, energy). To overcome the sparsity of these initial local samples, our framework automatically merges them with TimeTrack, our publicly available, high-resolution dataset collected at 45-second intervals. This synergizes TimeTrack's foundational, high-frequency temporal patterns with the precise calibration of the local node data. Processed through a Neural Architecture Search (NAS) engine, the system automatically generates highly accurate baseline models. Experimental results demonstrate that merging the target data with TimeTrack effectively mitigates the cold start challenge. This integration significantly improves forecasting accuracy measured in Mean Squared Error (MSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) and accelerates convergence compared to training on the sparse local samples alone, training solely on generic datasets, or mixing the target data with standard alternative datasets, establishing a robust foundation for continuous MLOps deployment.

Large models for time-series forecasting have been emerged as a promising paradigm for training models on heterogeneous collections of signals. These models typically rely on causal autoregressive architectures, where each observation is sequentially predicted from past. In practice, real-world time-series exhibit non-stationarities, which significantly influence predictive performance. To mitigate this, normalization is commonly employed. However, in efficient causal settings it might induce information leakage from future observations during training. Recent alternatives, including causal normalization and statistics computed from initial observations, have been proposed to address this issue, but their practical implications remain insufficiently understood. In this work, we evaluate normalization strategies for transformer-based large time-series models trained with patching and efficient causal strategy. We showcase that normalization choice significantly influences both training convergence and forecasting performance.

Global wind power capacity, especially in China, is booming, with new farms spanning diverse terrains and climates. The industry urgently needs accurate wind power foundation models to shorten commissioning and accelerate grid connection. This is because site-specific time series models (TSMs) are not well suited to data-scarce scenarios and generalize poorly, while generic large time series models (LTSMs) are mostly limited to univariate inputs and cannot fully exploit static site attributes or the dependencies between power and meteorological covariates, leading to insufficient accuracy. To fill this gap, we propose \textbf{Tyan-WP}, the first wind power foundation model for ultra-short-term probabilistic forecasting. Pretrained on a large-scale wind power dataset covering more than 126,000 U.S. sites over seven years, Tyan-WP further improves zero-shot forecasting through two domain-specific module designs: static site embedding using coordinate, terrain, and ecoregion metadata, and a power-aware meteorological fusion (PAMF) module that models interactions between historical power and meteorological covariates. Under a unified evaluation protocol, Tyan-WP surpasses eight site-specific supervised TSMs on 10 in-domain sites and outperforms eleven generic LTSMs on 127 in-domain sites, reducing MAE by 19.9%, RMSE by 16.6%, CRPS by 22.2%, and AQL by 21.7%, while raising R^2 by 16.7%. It further demonstrates strong cross-geography generalization on six real U.K. sites. These results show that the wind power foundation model can achieve accurate zero-shot forecasting without target-site training, providing a practical pathway for rapid turbine onboarding and probabilistic risk management at new wind farms.

Recently, large time series models (LTSMs) have gained increasing attention due to their similarities to large language models, including flexible context length, scalability, and task generality, outperforming advanced task-specific models. However, prior studies indicate that pre-trained LTSMs may exhibit a poorly conditioned non-convex loss landscape, leading to limited trainability. As a result, direct fine-tuning tends to cause overfitting and suboptimal performance, sometimes even worse than training from scratch, substantially diminishing the benefits of pre-training. To overcome this limitation, we propose Smoothed Full Fine-tuning (SFF), a novel fine-tuning technology. Specifically, we construct an auxiliary LTSM via random initialization to obtain a smoother loss landscape, and then linearly interpolate its weights with those of the pre-trained model to smooth the original landscape. This process improves trainability while preserving pre-trained knowledge, thereby enabling more effective downstream fine-tuning. From an optimization perspective, SFF perturbs sharp minima without significantly harming flat regions, facilitating escape from poor local basins toward smoother and more generalizable solutions. Extensive experiments on benchmark datasets demonstrate consistent improvements across eight representative LTSMs, including Timer, TimesFM, MOMENT, UniTS, MOIRAI, Chronos, TTMs, and Sundial, on diverse downstream tasks. The code is available at the link: https://github.com/Meteor-Stars/SFF.

This paper investigates a novel concept of time series geolocalization, where the goal is to infer the geographic origin of each raw time series. Successful geolocalization can provide spatial context to time series, enabling downstream location-aware applications. We formalize the problem, adapt core ideas from image geolocalization to establish strong baselines, and propose GeoGNN, a two-tower architecture. During training, GeoGNN's spatial tower learns embeddings of geographic cell candidates by leveraging the geographic adjacency graph, while the temporal tower extracts informative representations from time series. During inference, each temporal representation is matched against candidate geographic embeddings using dot-product similarity, combined with an auxiliary classification head, to predict the time series' associated geographic origin. Experiments on large-scale, countrywide electricity-consumption datasets demonstrate that GeoGNN achieves the best performance across datasets and enhances both fine- and coarse-grained geolocalization accuracy by ~27% on average.

Recent advances in Large Language Models (LLMs) have opened new possibilities for time series forecasting by enabling alignment between temporal patterns and pretrained word embeddings. However, most LLM-based methods overlook the heterogeneous nature of time series, where dynamic fluctuations and invariant semantics are entangled. This entanglement introduces spurious correlations during the alignment, as dynamic components act as confounders by simultaneously influencing invariant components and the resulting aligned embeddings. To address this issue, a variable-level alignment framework CVAformer is proposed. CVAformer explicitly disentangles each variable into invariant and dynamic components just before alignment, and applies causal intervention to mitigate the confounding effect of the dynamics. To better support variable-level alignment, CVAformer replaces the standard causal attention in LLMs with a non-causal attention mechanism that captures interactions among variables at each time step. Extensive experiments across long-term, short-term, few-shot, and zero-shot forecasting settings indicate that CVAformer matches or exceeds state-of-the-art performance on most datasets, and in some cases achieves notably better accuracy. Experimental results validate the effectiveness of variable-level alignment and dynamic disentanglement in CVAformer, offering a new perspective for LLM-based time series tasks.

Multivariate time series forecasting requires capturing the continuously evolving correlation structure among interacting variables. Existing state-space models process time series by scanning tokenized temporal or spatial sequences, discarding the evolutionary geometric structure. We address this limitation by introducing manifold constraints into state-space modeling: treating the cross-variable correlation structure as a continuous trajectory on the symmetric positive definite manifold, whose Riemannian geometric features, tangent space linearity, and Frechet mean centrality act as a principled geometric regularizer that guides and stabilizes the selective scanning dynamics of SSMs. We propose SPDM, a geometry-aware SSM architecture that realizes this principle through two cooperating mechanisms: a manifold trajectory path that projects dynamically evolving covariance matrices from the SPD manifold to a Euclidean tangent space, and a geometric gating scheme that directly modulates SSM's internal selective parameters based on geometric signals derived from the manifold trajectory. The parameterization preserves the linear-time complexity of the Mamba parallel scan while embedding rich structural constraints, making the architecture preserve prediction accuracy and computational efficiency simultaneously. Extensive experiments on eleven real-world benchmark datasets establish state-of-the-art forecasting performance, and further studies confirm that geometrically constrained state-space dynamics are the dominant architectural factor behind its performance gains.