A Correction for the Paper "Symplectic geometry mode decomposition and its application to rotating machinery compound fault diagnosis"

The symplectic geometry mode decomposition (SGMD) is a powerful method for decomposing time series, which is based on the diagonal averaging principle (DAP) inherited from the singular spectrum analysis (SSA). Although the authors of SGMD method generalized the form of the trajectory matrix in SSA, the DAP is not updated simultaneously. In this work, we pointed out the limitations of the SGMD method and fixed the bugs with the pulling back theorem for computing the given component of time series from the corresponding component of trajectory matrix.

Semantic-Enhanced Time-Series Forecasting via Large Language Models

Time series forecasting plays a significant role in finance, energy, meteorology, and IoT applications. Recent studies have leveraged the generalization capabilities of large language models (LLMs) to adapt to time series forecasting, achieving promising performance. However, existing studies focus on token-level modal alignment, instead of bridging the intrinsic modality gap between linguistic knowledge structures and time series data patterns, greatly limiting the semantic representation. To address this issue, we propose a novel Semantic-Enhanced LLM (SE-LLM) that explores the inherent periodicity and anomalous characteristics of time series to embed into the semantic space to enhance the token embedding. This process enhances the interpretability of tokens for LLMs, thereby activating the potential of LLMs for temporal sequence analysis. Moreover, existing Transformer-based LLMs excel at capturing long-range dependencies but are weak at modeling short-term anomalies in time-series data. Hence, we propose a plugin module embedded within self-attention that models long-term and short-term dependencies to effectively adapt LLMs to time-series analysis. Our approach freezes the LLM and reduces the sequence dimensionality of tokens, greatly reducing computational consumption. Experiments demonstrate the superiority performance of our SE-LLM against the state-of-the-art (SOTA) methods.

Prediction and Causality of functional MRI and synthetic signal using a Zero-Shot Time-Series Foundation Model

Time-series forecasting and causal discovery are central in neuroscience, as predicting brain activity and identifying causal relationships between neural populations and circuits can shed light on the mechanisms underlying cognition and disease. With the rise of foundation models, an open question is how they compare to traditional methods for brain signal forecasting and causality analysis, and whether they can be applied in a zero-shot setting. In this work, we evaluate a foundation model against classical methods for inferring directional interactions from spontaneous brain activity measured with functional magnetic resonance imaging (fMRI) in humans. Traditional approaches often rely on Wiener-Granger causality. We tested the forecasting ability of the foundation model in both zero-shot and fine-tuned settings, and assessed causality by comparing Granger-like estimates from the model with standard Granger causality. We validated the approach using synthetic time series generated from ground-truth causal models, including logistic map coupling and Ornstein-Uhlenbeck processes. The foundation model achieved competitive zero-shot forecasting fMRI time series (mean absolute percentage error of 0.55 in controls and 0.27 in patients). Although standard Granger causality did not show clear quantitative differences between models, the foundation model provided a more precise detection of causal interactions. Overall, these findings suggest that foundation models offer versatility, strong zero-shot performance, and potential utility for forecasting and causal discovery in time-series data.

FeDaL: Federated Dataset Learning for Time Series Foundation Models

Dataset-wise heterogeneity introduces significant domain biases that fundamentally degrade generalization on Time Series Foundation Models (TSFMs), yet this challenge remains underexplored. This paper rethink the development of TSFMs using the paradigm of federated learning. We propose a novel Federated Dataset Learning (FeDaL) approach to tackle heterogeneous time series by learning dataset-agnostic temporal representations. Specifically, the distributed architecture of federated learning is a nature solution to decompose heterogeneous TS datasets into shared generalized knowledge and preserved personalized knowledge. Moreover, based on the TSFM architecture, FeDaL explicitly mitigates both local and global biases by adding two complementary mechanisms: Domain Bias Elimination (DBE) and Global Bias Elimination (GBE). FeDaL`s cross-dataset generalization has been extensively evaluated in real-world datasets spanning eight tasks, including both representation learning and downstream time series analysis, against 54 baselines. We further analyze federated scaling behavior, showing how data volume, client count, and join rate affect model performance under decentralization.

L-GTA: Latent Generative Modeling for Time Series Augmentation

Data augmentation is gaining importance across various aspects of time series analysis, from forecasting to classification and anomaly detection tasks. We introduce the Latent Generative Transformer Augmentation (L-GTA) model, a generative approach using a transformer-based variational recurrent autoencoder. This model uses controlled transformations within the latent space of the model to generate new time series that preserve the intrinsic properties of the original dataset. L-GTA enables the application of diverse transformations, ranging from simple jittering to magnitude warping, and combining these basic transformations to generate more complex synthetic time series datasets. Our evaluation of several real-world datasets demonstrates the ability of L-GTA to produce more reliable, consistent, and controllable augmented data. This translates into significant improvements in predictive accuracy and similarity measures compared to direct transformation methods.

Salt-Rock Creep Deformation Forecasting Using Deep Neural Networks and Analytical Models for Subsurface Energy Storage Applications

This study provides an in-depth analysis of time series forecasting methods to predict the time-dependent deformation trend (also known as creep) of salt rock under varying confining pressure conditions. Creep deformation assessment is essential for designing and operating underground storage facilities for nuclear waste, hydrogen energy, or radioactive materials. Salt rocks, known for their mechanical properties like low porosity, low permeability, high ductility, and exceptional creep and self-healing capacities, were examined using multi-stage triaxial (MSTL) creep data. After resampling, axial strain datasets were recorded at 5--10 second intervals under confining pressure levels ranging from 5 to 35 MPa over 5.8--21 days. Initial analyses, including Seasonal-Trend Decomposition (STL) and Granger causality tests, revealed minimal seasonality and causality between axial strain and temperature data. Further statistical tests, such as the Augmented Dickey-Fuller (ADF) test, confirmed the stationarity of the data with p-values less than 0.05, and wavelet coherence plot (WCP) analysis indicated repeating trends. A suite of deep neural network (DNN) models (Neural Basis Expansion Analysis for Time Series (N-BEATS), Temporal Convolutional Networks (TCN), Recurrent Neural Networks (RNN), and Transformers (TF)) was utilized and compared against statistical baseline models. Predictive performance was evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Symmetric Mean Absolute Percentage Error (SMAPE). Results demonstrated that N-BEATS and TCN models outperformed others across various stress levels, respectively. DNN models, particularly N-BEATS and TCN, showed a 15--20\% improvement in accuracy over traditional analytical models, effectively capturing complex temporal dependencies and patterns.

FoundationalECGNet: A Lightweight Foundational Model for ECG-based Multitask Cardiac Analysis

Cardiovascular diseases (CVDs) remain a leading cause of mortality worldwide, underscoring the importance of accurate and scalable diagnostic systems. Electrocardiogram (ECG) analysis is central to detecting cardiac abnormalities, yet challenges such as noise, class imbalance, and dataset heterogeneity limit current methods. To address these issues, we propose FoundationalECGNet, a foundational framework for automated ECG classification. The model integrates a dual-stage denoising by Morlet and Daubechies wavelets transformation, Convolutional Block Attention Module (CBAM), Graph Attention Networks (GAT), and Time Series Transformers (TST) to jointly capture spatial and temporal dependencies in multi-channel ECG signals. FoundationalECGNet first distinguishes between Normal and Abnormal ECG signals, and then classifies the Abnormal signals into one of five cardiac conditions: Arrhythmias, Conduction Disorders, Myocardial Infarction, QT Abnormalities, or Hypertrophy. Across multiple datasets, the model achieves a 99% F1-score for Normal vs. Abnormal classification and shows state-of-the-art performance in multi-class disease detection, including a 99% F1-score for Conduction Disorders and Hypertrophy, as well as a 98.9% F1-score for Arrhythmias. Additionally, the model provides risk level estimations to facilitate clinical decision-making. In conclusion, FoundationalECGNet represents a scalable, interpretable, and generalizable solution for automated ECG analysis, with the potential to improve diagnostic precision and patient outcomes in healthcare settings. We'll share the code after acceptance.

Deep Residual Echo State Networks: exploring residual orthogonal connections in untrained Recurrent Neural Networks

Echo State Networks (ESNs) are a particular type of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) framework, popular for their fast and efficient learning. However, traditional ESNs often struggle with long-term information processing. In this paper, we introduce a novel class of deep untrained RNNs based on temporal residual connections, called Deep Residual Echo State Networks (DeepResESNs). We show that leveraging a hierarchy of untrained residual recurrent layers significantly boosts memory capacity and long-term temporal modeling. For the temporal residual connections, we consider different orthogonal configurations, including randomly generated and fixed-structure configurations, and we study their effect on network dynamics. A thorough mathematical analysis outlines necessary and sufficient conditions to ensure stable dynamics within DeepResESN. Our experiments on a variety of time series tasks showcase the advantages of the proposed approach over traditional shallow and deep RC.

From Entanglement to Alignment: Representation Space Decomposition for Unsupervised Time Series Domain Adaptation

Domain shift poses a fundamental challenge in time series analysis, where models trained on source domain often fail dramatically when applied in target domain with different yet similar distributions. While current unsupervised domain adaptation (UDA) methods attempt to align cross-domain feature distributions, they typically treat features as indivisible entities, ignoring their intrinsic compositions that governs domain adaptation. We introduce DARSD, a novel UDA framework with theoretical explainability that explicitly realizes UDA tasks from the perspective of representation space decomposition. Our core insight is that effective domain adaptation requires not just alignment, but principled disentanglement of transferable knowledge from mixed representations. DARSD consists three synergistic components: (I) An adversarial learnable common invariant basis that projects original features into a domain-invariant subspace while preserving semantic content; (II) A prototypical pseudo-labeling mechanism that dynamically separates target features based on confidence, hindering error accumulation; (III) A hybrid contrastive optimization strategy that simultaneously enforces feature clustering and consistency while mitigating emerging distribution gaps. Comprehensive experiments conducted on four benchmark datasets (WISDM, HAR, HHAR, and MFD) demonstrate DARSD's superiority against 12 UDA algorithms, achieving optimal performance in 35 out of 53 cross-domain scenarios.

MAESTRO: Multi-modal Adaptive Ensemble for Spectro-Temporal Robust Optimization

Timely and robust influenza incidence forecasting is critical for public health decision-making. To address this, we present MAESTRO, a Multi-modal Adaptive Ensemble for Spectro-Temporal Robust Optimization. MAESTRO achieves robustness by adaptively fusing multi-modal inputs-including surveillance, web search trends, and meteorological data-and leveraging a comprehensive spectro-temporal architecture. The model first decomposes time series into seasonal and trend components. These are then processed through a hybrid feature enhancement pipeline combining Transformer-based encoders, a Mamba state-space model for long-range dependencies, multi-scale temporal convolutions, and a frequency-domain analysis module. A cross-channel attention mechanism further integrates information across the different data modalities. Finally, a temporal projection head performs sequence-to-sequence forecasting, with an optional estimator to quantify prediction uncertainty. Evaluated on over 11 years of Hong Kong influenza data (excluding the COVID-19 period), MAESTRO shows strong competitive performance, demonstrating a superior model fit and relative accuracy, achieving a state-of-the-art R-square of 0.956. Extensive ablations confirm the significant contributions of both multi-modal fusion and the spectro-temporal components. Our modular and reproducible pipeline is made publicly available to facilitate deployment and extension to other regions and pathogens.Our publicly available pipeline presents a powerful, unified framework, demonstrating the critical synergy of advanced spectro-temporal modeling and multi-modal data fusion for robust epidemiological forecasting.