Time series analysis comprises statistical methods for analyzing a sequence of data points collected over an interval of time to identify interesting patterns and trends.
Fault diagnosis in Cyber-Physical Systems (CPSs) is essential for ensuring system dependability and operational efficiency by accurately detecting anomalies and identifying their root causes. However, the manual modeling of faulty behaviors often demands extensive domain expertise and produces models that are complex, error-prone, and difficult to interpret. To address this challenge, we present a novel unsupervised fault diagnosis methodology that integrates collective anomaly detection in multivariate time series, process mining, and stochastic simulation. Initially, collective anomalies are detected from low-level sensor data using multivariate time-series analysis. These anomalies are then transformed into structured event logs, enabling the discovery of interpretable process models through process mining. By incorporating timing distributions into the extracted Petri nets, the approach supports stochastic simulation of faulty behaviors, thereby enhancing root cause analysis and behavioral understanding. The methodology is validated using the Robotic Arm Dataset (RoAD), a widely recognized benchmark in smart manufacturing. Experimental results demonstrate its effectiveness in modeling, simulating, and classifying faulty behaviors in CPSs. This enables the creation of comprehensive fault dictionaries that support predictive maintenance and the development of digital twins for industrial environments.
The long horizon forecasting (LHF) problem has come up in the time series literature for over the last 35 years or so. This review covers aspects of LHF in this period and how deep learning has incorporated variants of trend, seasonality, fourier and wavelet transforms, misspecification bias reduction and bandpass filters while contributing using convolutions, residual connections, sparsity reduction, strided convolutions, attention masks, SSMs, normalization methods, low-rank approximations and gating mechanisms. We highlight time series decomposition techniques, input data preprocessing and dataset windowing schemes that improve performance. Multi-layer perceptron models, recurrent neural network hybrids, self-attention models that improve and/or address the performances of the LHF problem are described, with an emphasis on the feature space construction. Ablation studies are conducted over the ETTm2 dataset in the multivariate and univariate high useful load (HUFL) forecasting contexts, evaluated over the last 4 months of the dataset. The heatmaps of MSE averages per time step over test set series in the horizon show that there is a steady increase in the error proportionate to its length except with xLSTM and Triformer models and motivate LHF as an error propagation problem. The trained models are available here: https://bit.ly/LHFModelZoo




Satellite image time-series analysis demands fine-grained spatial-temporal reasoning, which remains a challenge for existing multimodal large language models (MLLMs). In this work, we study the capabilities of MLLMs on a novel task that jointly targets temporal change understanding and future scene generation, aiming to assess their potential for modeling complex multimodal dynamics over time. We propose TAMMs, a Temporal-Aware Multimodal Model for satellite image change understanding and forecasting, which enhances frozen MLLMs with lightweight temporal modules for structured sequence encoding and contextual prompting. To guide future image generation, TAMMs introduces a Semantic-Fused Control Injection (SFCI) mechanism that adaptively combines high-level semantic reasoning and structural priors within an enhanced ControlNet. This dual-path conditioning enables temporally consistent and semantically grounded image synthesis. Experiments demonstrate that TAMMs outperforms strong MLLM baselines in both temporal change understanding and future image forecasting tasks, highlighting how carefully designed temporal reasoning and semantic fusion can unlock the full potential of MLLMs for spatio-temporal understanding.




Artificial Night-Time Light (NTL) remote sensing is a vital proxy for quantifying the intensity and spatial distribution of human activities. Although the NPP-VIIRS sensor provides high-quality NTL observations, its temporal coverage, which begins in 2012, restricts long-term time-series studies that extend to earlier periods. Despite the progress in extending VIIRS-like NTL time-series, current methods still suffer from two significant shortcomings: the underestimation of light intensity and the structural omission. To overcome these limitations, we propose a novel reconstruction framework consisting of a two-stage process: construction and refinement. The construction stage features a Hierarchical Fusion Decoder (HFD) designed to enhance the fidelity of the initial reconstruction. The refinement stage employs a Dual Feature Refiner (DFR), which leverages high-resolution impervious surface masks to guide and enhance fine-grained structural details. Based on this framework, we developed the Extended VIIRS-like Artificial Nighttime Light (EVAL) product for China, extending the standard data record backwards by 26 years to begin in 1986. Quantitative evaluation shows that EVAL significantly outperforms existing state-of-the-art products, boosting the $\text{R}^2$ from 0.68 to 0.80 while lowering the RMSE from 1.27 to 0.99. Furthermore, EVAL exhibits excellent temporal consistency and maintains a high correlation with socioeconomic parameters, confirming its reliability for long-term analysis. The resulting EVAL dataset provides a valuable new resource for the research community and is publicly available at https://doi.org/10.11888/HumanNat.tpdc.302930.
Recent advances in Large Language Models (LLMs) have demonstrated new possibilities for accurate and efficient time series analysis, but prior work often required heavy fine-tuning and/or ignored inter-series correlations. In this work, we explore simple and flexible prompt-based strategies that enable LLMs to perform time series forecasting without extensive retraining or the use of a complex external architecture. Through the exploration of specialized prompting methods that leverage time series decomposition, patch-based tokenization, and similarity-based neighbor augmentation, we find that it is possible to enhance LLM forecasting quality while maintaining simplicity and requiring minimal preprocessing of data. To this end, we propose our own method, PatchInstruct, which enables LLMs to make precise and effective predictions.
With advancements in computing and communication technologies, the Internet of Things (IoT) has seen significant growth. IoT devices typically collect data from various sensors, such as temperature, humidity, and energy meters. Much of this data is temporal in nature. Traditionally, data from IoT devices is centralized for analysis, but this approach introduces delays and increased communication costs. Federated learning (FL) has emerged as an effective alternative, allowing for model training across distributed devices without the need to centralize data. In many applications, such as smart home energy and environmental monitoring, the data collected by IoT devices across different locations can exhibit significant variation in trends and seasonal patterns. Accurately forecasting such non-stationary, non-linear time-series data is crucial for applications like energy consumption estimation and weather forecasting. However, these data variations can severely impact prediction accuracy. The key contributions of this paper are: (1) Investigating how non-linear, non-stationary time-series data distributions, like generalized extreme value (gen-extreme) and log norm distributions, affect FL performance. (2) Analyzing how different detrending techniques for non-linear time-series data influence the forecasting model's performance in a FL setup. We generated several synthetic time-series datasets using non-linear data distributions and trained an LSTM-based forecasting model using both centralized and FL approaches. Additionally, we evaluated the impact of detrending on real-world datasets with non-linear time-series data distributions. Our experimental results show that: (1) FL performs worse than centralized approaches when dealing with non-linear data distributions. (2) The use of appropriate detrending techniques improves FL performance, reducing loss across different data distributions.
While adversarial robustness and generalization have individually received substantial attention in the recent literature on quantum machine learning, their interplay is much less explored. In this chapter, we address this interplay for variational quantum models, which were recently proposed as function approximators in supervised learning. We discuss recent results quantifying both robustness and generalization via Lipschitz bounds, which explicitly depend on model parameters. Thus, they give rise to a regularization-based training approach for robust and generalizable quantum models, highlighting the importance of trainable data encoding strategies. The practical implications of the theoretical results are demonstrated with an application to time series analysis.
Transformer-based models have gained increasing attention in time series research, driving interest in Large Language Models (LLMs) and foundation models for time series analysis. As the field moves toward multi-modality, Large Vision Models (LVMs) are emerging as a promising direction. In the past, the effectiveness of Transformer and LLMs in time series has been debated. When it comes to LVMs, a similar question arises: are LVMs truely useful for time series analysis? To address it, we design and conduct the first principled study involving 4 LVMs, 8 imaging methods, 18 datasets and 26 baselines across both high-level (classification) and low-level (forecasting) tasks, with extensive ablation analysis. Our findings indicate LVMs are indeed useful for time series classification but face challenges in forecasting. Although effective, the contemporary best LVM forecasters are limited to specific types of LVMs and imaging methods, exhibit a bias toward forecasting periods, and have limited ability to utilize long look-back windows. We hope our findings could serve as a cornerstone for future research on LVM- and multimodal-based solutions to different time series tasks.
The widespread adoption of Artificial Intelligence (AI) and Machine Learning (ML) comes with a significant environmental impact, particularly in terms of energy consumption and carbon emissions. This pressing issue highlights the need for innovative solutions to mitigate AI's ecological footprint. One of the key factors influencing the energy consumption of ML model training is the size of the training dataset. ML models are often trained on vast amounts of data continuously generated by sensors and devices distributed across multiple locations. To reduce data transmission costs and enhance privacy, Federated Learning (FL) enables model training without the need to move or share raw data. While FL offers these advantages, it also introduces challenges due to the heterogeneity of data sources (related to volume and quality), computational node capabilities, and environmental impact. This paper contributes to the advancement of Green AI by proposing a data-centric approach to Green Federated Learning. Specifically, we focus on reducing FL's environmental impact by minimizing the volume of training data. Our methodology involves the analysis of the characteristics of federated datasets, the selecting of an optimal subset of data based on quality metrics, and the choice of the federated nodes with the lowest environmental impact. We develop a comprehensive methodology that examines the influence of data-centric factors, such as data quality and volume, on FL training performance and carbon emissions. Building on these insights, we introduce an interactive recommendation system that optimizes FL configurations through data reduction, minimizing environmental impact during training. Applying this methodology to time series classification has demonstrated promising results in reducing the environmental impact of FL tasks.
Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite the advantage of linearity, the operator is generally infinite-dimensional. Therefore, the objective is to learn measurement functions that yield a tractable finite-dimensional Koopman operator approximation. In this work, we establish a connection between Koopman operator approximation and linear Recurrent Neural Networks (RNNs), which have recently demonstrated remarkable success in sequence modeling. We show that by considering an extended state consisting of lagged observations, we can establish an equivalence between a structured Koopman operator and linear RNN updates. Building on this connection, we present SKOLR, which integrates a learnable spectral decomposition of the input signal with a multilayer perceptron (MLP) as the measurement functions and implements a structured Koopman operator via a highly parallel linear RNN stack. Numerical experiments on various forecasting benchmarks and dynamical systems show that this streamlined, Koopman-theory-based design delivers exceptional performance.