Rethinking Remaining Useful Life Prediction with Scarce Time Series Data: Regression under Indirect Supervision

Supervised time series prediction relies on directly measured target variables, but real-world use cases such as predicting remaining useful life (RUL) involve indirect supervision, where the target variable is labeled as a function of another dependent variable. Trending temporal regression techniques rely on sequential time series inputs to capture temporal patterns, requiring interpolation when dealing with sparsely and irregularly sampled covariates along the timeline. However, interpolation can introduce significant biases, particularly with highly scarce data. In this paper, we address the RUL prediction problem with data scarcity as time series regression under indirect supervision. We introduce a unified framework called parameterized static regression, which takes single data points as inputs for regression of target values, inherently handling data scarcity without requiring interpolation. The time dependency under indirect supervision is captured via a parametrical rectification (PR) process, approximating a parametric function during inference with historical posteriori estimates, following the same underlying distribution used for labeling during training. Additionally, we propose a novel batch training technique for tasks in indirect supervision to prevent overfitting and enhance efficiency. We evaluate our model on public benchmarks for RUL prediction with simulated data scarcity. Our method demonstrates competitive performance in prediction accuracy when dealing with highly scarce time series data.

Temporal Dynamic Embedding for Irregularly Sampled Time Series

In several practical applications, particularly healthcare, clinical data of each patient is individually recorded in a database at irregular intervals as required. This causes a sparse and irregularly sampled time series, which makes it difficult to handle as a structured representation of the prerequisites of neural network models. We therefore propose temporal dynamic embedding (TDE), which enables neural network models to receive data that change the number of variables over time. TDE regards each time series variable as an embedding vector evolving over time, instead of a conventional fixed structured representation, which causes a critical missing problem. For each time step, TDE allows for the selective adoption and aggregation of only observed variable subsets and represents the current status of patient based on current observations. The experiment was conducted on three clinical datasets: PhysioNet 2012, MIMIC-III, and PhysioNet 2019. The TDE model performed competitively or better than the imputation-based baseline and several recent state-of-the-art methods with reduced training runtime.

PatchTrAD: A Patch-Based Transformer focusing on Patch-Wise Reconstruction Error for Time Series Anomaly Detection

Time series anomaly detection (TSAD) focuses on identifying whether observations in streaming data deviate significantly from normal patterns. With the prevalence of connected devices, anomaly detection on time series has become paramount, as it enables real-time monitoring and early detection of irregular behaviors across various application domains. In this work, we introduce PatchTrAD, a Patch-based Transformer model for time series anomaly detection. Our approach leverages a Transformer encoder along with the use of patches under a reconstructionbased framework for anomaly detection. Empirical evaluations on multiple benchmark datasets show that PatchTrAD is on par, in terms of detection performance, with state-of-the-art deep learning models for anomaly detection while being time efficient during inference.

Temporal Gaussian Copula For Clinical Multivariate Time Series Data Imputation

The imputation of the Multivariate time series (MTS) is particularly challenging since the MTS typically contains irregular patterns of missing values due to various factors such as instrument failures, interference from irrelevant data, and privacy regulations. Existing statistical methods and deep learning methods have shown promising results in time series imputation. In this paper, we propose a Temporal Gaussian Copula Model (TGC) for three-order MTS imputation. The key idea is to leverage the Gaussian Copula to explore the cross-variable and temporal relationships based on the latent Gaussian representation. Subsequently, we employ an Expectation-Maximization (EM) algorithm to improve robustness in managing data with varying missing rates. Comprehensive experiments were conducted on three real-world MTS datasets. The results demonstrate that our TGC substantially outperforms the state-of-the-art imputation methods. Additionally, the TGC model exhibits stronger robustness to the varying missing ratios in the test dataset. Our code is available at https://github.com/MVL-Lab/TGC-MTS.

Taylor Series-Inspired Local Structure Fitting Network for Few-shot Point Cloud Semantic Segmentation

Few-shot point cloud semantic segmentation aims to accurately segment "unseen" new categories in point cloud scenes using limited labeled data. However, pretraining-based methods not only introduce excessive time overhead but also overlook the local structure representation among irregular point clouds. To address these issues, we propose a pretraining-free local structure fitting network for few-shot point cloud semantic segmentation, named TaylorSeg. Specifically, inspired by Taylor series, we treat the local structure representation of irregular point clouds as a polynomial fitting problem and propose a novel local structure fitting convolution, called TaylorConv. This convolution learns the low-order basic information and high-order refined information of point clouds from explicit encoding of local geometric structures. Then, using TaylorConv as the basic component, we construct two variants of TaylorSeg: a non-parametric TaylorSeg-NN and a parametric TaylorSeg-PN. The former can achieve performance comparable to existing parametric models without pretraining. For the latter, we equip it with an Adaptive Push-Pull (APP) module to mitigate the feature distribution differences between the query set and the support set. Extensive experiments validate the effectiveness of the proposed method. Notably, under the 2-way 1-shot setting, TaylorSeg-PN achieves improvements of +2.28% and +4.37% mIoU on the S3DIS and ScanNet datasets respectively, compared to the previous state-of-the-art methods. Our code is available at https://github.com/changshuowang/TaylorSeg.

Quantifying Robustness: A Benchmarking Framework for Deep Learning Forecasting in Cyber-Physical Systems

Cyber-Physical Systems (CPS) in domains such as manufacturing and energy distribution generate complex time series data crucial for Prognostics and Health Management (PHM). While Deep Learning (DL) methods have demonstrated strong forecasting capabilities, their adoption in industrial CPS remains limited due insufficient robustness. Existing robustness evaluations primarily focus on formal verification or adversarial perturbations, inadequately representing the complexities encountered in real-world CPS scenarios. To address this, we introduce a practical robustness definition grounded in distributional robustness, explicitly tailored to industrial CPS, and propose a systematic framework for robustness evaluation. Our framework simulates realistic disturbances, such as sensor drift, noise and irregular sampling, enabling thorough robustness analyses of forecasting models on real-world CPS datasets. The robustness definition provides a standardized score to quantify and compare model performance across diverse datasets, assisting in informed model selection and architecture design. Through extensive empirical studies evaluating prominent DL architectures (including recurrent, convolutional, attention-based, modular, and structured state-space models) we demonstrate the applicability and effectiveness of our approach. We publicly release our robustness benchmark to encourage further research and reproducibility.

Detection of Anomalous Vehicular Traffic and Sensor Failures Using Data Clustering Techniques

The increasing availability of traffic data from sensor networks has created new opportunities for understanding vehicular dynamics and identifying anomalies. In this study, we employ clustering techniques to analyse traffic flow data with the dual objective of uncovering meaningful traffic patterns and detecting anomalies, including sensor failures and irregular congestion events. We explore multiple clustering approaches, i.e partitioning and hierarchical methods, combined with various time-series representations and similarity measures. Our methodology is applied to real-world data from highway sensors, enabling us to assess the impact of different clustering frameworks on traffic pattern recognition. We also introduce a clustering-driven anomaly detection methodology that identifies deviations from expected traffic behaviour based on distance-based anomaly scores. Results indicate that hierarchical clustering with symbolic representations provides robust segmentation of traffic patterns, while partitioning methods such as k-means and fuzzy c-means yield meaningful results when paired with Dynamic Time Warping. The proposed anomaly detection strategy successfully identifies sensor malfunctions and abnormal traffic conditions with minimal false positives, demonstrating its practical utility for real-time monitoring. Real-world vehicular traffic data are provided by Autostrade Alto Adriatico S.p.A.

Generative Latent Neural PDE Solver using Flow Matching

Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion probabilistic model has been shown to enhance the temporal stability of neural solvers, while its stochastic inference mechanism enables ensemble predictions and uncertainty quantification. In principle, such training involves sampling a series of discretized diffusion timesteps during both training and inference, inevitably increasing computational overhead. In addition, most diffusion models apply isotropic Gaussian noise on structured, uniform grids, limiting their adaptability to irregular domains. We propose a latent diffusion model for PDE simulation that embeds the PDE state in a lower-dimensional latent space, which significantly reduces computational costs. Our framework uses an autoencoder to map different types of meshes onto a unified structured latent grid, capturing complex geometries. By analyzing common diffusion paths, we propose to use a coarsely sampled noise schedule from flow matching for both training and testing. Numerical experiments show that the proposed model outperforms several deterministic baselines in both accuracy and long-term stability, highlighting the potential of diffusion-based approaches for robust data-driven PDE learning.

MobiVital: Self-supervised Time-series Quality Estimation for Contactless Respiration Monitoring Using UWB Radar

Respiration waveforms are increasingly recognized as important biomarkers, offering insights beyond simple respiration rates, such as detecting breathing irregularities for disease diagnosis or monitoring breath patterns to guide rehabilitation training. Previous works in wireless respiration monitoring have primarily focused on estimating respiration rate, where the breath waveforms are often generated as a by-product. As a result, issues such as waveform deformation and inversion have largely been overlooked, reducing the signal's utility for applications requiring breathing waveforms. To address this problem, we present a novel approach, MobiVital, that improves the quality of respiration waveforms obtained from ultra-wideband (UWB) radar data. MobiVital combines a self-supervised autoregressive model for breathing waveform extraction with a biology-informed algorithm to detect and correct waveform inversions. To encourage reproducible research efforts for developing wireless vital signal monitoring systems, we also release a 12-person, 24-hour UWB radar vital signal dataset, with time-synchronized ground truth obtained from wearable sensors. Our results show that the respiration waveforms produced by our system exhibit a 7-34% increase in fidelity to the ground truth compared to the baselines and can benefit downstream tasks such as respiration rate estimation.

Can Multimodal LLMs Perform Time Series Anomaly Detection?

Large language models (LLMs) have been increasingly used in time series analysis. However, the potential of multimodal LLMs (MLLMs), particularly vision-language models, for time series remains largely under-explored. One natural way for humans to detect time series anomalies is through visualization and textual description. Motivated by this, we raise a critical and practical research question: Can multimodal LLMs perform time series anomaly detection? To answer this, we propose VisualTimeAnomaly benchmark to evaluate MLLMs in time series anomaly detection (TSAD). Our approach transforms time series numerical data into the image format and feed these images into various MLLMs, including proprietary models (GPT-4o and Gemini-1.5) and open-source models (LLaVA-NeXT and Qwen2-VL), each with one larger and one smaller variant. In total, VisualTimeAnomaly contains 12.4k time series images spanning 3 scenarios and 3 anomaly granularities with 9 anomaly types across 8 MLLMs. Starting with the univariate case (point- and range-wise anomalies), we extend our evaluation to more practical scenarios, including multivariate and irregular time series scenarios, and variate-wise anomalies. Our study reveals several key insights: 1) MLLMs detect range- and variate-wise anomalies more effectively than point-wise anomalies. 2) MLLMs are highly robust to irregular time series, even with 25% of the data missing. 3) Open-source MLLMs perform comparably to proprietary models in TSAD. While open-source MLLMs excel on univariate time series, proprietary MLLMs demonstrate superior effectiveness on multivariate time series. To the best of our knowledge, this is the first work to comprehensively investigate MLLMs for TSAD, particularly for multivariate and irregular time series scenarios. We release our dataset and code at https://github.com/mllm-ts/VisualTimeAnomaly to support future research.