Digital Twin technology creates virtual replicas of physical objects, processes, or systems by replicating their properties, data, and behaviors. This advanced technology offers a range of intelligent functionalities, such as modeling, simulation, and data-driven decision-making, that facilitate design optimization, performance estimation, and monitoring operations. Forecasting plays a pivotal role in Digital Twin technology, as it enables the prediction of future outcomes, supports informed decision-making, minimizes risks, driving improvements in efficiency, productivity, and cost reduction. Recently, Digital Twin technology has leveraged Graph forecasting techniques in large-scale complex sensor networks to enable accurate forecasting and simulation of diverse scenarios, fostering proactive and data-driven decision making. However, existing Graph forecasting techniques lack scalability for many real-world applications. They have limited ability to adapt to non-stationary environments, retain past knowledge, lack a mechanism to capture the higher order spatio-temporal dynamics, and estimate uncertainty in model predictions. To surmount the challenges, we introduce a hybrid architecture that enhances the hypergraph representation learning backbone by incorporating fast adaptation to new patterns and memory-based retrieval of past knowledge. This balance aims to improve the slowly-learned backbone and achieve better performance in adapting to recent changes. In addition, it models the time-varying uncertainty of multi-horizon forecasts, providing estimates of prediction uncertainty. Our forecasting architecture has been validated through ablation studies and has demonstrated promising results across multiple benchmark datasets, surpassing state-ofthe-art forecasting methods by a significant margin.

Structural health monitoring (SHM) has emerged as a vital field of research, geared towards preserving the longevity and safety of civil infrastructure [1]. A critical component of SHM is the analysis of vibration time series data, which offers insights into the behavior, health, and performance of structures [2]. As infrastructure, especially in urban regions, is subject to a myriad of dynamic forces--ranging from wind to traffic loads - it becomes pivotal to extract clear and meaningful data from the complex vibration signatures that these forces induce. However, one of the significant challenges plaguing SHM practitioners is the interference of noise in these vibration signals, which can distort interpretations and lead to unreliable conclusions. The dynamic response of structures is often manifested as multimodal vibrations, meaning multiple modes or patterns of vibration coexist. These modes, each characterized by its frequency and shape, provide a fingerprint of the structure's health and dynamic properties.

Modern Internet of Things (IoT) environments are monitored via a large number of IoT enabled sensing devices, with the data acquisition and processing infrastructure setting restrictions in terms of computational power and energy resources. To alleviate this issue, sensors are often configured to operate at relatively low sampling frequencies, yielding a reduced set of observations. Nevertheless, this can hamper dramatically subsequent decision-making, such as forecasting. To address this problem, in this work we evaluate short-term forecasting in highly underdetermined cases, i.e., the number of sensor streams is much higher than the number of observations. Several statistical, machine learning and neural network-based models are thoroughly examined with respect to the resulting forecasting accuracy on five different real-world datasets. The focus is given on a unified experimental protocol especially designed for short-term prediction of multiple time series at the IoT edge. The proposed framework can be considered as an important step towards establishing a solid forecasting strategy in resource constrained IoT applications.

Originally published on Towards AI the World's Leading AI and Technology News and Media Company. If you are building an AI-related product or service, we invite you to consider becoming an AI sponsor. At Towards AI, we help scale AI and technology startups. Let us help you unleash your technology to the masses. Time series data is one of the most common data types in the industry and you will probably be working with it in your career. Therefore understanding how to work with it and how to apply analytical and forecasting techniques are critical for every aspiring data scientist. In this series of articles, I will go through the basic techniques to work with time-series data, starting with data manipulation, analysis, and visualization to understand your data and prepare it for and then using statistical, machine learning, and deep learning techniques for forecasting and classification. It will be more of a practical guide in which I will be applying each discussed and explained concept to real data. All the codes and datasets used in this article can be found in this repository. In this section, we will learn how to leverage basic plottings tools in Python, and how to annotate and personalize your time series plots.

Researchers design a user-friendly interface that helps nonexperts make forecasts using data collected over time. Whether someone is trying to predict tomorrow's weather, forecast future stock prices, identify missed opportunities for sales in retail, or estimate a patient's risk of developing a disease, they will likely need to interpret time-series data, which are a collection of observations recorded over time. Making predictions using time-series data typically requires several data-processing steps and the use of complex machine-learning algorithms, which have such a steep learning curve they aren't readily accessible to nonexperts. To make these powerful tools more user-friendly, MIT researchers developed a system that directly integrates prediction functionality on top of an existing time-series database. Their simplified interface, which they call tspDB (time series predict database), does all the complex modeling behind the scenes so a nonexpert can easily generate a prediction in only a few seconds. MIT researchers created a tool that enables people to make highly accurate predictions using multiple time-series data with just a few keystrokes.

Anomaly detection is a widely studied task for a broad variety of data types; among them, multiple time series appear frequently in applications, including for example, power grids and traffic networks. Detecting anomalies for multiple time series, however, is a challenging subject, owing to the intricate interdependencies among the constituent series. We hypothesize that anomalies occur in low density regions of a distribution and explore the use of normalizing flows for unsupervised anomaly detection, because of their superior quality in density estimation. Moreover, we propose a novel flow model by imposing a Bayesian network among constituent series. A Bayesian network is a directed acyclic graph (DAG) that models causal relationships; it factorizes the joint probability of the series into the product of easy-to-evaluate conditional probabilities. We call such a graph-augmented normalizing flow approach GANF and propose joint estimation of the DAG with flow parameters. We conduct extensive experiments on real-world datasets and demonstrate the effectiveness of GANF for density estimation, anomaly detection, and identification of time series distribution drift.

We investigate the problem of discovering and modeling regime shifts in an ecosystem comprising multiple time series known as co-evolving time series. Regime shifts refer to the changing behaviors exhibited by series at different time intervals. Learning these changing behaviors is a key step toward time series forecasting. While advances have been made, existing methods suffer from one or more of the following shortcomings: (1) failure to take relationships between time series into consideration for discovering regimes in multiple time series; (2) lack of an effective approach that models time-dependent behaviors exhibited by series; (3) difficulties in handling data discontinuities which may be informative. Most of the existing methods are unable to handle all of these three issues in a unified framework. This, therefore, motivates our effort to devise a principled approach for modeling interactions and time-dependency in co-evolving time series. Specifically, we model an ecosystem of multiple time series by summarizing the heavy ensemble of time series into a lighter and more meaningful structure called a \textit{mapping grid}. By using the mapping grid, our model first learns time series behavioral dependencies through a dynamic network representation, then learns the regime transition mechanism via a full time-dependent Cox regression model. The originality of our approach lies in modeling interactions between time series in regime identification and in modeling time-dependent regime transition probabilities, usually assumed to be static in existing work.

Analyzing time series data is important to predict future events and changes in finance, manufacturing, and administrative decisions. Gaussian processes (GPs) solve regression and classification problems by choosing appropriate kernels capturing covariance structure of data. In time series analysis, GP based regression methods recently demonstrate competitive performance by decomposing temporal covariance structure. Such covariance structure decomposition allows exploiting shared parameters over a set of multiple but selected time series. In this paper, we handle multiple time series by placing an Indian Buffet Process (IBP) prior on the presence of shared kernels. We investigate the validity of model when infinite latent components are introduced. We also propose an improved search algorithm to find interpretable kernels among multiple time series along with comparison reports. Experiments are conducted on both synthetic data sets and real world data sets, showing promising results in term of structure discoveries and predictive performances.