Semiconductor manufacturing is an extremely complex process, characterized by thousands of interdependent parameters collected across diverse tools and process steps. Multi-variate time-series (MTS) analysis has emerged as a critical methodology for enabling real-time monitoring, fault detection, and predictive maintenance in such environments. However, anomaly prediction in semiconductor fabrication presents several critical challenges, including high data dimensionality, severe class imbalance due to the rarity of true faults, noisy and missing measurements, and non-stationary behavior of production systems. Furthermore, the complex interdependencies between variables and the delayed emergence of faults across downstream stages complicate both anomaly detection and root-cause-analysis. This paper presents a novel and generic approach for anomaly detection in MTS data using machine learning. The proposed methodology consists of three main steps: a) converting MTS data into image-based representations using the Continuous Wavelet Transform, b) developing a multi-class image classifier by fine-tuning a pretrained VGG-16 architecture on custom CWT image datasets, and c) constructing a Siamese network composed of two identical sub-networks, each utilizing the fine-tuned VGG-16 as a backbone. The network takes pairs of CWT images as input -one serving as a reference or anchor (representing a known-good signal), and the other as a query (representing an unknown signal). The model then compares the embeddings of both inputs to determine whether they belong to the same class at a given time step. Our approach demonstrates high accuracy in identifying anomalies on a real FAB process time-series dataset, offering a promising solution for offline anomaly detection in process and tool trace data. Moreover, the approach is flexible and can be applied in both supervised and semi-supervised settings.

Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from such a multi-variate time series is of a fundamental importance for many monitoring and control tasks. For a periodic time series this is equivalent to determining its period length. In this work we present a persistent homology framework to estimate recurrence times in multi-variate time series with different generalizations of cyclic behavior (periodic, repetitive, and recurring). To this end, we provide three specialized methods within our framework that are provably stable and validate them using real-world data, including a new benchmark dataset from an injection molding machine.

Summary and Contributions: The authors propose a method that learns a model that can classify a given multi-variate time series. Their learned system is a recurrent neural network (RNN) that maps a multi-variate time series (which represents an individual patient) into a vector, and a classifier that maps that vector to one of C possible classes. They propose an algorithm to learn the weights of the RNN, the classifier, and the weights. They validate their proposed algorithm in a clinical dataset, where each patient is defined by a 96-dimensional time series. Each of the 96 time series represents the measurement of a variable over time (e.g.

In the trend of hybrid Artificial Intelligence (AI) techniques, Physic Informed Machine Learning has seen a growing interest. It operates mainly by imposing a data, learning or inductive bias with simulation data, Partial Differential Equations or equivariance and invariance properties. While these models have shown great success on tasks involving one physical domain such as fluid dynamics, existing methods still struggle on tasks with complex multi-physical and multi-domain phenomena. To address this challenge, we propose to leverage Bond Graphs, a multi-physics modeling approach together with Graph Neural Network. We thus propose Neural Bond Graph Encoder (NBgE), a model agnostic physical-informed encoder tailored for multi-physics systems. It provides an unified framework for any multi-physics informed AI with a graph encoder readable for any deep learning model. Our experiments on two challenging multi-domain physical systems - a Direct Current Motor and the Respiratory system - demonstrate the effectiveness of our approach on a multi-variate time series forecasting task.

In recent times, Large Language Models (LLMs) have captured a global spotlight and revolutionized the field of Natural Language Processing. One of the factors attributed to the effectiveness of LLMs is the model architecture used for training, transformers. Transformer models excel at capturing contextual features in sequential data since time series data are sequential, transformer models can be leveraged for more efficient time series data prediction. The field of prognostics is vital to system health management and proper maintenance planning. A reliable estimation of the remaining useful life (RUL) of machines holds the potential for substantial cost savings. This includes avoiding abrupt machine failures, maximizing equipment usage, and serving as a decision support system (DSS). This work proposed an encoder-transformer architecture-based framework for multivariate time series prediction for a prognostics use case. We validated the effectiveness of the proposed framework on all four sets of the C-MAPPS benchmark dataset for the remaining useful life prediction task. To effectively transfer the knowledge and application of transformers from the natural language domain to time series, three model-specific experiments were conducted. Also, to enable the model awareness of the initial stages of the machine life and its degradation path, a novel expanding window method was proposed for the first time in this work, it was compared with the sliding window method, and it led to a large improvement in the performance of the encoder transformer model. Finally, the performance of the proposed encoder-transformer model was evaluated on the test dataset and compared with the results from 13 other state-of-the-art (SOTA) models in the literature and it outperformed them all with an average performance increase of 137.65% over the next best model across all the datasets.

We introduce a novel, practically relevant variation of the anomaly detection problem in multi-variate time series: intrinsic anomaly detection. It appears in diverse practical scenarios ranging from DevOps to IoT, where we want to recognize failures of a system that operates under the influence of a surrounding environment. Intrinsic anomalies are changes in the functional dependency structure between time series that represent an environment and time series that represent the internal state of a system that is placed in said environment. We formalize this problem, provide under-studied public and new purpose-built data sets for it, and present methods that handle intrinsic anomaly detection. These address the short-coming of existing anomaly detection methods that cannot differentiate between expected changes in the system's state and unexpected ones, i.e., changes in the system that deviate from the environment's influence. Our most promising approach is fully unsupervised and combines adversarial learning and time series representation learning, thereby addressing problems such as label sparsity and subjectivity, while allowing to navigate and improve notoriously problematic anomaly detection data sets.

Network estimation from multi-variate point process or time series data is a problem of fundamental importance. Prior work has focused on parametric approaches that require a known parametric model, which makes estimation procedures less robust to model mis-specification, non-linearities and heterogeneities. In this paper, we develop a semi-parametric approach based on the monotone single-index multi-variate autoregressive model (SIMAM) which addresses these challenges. We provide theoretical guarantees for dependent data and an alternating projected gradient descent algorithm. Significantly we do not explicitly assume mixing conditions on the process (although we do require conditions analogous to restricted strong convexity) and we achieve rates of the form $O(T^{-\frac{1}{3}} \sqrt{s\log(TM)})$ (optimal in the independent design case) where $s$ is the threshold for the maximum in-degree of the network that indicates the sparsity level, $M$ is the number of actors and $T$ is the number of time points. In addition, we demonstrate the superior performance both on simulated data and two real data examples where our SIMAM approach out-performs state-of-the-art parametric methods both in terms of prediction and network estimation.