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Motivated by an example from remote sensing of gas emission sources, we derive two novel change point procedures for multivariate time series where, in contrast to classical change point literature, the changes are not required to be…

In complex large-scale systems such as climate, important effects are caused by a combination of confounding processes that are not fully observable. The identification of sources from observations of system state is vital for attribution…

This paper introduces TRACE-GPT, which stands for Time-seRies Anomaly-detection with Convolutional Embedding and Generative Pre-trained Transformers. TRACE-GPT is designed to pre-train univariate time-series sensor data and detect faults on…

The problem of sequential anomaly detection is considered, where multiple data sources are monitored in real time and the goal is to identify the "anomalous" ones among them, when it is not possible to sample all sources at all times. A…

Anomaly localization in images -- identifying regions that deviate from normal patterns -- is vital in applications such as medical diagnosis and industrial inspection. A recent trend is the use of image generation models in anomaly…

In this article, we study wavelet collocation methods based on Taylor and Chebyshev wavelets for the source identification in parabolic inverse problem. In the proposed method, highest order derivative is written in terms of Taylor and…

In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled…

The use of video-imaging data for in-line process monitoring applications has become more and more popular in the industry. In this framework, spatio-temporal statistical process monitoring methods are needed to capture the relevant…

When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…

In time-reversal invariant electronic systems the scattering matrix is anti-symmetric. This property enables an effect, designated here as "scattering anomaly", such that the electron transport does not suffer from back reflections,…

We propose an adaptive algorithm for identifying the unknown parameter in a linear exponentially stable single-input single-output infinite-dimensional system. We assume that the transfer function of the infinite-dimensional system can be…

In this paper, we develop an asymptotic expansion-regularization (AER) method for inverse source problems in two-dimensional nonlinear and nonstationary singularly perturbed partial differential equations (PDEs). The key idea of this…

Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…

This paper investigates the solution of a parabolic inverse problem based upon the convection-diffusion-reaction equation, which can be used to estimate both water and air pollution. We will consider both known and unknown source location:…

In recent years, a number of process-based anomaly detection schemes for Industrial Control Systems were proposed. In this work, we provide the first systematic analysis of such schemes, and introduce a taxonomy of properties that are…

Strange correlator is a powerful tool widely used in detecting symmetry-protected topological (SPT) phases. However, the result of strange correlator crucially relies on the adoption of the reference state. In this work, we report that an…

High fidelity models used in many science and engineering applications couple multiple physical states and parameters. Inverse problems arise when a model parameter cannot be determined directly, but rather is estimated using (typically…

Anomaly detection or outlier detection is a common task in various domains, which has attracted significant research efforts in recent years. Existing works mainly focus on structured data such as numerical or categorical data; however,…

Identifying anomalous patterns in real-world data is essential for understanding where, when, and how systems deviate from their expected dynamics. Yet methods that separately consider the anomalousness of each individual data point have…

Previous transfer methods for anomaly detection generally assume the availability of labeled data in source or target domains. However, such an assumption is not valid in most real applications where large-scale labeled data are too…