Related papers: Abnormal source identification for parabolic distr…

Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…

A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…

We consider an inverse source two-parameter sub-diffusion model subject to a nonlocal initial condition. The problem models several physical processes, among them are the microwave heating and light propagation in photoelectric cells. A…

This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness of…

Numerous industrial thermal processes and fluid processes can be described by distributed parameter systems (DPSs), wherein many process parameters and variables vary in space and time. Early internal abnormalities in the DPS may develop…

In this paper, adaptive set-point regulation controllers for discrete-time nonlinear systems are constructed. The system to be controlled is assumed to have a parametric uncertainty, and an excitation signal is used in order to obtain the…

This article is devoted to inverse problems of recovering point sources in mathematical models of heat and mass transfer. The main attention is paid to well-posedness questions of these inverse problems with pointwise overdetermination…

This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…

This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been…

Solar thermal systems (STS) present a promising avenue for low-carbon heat generation, with a well-running system providing heat at minimal cost and carbon emissions. However, STS can exhibit faults due to improper installation,…

This paper is devoted to the study of source reconstruction algorithms for coupled systems of heat equations, with either constant or spatially dependent coupling terms, where internal measurements are available from a reduced number of…

We consider a network of sensors deployed to sense a spatio-temporal field and estimate a parameter of interest. We are interested in the case where the temporal process sensed by each sensor can be modeled as a state-space process that is…

In this work we introduce a novel adaptive anomaly detection framework specifically designed for monitoring sequential random finite set (RFS) observations. Our approach effectively distinguishes between In-Control data (normal) and…

In this article, we investigate inverse source problems for a wide range of PDEs of parabolic and hyperbolic types as well as time-fractional evolution equations by partial interior observation. Restricting the source terms to the form of…

We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from any nonempty open subset of the boundary can uniquely…

Accurate detection and diagnosis of abnormal behaviors such as network attacks from multivariate time series (MTS) are crucial for ensuring the stable and effective operation of industrial cyber-physical systems (CPS). However, existing…

This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a…

Anomaly detection is a fundamental task in machine learning and data mining, with significant applications in cybersecurity, industrial fault diagnosis, and clinical disease monitoring. Traditional methods, such as statistical modeling and…

This paper explores the utility of diffusion-based models for anomaly detection, focusing on their efficacy in identifying deviations in both compact and high-resolution datasets. Diffusion-based architectures, including Denoising Diffusion…

We present a simple, analytic point source model for both static and time-varying point-like heat sources and the resulting temperature profile that solves the heat equation in dimension three. Simple algorithms to detect the location and…