arXiv subjects

Marco Mattuschka

Publications and source records attributed to Marco Mattuschka.

5 recordsLinked to original sources

arXiv2026

Sparsity-Driven Source Localization in Tomographic Sensing Applications

Hyperspectral standoff detection systems such as Focal Plane Array (FPA) Fourier Transform Infrared (FTIR) spectrometers provide high spatial resolution in detecting airborne chemical contaminants that are invisible to the human eye but potentially hazardous. When two such systems are operated simultaneously with a suitable opening angle, they enable tomographic reconstruction of contaminant plumes with improved spatial and temporal accuracy. This work presents a mathematical model of these measurement capabilities and an algorithm to identify, localize, and quantify contaminant release sources. The objective is to develop a a tool that reconstructs release locations and predict the future plume evolution from standoff measurement data, thereby supporting early warning and situational awareness in hazardous material release scenarios. The transport of contaminants is modeled by an advection-diffusion equation, and the corresponding inverse problem for source identification is formulated accordingly. Owing to the severe ill-posedness and underdetermination of the problem, a sparsity-promoting regularization approach is employed together with a high-performance optimization algorithm. To incorporate the tomographic measurement data into the discrete formulation, a level-set description of a threshold concentration is used, allowing the measurements to be represented independently of the computational mesh and avoiding costly remeshing procedures.

math.NA↗

arXiv2026

Rapid Identification of Moving Contaminant Sources Through Physics-Based Modelling

In an act of sabotage or terrorism, hazardous material might be released deliberately into the atmosphere to threaten individuals, e.g., those operating critical infrastructure. Hazardous materials in such a scenario include toxic industrial chemicals (TICs), which are often invisible to the human eye, making it difficult to detect and respond to releases in a timely manner. This contribution considers the scenario of an airborne hazardous release requiring rapid and reliable assessment, with a chemical, biological, radiological, and nuclear (CBRN) sensor system providing scarce and local measurements. We present a novel algorithm that couples these data with an advection-diffusion model to detect, localize, and quantify a moving and time-varying contaminant source. Unlike many existing methods, the approach identifies sources with unknown occurrence time and trajectory by incorporating spatial sparsity as prior information. The feasibility of the approach is demonstrated in a two-dimensional computational domain. To further increase the technology readiness level, we additionally propose a calibration methodology for the required three-dimensional flow models based on wind tunnel experiments. Finally, a strategy for coupling the framework with real-time sensor data within a digital twin environment is outlined to enable predictive decision support in emergency scenarios.

math.NA↗

arXiv2025

Sparse Source Identification in Transient Advection-Diffusion Problems with a Primal-Dual-Active-Point Strategy

This work presents a mathematical model to enable rapid prediction of airborne contaminant transport based on scarce sensor measurements. The method is designed for applications in critical infrastructure protection (CIP), such as evacuation planning following contaminant release. In such scenarios, timely and reliable decision-making is essential, despite limited observation data. To identify contaminant sources, we formulate an inverse problem governed by an advection-diffusion equation. Given the problem's underdetermined nature, we further employ a variational regularization ansatz and model the unknown contaminant sources as distribution over the spatial domain. To efficiently solve the arising inverse problem, we employ a problem-specific variant of the Primal-Dual-Active-Point (PDAP) algorithm which efficiently approximates sparse minimizers of the inverse problem by alternating between greedy location updates and source intensity optimization. The approach is demonstrated on two- and three-dimensional test cases involving both instantaneous and continuous contaminant sources and outperforms state-of-the-art techniques with $L^2$-regularization. Its effectiveness is further illustrated in complex domains with real-world building geometries imported from OpenStreetMap.

math.NA↗

arXiv2025

Goal-oriented optimal sensor placement for PDE-constrained inverse problems in crisis management

This paper presents a novel framework for goal-oriented optimal static sensor placement and dynamic sensor steering in PDE-constrained inverse problems, utilizing a Bayesian approach accelerated by low-rank approximations. The framework is applied to airborne contaminant tracking, extending recent dynamic sensor steering methods to complex geometries for computational efficiency. A C-optimal design criterion is employed to strategically place sensors, minimizing uncertainty in predictions. Numerical experiments validate the approach's effectiveness for source identification and monitoring, highlighting its potential for real-time decision-making in crisis management scenarios.

math.NA↗

arXiv2024

Contaminant Dispersion Simulation in a Digital Twin Framework for Critical Infrastructure Protection

A digital twin framework for rapid predictions of atmospheric contaminant dispersion is developed to support informed decision making in emergency situations. In an offline preparation phase, the geometry of a built environment is discretized with a finite element (FEM) mesh and a reduced-order model (ROM) of the steady-state incompressible Navier-Stokes equations is constructed for various wind conditions. Subsequently, the ROM provides a fast wind field estimate based on the current wind speed during the online phase. To support crisis management, several methodological building blocks are combined. Automatic FEM meshing of built environments and numerical flow solver capabilities enable fast forward-simulations of contaminant dispersion using the advection-diffusion equation as transport model. Further methods are integrated in the framework to address inverse problems such as contaminant source localization based on sparse concentration measurements. Additionally, the contaminant dispersion model is coupled with a continuum-based pedestrian crowd model to derive fast and safe evacuation routes for people seeking protection during contaminant dispersion emergencies. The interplay of these methods is demonstrated in two critical infrastructure protection (CIP) test cases. Based on simulated real world interaction (measurements, communication), this article demonstrates a full Measurement-Inversion-Prediction-Steering (MIPS) cycle including a Bayesian formulation of the inverse problem.

cs.CE↗