arXiv subjects

Max von Danwitz

Publications and source records attributed to Max von Danwitz.

15 recordsLinked to original sources

arXiv2026

Intrusive and Non-Intrusive Model Order Reduction for Airborne Contaminant Transport: Comparative Analysis and Uncertainty Quantification

Numerical simulations of contaminant dispersion after a gas leakage incident at a chemical plant can provide valuable insights for both emergency response and preparedness. High-fidelity simulation approaches combine incompressible Navier-Stokes (INS) equations with advection-diffusion processes to model wind and concentration field. However, their computational cost increases rapidly for complex geometries and extended domains like urban environments. This renders them unfeasible in time-critical or multi-query "what-if" scenarios, making model order reduction (MOR) techniques particularly valuable for enabling fast, accurate predictions. This study describes a MOR-based, application-driven workflow for uncertainty-aware contaminant concentration prediction, demonstrated for a two-dimensional benchmark system. Starting with the model selection, relevant comparison criteria and trade-offs are discussed for well-established proper orthogonal decomposition based (non-)intrusive methods, applied to the computationally more demanding parametric INS problem. They include accuracy, computational efficiency, data requirements, and extrapolation capability. Based on these insights, a non-intrusive parametric reduced-order model is constructed that enables accelerated Monte Carlo simulations for estimating the influence of potential wind measurement uncertainties on the spatio-temporal concentration field. This enables extracting valuable information for local consequence analyses and evacuation planning. Simulation results are furthermore interactively visualized in a dashboard and can serve as a building block within broader decision-support systems.

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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

High-Fidelity Numerical Modeling for the Mechanical Characterization of a Full-Scale Test Bridge

Bridges are vital components of transportation networks, serving as critical lifelines that ensure the safe and efficient movement of people, goods, and emergency services. With aging infrastructures, increasing traffic volumes and loads, and growing impact of extreme weather events driven by climate change, the development of reliable structural health monitoring (SHM) strategies has become of utmost importance. A key challenge in this domain is the scarcity of data on well-characterized damage states. To address this, a monitoring campaign was recently conducted on a full-scale, two-span test bridge specifically designed and built at the University of the Bundeswehr Munich to investigate damage scenarios related to specific structural deficiencies of the deck and to foundations settlement, the latter being connected to failure mechanisms typical in the context of floodings, when scour, i.e., washing out of the foundations, might happen. The test bridge is a crucial intermediate step between laboratory-scale experiments and real-world monitoring. In this study, a high-fidelity, physics-based numerical model of the same structure is presented as a complementary tool. The model enables accurate performances assessment and provides a detailed reference to interpret measured responses under varying environmental conditions and artificial damage scenarios. Experimental data collected under operational conditions were used to refine the model's mechanical characterization through Bayesian updating. The goal is to develop a functional digital twin of the test bridge, acting as a dynamic, data-driven shadow of the physical structure, to support informed maintenance decisions, extend service life, and enhance safety in future studies applied to real-world infrastructures.

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arXiv2026

Physics-Informed Sensitivity Analysis for Enhanced Structural Health Assessment: Test-Case for a Mixed Steel-Concrete Bridge

Bridges are vital components of transportation systems, that serve as essential links ensuring the safe and efficient movement of people, goods, and emergency responders, especially during crises. With aging infrastructures, increasing traffic volumes and loads, and the intensifying impacts of extreme weather events due to climate change, the development of effective physics-informed structural health monitoring (SHM) frameworks has become critically important, more so when combined with sensitivity analysis (SA), which identifies the most influential structural parameters in the bridge's response. To support this, a high-fidelity, physics-based numerical model of a full-scale, two-span, mixed steel-concrete test bridge has been developed. This model serves as a virtual replica of a real structure located at the University of the Bundeswehr Munich. The numerical model is used as a complementary tool to improve prognostic capabilities and quantify uncertainty. A SA study is conducted to evaluate the structure's response under various mechanical conditions. Assessing these operational variations' effects on structural behavior forms part of an integrated, systematic evaluation framework aimed at combining SHM and SA.

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arXiv2026

Towards Interpretable Damage Detection based on Aerodynamic Pressure Measurements

The increasing flexibility of modern large wind turbine blades necessitates cost-efficient and reliable structural monitoring solutions. For this purpose, we propose to use aerodynamic pressure measurements obtained via Aerosense, a novel, non-intrusive and economical sensing system. In former work [Franz et al., 2025], we investigated the potential of aerodynamic pressure measurements for structural damage detection on elastic and aerodynamically loaded structures. An experimental campaign was conducted on a NACA 633418 airfoil mounted on a vertically vibrating cantilever beam within an open wind tunnel. Structural damage was introduced progressively through controlled saw cuts near the beam support. Aerodynamic pressure distributions were recorded under varying inflow conditions and structural states. Based on this data set, we developed a convolutional neural network to detect structural damage and classify its severity using only aerodynamic pressure signals. The results demonstrate that pressure measurements can effectively enable real-time detection and quantification of damage in elastic, beam-like structures subjected to mildly turbulent flow and varying operational conditions. Recognizing the limitations of pure black-box classification, in this study, we further incorporate physics-based insights and explainable machine learning methods to interpret how structural damage influences both the dynamic response and the aerodynamic pressure field. This leads to an enhanced damage detection pipeline, aiming to improve transparency, robustness, and physical consistency in data-driven monitoring of elastic, aerodynamically loaded structures.

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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↗

arXiv2026

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.

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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.

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arXiv2024

Towards Real-Time Urban Physics Simulations with Digital Twins

Urban populations continue to grow, highlighting the critical need to safeguard civilians against potential disruptions, such as dangerous gas contaminant dispersion. The digital twin (DT) framework offers promise in analyzing and predicting such events. This study presents a computational framework for modelling airborne contaminant dispersion in built environments. Leveraging automatic generation of computational domains and solution processes, the proposed framework solves the underlying physical model equations with the finite element method (FEM) for numerical solutions. Model order reduction (MOR) methods are investigated to enhance computational efficiency without compromising accuracy. The study outlines the automatic model generation process, the details of the employed model, and the future perspectives for the realization of a DT. Throughout this research, the aim is to develop a reliable predictive model combining physics and data in a hybrid DT to provide informed real-time support within evacuation scenarios.

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arXiv2024

Towards a Hybrid Digital Twin: Physics-Informed Neural Networks as Surrogate Model of a Reinforced Concrete Beam

In this study, we investigate the potential of fast-to-evaluate surrogate modeling techniques for developing a hybrid digital twin of a steel-reinforced concrete beam, serving as a representative example of a civil engineering structure. As surrogates, two distinct models are developed utilizing physics-informed neural networks, which integrate experimental data with given governing laws of physics. The experimental data (sensor data) is obtained from a previously conducted four-point bending test. The first surrogate model predicts strains at fixed locations along the center line of the beam for various time instances. This time-dependent surrogate model is inspired by the motion of a harmonic oscillator. For this study, we further compare the physics-based approach with a purely data-driven method, revealing the significance of physical laws for the extrapolation capabilities of models in scenarios with limited access to experimental data. Furthermore, we identify the natural frequency of the system by utilizing the physics-based model as an inverse solver. For the second surrogate model, we then focus on a fixed instance in time and combine the sensor data with the equations of linear elasticity to predict the strain distribution within the beam. This example reveals the importance of balancing different loss components through the selection of suitable loss weights.

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arXiv2023

Model Order Reduction for Deforming Domain Problems in a Time-Continuous Space-Time Setting

In the context of simulation-based methods, multiple challenges arise, two of which are considered in this work. As a first challenge, problems including time-dependent phenomena with complex domain deformations, potentially even with changes in the domain topology, need to be tackled appropriately. The second challenge arises when computational resources and the time for evaluating the model become critical in so-called many query scenarios for parametric problems. For example, these problems occur in optimization, uncertainty quantification (UQ), or automatic control and using highly resolved full-order models (FOMs) may become impractical. To address both types of complexity, we present a novel projection-based model order reduction (MOR) approach for deforming domain problems that takes advantage of the time-continuous space-time formulation. We apply it to two examples that are relevant for engineering or biomedical applications and conduct an error and performance analysis. In both cases, we are able to drastically reduce the computational expense for a model evaluation and, at the same time, to maintain an adequate accuracy level. All in all, this work indicates the effectiveness of the presented MOR approach for deforming domain problems taking advantage of a time-continuous space-time setting.

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arXiv2022

Time-Continuous and Time-Discontinuous Space-Time Finite Elements for Advection-Diffusion Problems

We construct four variants of space-time finite element discretizations based on linear tensor-product and simplex-type finite elements. The resulting discretizations are continuous in space, and continuous or discontinuous in time. In a first test run, all four methods are applied to a linear scalar advection-diffusion model problem. Then, the convergence properties of the time-discontinuous space-time finite element discretizations are studied in numerical experiments. Advection velocity and diffusion coefficient are varied, such that the parabolic case of pure diffusion (heat equation), as well as, the hyperbolic case of pure advection (transport equation) are included in the study. For each model parameter set, the L2 error at the final time is computed for spatial and temporal element lengths ranging over several orders of magnitude to allow for an individual evaluation of the methods' spatial, temporal, and spacetime accuracy. In the parabolic case, particular attention is paid to the influence of time-dependent boundary conditions. Key findings include a spatial accuracy of second order and a temporal accuracy between second and third order. The temporal accuracy tends towards third order depending on how advection-dominated the test case is, on the choice of the specific discretization method, and on the time-(in)dependence and treatment of the boundary conditions. Additionally, the potential of time-continuous simplex space-time finite elements for heat flux computations is demonstrated with a piston ring pack test case.

math.NA↗

arXiv2020

Four-Dimensional Elastically Deformed Simplex Space-Time Meshes for Domains with Time Variant Topology

Thinking of the flow through biological or technical valves, there is a variety of applications in which the topology of a fluid domain changes over time. This topology change is characteristic for the physical behaviour, but poses a particular challenge in computer simulations. A way to overcome this challenge is to consider the space-time extent of the application as a contiguous computational domain. In this work, we obtain a boundary conforming discretization of the space-time domain with four-dimensional simplex elements (pentatopes). To facilitate the construction of pentatope meshes for complex geometries, the widely used elastic mesh update method is extended to four-dimensional meshes. In the resulting workflow, the topology change is elegantly included in the pentatope mesh and does not require any additional treatment during the simulation. The potential of simplex space-time meshes for domains with time variant topology is demonstrated in a valve simulation and a flow simulation inspired by a clamped artery.

math.NA↗

arXiv2018

Simplex Space-Time Meshes in Compressible Flow Simulations

Employing simplex space-time meshes enlarges the scope of compressible flow simulations. The simultaneous discretization of space and time with simplex elements extends the flexibility of unstructured meshes from space to time. In this work, we adopt a finite element formulation for compressible flows to simplex space-time meshes. The method obtained allows, e.g., flow simulations on spatial domains that change topology with time. We demonstrate this with the two-dimensional simulation of compressible flow in a valve that fully closes and opens again. Furthermore, simplex space-time meshes facilitate local temporal refinement. A three-dimensional transient simulation of blow-by past piston rings is run in parallel on 120 cores. The timings point out savings of computation time gained from local temporal refinement in space-time meshes.

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