GAMM2025

Session

S15: Uncertainty quantification

S15

8 Apr 2025, 08:30

Lecture and Conference Centre

Conveners

S15: Uncertainty quantification: S15.01

• Roland Pulch
• Magdalena Łasecka-Plura

S15: Uncertainty quantification: S15.02

• Ulrich Römer
• Kerstin Lux-Gottschalk

S15: Uncertainty quantification: S15.03

• Magdalena Łasecka-Plura
• Roland Pulch

S15: Uncertainty quantification: S15.04

• Ulrich Römer
• Andrea Barth

S15: Uncertainty quantification: S15.05

• Ulrich Römer
• Roland Pulch

Description

The session especially welcomes contributions to the following topics: uncertainty quantification; risk analysis and assessment; Bayesian methods in engineering; decision analysis; stochastic modeling (including spatio-temporal modeling); stochastic mechanics; stochastic algorithms and simulation; stochastic processes (including time series); resampling methods; stochastic networks. Applications to large scaled problems are encouraged.

397. On significance of probabilistic entropy and distance in elasto-plasticity problems

Marcin Kamiński

08/04/2025, 08:30

This work's main aim is to quantify uncertainty in some elastoplasticity problems using probabilistic entropy and probabilistic distance. Classical theoretical and computational approaches based on probabilistic moments and characteristics are contrasted with Shannon entropy in order to obtain and test a single uncertainty measure in certain nonlinear problems of solid mechanics. A general...

402. Random vibrations of internally supported plates by the Boundary Element Method

Michał Guminiak

08/04/2025, 09:10

The main aim is to study natural vibrations of the Kirchhoff-Love elastic plates by various probabilistic extensions of the Boundary Element Method. Uncertainty quantification is provided for various material and geometrical parameters including especially a plate thickness [1,2]. They are traditionally considered as Gaussian due to the Maximum Entropy Principle, nevertheless the methodology...

403. Combining first-order second-moment method and internal numerical differentiation for efficient uncertainty quantification

Jendrik-Alexander Tröger

08/04/2025, 09:30

Calibrating constitutive models based on experimental data is a common task to ensure the reliability of numerical models in solid mechanics. This calibration is usually accompanied by quantifying material parameter uncertainties, either through approximations considering asymptotic normality or stochastic approaches such as Bayesian methods. However, propagating these material parameter...

406. On modeling of porous-media wetting with randomly distributed hydrophobic defects

Lisanne Gossel

08/04/2025, 09:50

Capillary flow through porous media plays a crucial role in applications ranging from material science to biological systems. We are interested in quantifying the effect of hydrophobic defects in a heterogeneous wetting problem, which can for example occur in powder processing problems for food technologies [1]. In real-world applications such as the one mentioned before, the amount and...

407. Estimates of errors generated by uncertain data in a coupled pieso-electric problem

Tatiana Samrowski

08/04/2025, 10:10

The paper is concerned with a coupled piezo-electric problem with incompletely known coefficients of the elasticity tensor and two other tensors that define electric properties of the media. Due to this uncertainty, the problem possesses a set (cloud) of equally probable solutions instead of the unique solution. Quantitative characteristics of this set are derived by a posteriori estimates of...

412. Deep learning methods for stochastic Galerkin approximations of ranodm PDEs

Andrea Barth

08/04/2025, 16:30

In this talk we consider stochastic Galerkin approximations of linear elliptic partial differential equations with stochastic forcing terms and stochastic diffusion coefficients, that cannot be bounded uniformly away from zero and infinity. A traditional numerical method for solving the resulting high-dimensional coupled system of PDEs is replaced by deep learning techniques. In order to...

417. Stochastic Galerkin method for delay differential equations with random parameters

Roland Pulch

08/04/2025, 16:50

We consider systems of delay differential equations (DDEs) with discrete delays, where the right-hand side is linear or a polynomial of low degree. Physical parameters are replaced by random variables to model and quantify uncertainties. Thus the solutions represent random processes. We expand a random process into the generalised polynomial chaos, which is a series consisting of orthogonal...

423. Markov chain Monte Carlo with particle-solver-based likelihoods

Emil Løvbak

08/04/2025, 17:10

In various application domains, one wishes to determine which parameter values should be used for a model to match its simulation output with measurement data. In practice however, measurement error on the data means that, at best, one can produce a so-called posterior probability distribution of these parameter values, given an assumed noise model. The Markov chain Monte Carlo method is a...

430. An adaptive Quasi Monte Carlo approach for concentrated distributions

Jinyi Zhou

08/04/2025, 17:30

Quasi Monte Carlo methods are very popular in uncertainty quatification because of their high convergence order compared to Monte Carlo methods. Their downside is that they sample from a uniform distribution and, therefore, they become inefficient for problems with complex and concentrated distributions. We have developed an adaptive Quasi-Monte Carlo (aQMC) quadrature which concentrates the...

434. Earthquake-induced multimodal non-linear stochastic response of the guy line in the guyed tower

Hanna Weber

08/04/2025, 17:50

Ropes are used in modern structures as load-bearing elements for various applications, e.g. the main cables or cross-ties in cable-stayed bridges, cable roof structures, or high-voltage transmissions lines. Guy lines are designed to stabilize the structure and keep it in the right position against external loads.

Since the ropes do not transfer compressive forces, they require significant...

449. Uncertainty Quantification For Lévy Random Fields - Theory and Numerics

Hanno Gottschalk

09/04/2025, 08:30

Uncertainty quantification for Gaussian Random Fields as coefficients in partial differential equations is a often studied problem. Here we review UQ for Lévy Random Fields and prove the convergence of a Karhunen-Loeve-like expansion. Also we deal with (learned) sparse grid quadratures for multivariate Lévy distributions and apply this to the Darcy flow equation.

452. Laplace Transform–Based Non-Probabilistic Uncertainty Analysis of Viscoelastically Damped Structures

Magdalena Łasecka-Plura

09/04/2025, 09:10

Contemporary issues in the dynamics of engineering systems are becoming increasingly complex due to growing demands for reliability, durability, and efficiency in structural designs. One of the key aspects of analyzing such systems is the consideration of uncertainties, which may arise from various sources, such as material variability, geometric imperfections, or difficulties in accurately...

461. Efficient first order second moment method for stochastic vibroacoustic problems with uncertain loads

Yannik Hüpel

09/04/2025, 09:30

Early design simulative cabin noise assessment is indispensable when designing novel aircraft. When considering an early design stage, many crucial parameters needed for the simulation, such as material parameters and excitation, are not known yet and make the noise assessment challenging. Therefore, uncertainties should be considered in the simulation chain, in order to obtain a more robust...

467. Incorporating Model Form Uncertainty in Digital Twins for Reliable Parameter Updating and Quantities of Interest Analysis

Daniel Andrés Arcones

09/04/2025, 09:50

With the rapid adoption of Digital Twins in recent years, simulation models designed to replicate real-world physical systems have become increasingly common. To achieve accurate representations, it is typically necessary to update model parameters based on observations collected from sensors or measurements of the physical asset. However, no model can fully capture the infinitely complex...

649. Sensitivity Analysis of Bifurcation Curves

Kerstin Lux-Gottschalk

09/04/2025, 16:30

Many real-world systems exhibit inherently nonlinear dynamics which can induce sudden, large and oftentimes irreversible changes when an external forcing parameter is varied. This phenomenon is known as tipping with Greenland Ice Sheet melting and the weakening of the Atlantic Meridional Overturning Circulation as prominent examples of climate tipping elements. We model these tipping phenomena...

650. Augmented First-Order Reliability Method for Estimation of Imprecise Failure Probabilities

Marcos Valdebenito

09/04/2025, 16:50

Probability theory offers a practical and sound framework for assessing the reliability (or its complement, the failure probability) of engineering systems. In such a framework, the uncertainty associated with the input variables of a numerical model is described in terms of a joint probability distribution. Then, the probability of failure of the system is computed by integrating such joint...

651. Reliability analysis of structures with correlated random variables considering uncertain distribution parameters

Peipei Li, Marcos A. Valdebenito, Matthias G.R. Faes

09/04/2025, 17:10

In engineering practice, epistemic uncertainty widely exists due to imperfect modeling, simplifications, and limited data. Among these uncertainties, uncertainty in distribution parameters has drawn significant attention. To comprehensively evaluate structural reliability under the distribution parameter uncertainty, often referred to as conditional failure probability, several methods have...

652. Sensitivity Estimation of Failure Probability with Respect to Input Distribution Parameters in Stochastic Computational Models

Xuan-Yi Zhang

09/04/2025, 17:30

Computational models play a crucial role in decision-making across various disciplines, including engineering, science, economics, policy-making, and beyond, especially when input randomness introduces stochasticity into the outputs. Sensitivity estimation (SE) is essential for understanding how input variability influences these stochastic outputs. Unlike traditional methods that focus...

653. Optimization of shell structures with fuzzy-probability based random fields using artificial neural networks

Maximilian Schweizer

09/04/2025, 17:50

The structural design optimization aims for a robust structure with minimal use of material resources, leading to slender and thin-walled structures, which entails a higher risk of stability problems. This issue is further influenced by geometrical imperfections, which are subject to uncertainties. In a common stochastic approach, imperfections can be simulated as random fields with the...

654. A high-performance multi-level stochastic gradient descent method with applications in optimal control under uncertainty

David Schneiderhan

09/04/2025, 18:10

We present a high-performance multi-level stochastic gradient descent method to optimally control the state of systems guided by partial differential equations under uncertain input data. The gradient descent method, used to find the optimal control, leverages a parallel budgeted multi-level Monte Carlo method as stochastic sub-gradient estimator. As a result, we get tight control over the...

655. Bayesian shape inversion in time-harmonic scattering

Laura Scarabosio

10/04/2025, 08:30

We consider the inverse problem of recovering the shape of an object from measurements of how it scatters time-harmonic waves. To quantify the uncertainy, the problem is cast in a Bayesian framework and we discuss possible choices for the prior distribution for the shape. As prototype of time-harmonic scattering, we consider the Helmholtz equation to relate the shape to the measurements and...

656. Sequential Quasi-Monte-Carlo Sampling for Bayesian Inference of Chemical Kinetic Models Utilizing Normalizing Flows

Andreas Panagiotopoulos

10/04/2025, 09:10

Chemical kinetic models pose particular challenges to Bayesian parameter estimation due to their high nonlinearity and sensitivity. Additionally, priors are largely unformative whereas experimental data has a comparatively high accuracy. As a consequence posteriors can become highly complex and localized compared to the prior. As a possible route to address such problems, we explore an...

657. Comparison of mono-level and bi-level approaches for surrogate-based robust optimization

Julius Schultz

10/04/2025, 09:30

Robust optimization is a crucial technique for enabling design optimization in safety-critical applications, such as those found in the aerospace industry. The objective is to identify an optimal design that is relatively insensitive to uncertainties arising from uncertain model parameters, the model form itself, or unknown environmental conditions. These uncertainties introduce randomness...

658. Infinite Dimensional Bayesian Inversion for Semiconductor Devices

Leila Taghizadeh

10/04/2025, 09:50

Semiconductor technology plays an essential role in modern life today. Devices in \linebreak nanoscale including sensors using semiconductor technology have crucial real-world applications ranging from bio-sensing medical applications to energy conversion in solar cells as well as the generation of security keys in cyber-security. Modeling charge transport in semiconductor devices has been of...

659. Exploring Imprecise Probabilities in Quantum Algorithms with Possibility Theory

Jan Schneider

10/04/2025, 10:10

Quantum computing harnesses the principles of quantum mechanics to tackle computational tasks that are infeasible for classical machines. Qubits, capable of existing in superposition and forming entangled states, enable quantum algorithms like Shor’s factoring method to surpass traditional techniques. This technology holds promise across numerous domains, including cryptography, pharmaceutical...