@article{MuellerMartinezLahuertaSekulicetal.2025, author = {M{\"u}ller, Gabriel and Mart{\´i}nez-Lahuerta, Victor J. and Sekulic, Ivan and Burger, Sven and Schneider, Philipp-Immanuel and Gaaloul, Naceur}, title = {Bayesian optimization for state engineering of quantum gases}, volume = {10}, journal = {Quantum Sci. Technol.}, arxiv = {http://arxiv.org/abs/2404.18234}, doi = {10.1088/2058-9565/ad9050}, pages = {015033}, year = {2025}, language = {en} } @article{ErbanWinkelmann2025, author = {Erban, Radek and Winkelmann, Stefanie}, title = {Multi-grid reaction-diffusion master equation: applications to morphogen gradient modelling}, volume = {87}, journal = {Bulletin of Mathematical Biology}, arxiv = {http://arxiv.org/abs/arXiv:2405.02117}, doi = {10.1007/s11538-024-01377-y}, pages = {6}, year = {2025}, abstract = {The multi-grid reaction-diffusion master equation (mgRDME) provides a generalization of stochastic compartment-based reaction-diffusion modelling described by the standard reaction-diffusion master equation (RDME). By enabling different resolutions on lattices for biochemical species with different diffusion constants, the mgRDME approach improves both accuracy and efficiency of compartment-based reaction-diffusion simulations. The mgRDME framework is examined through its application to morphogen gradient formation in stochastic reaction-diffusion scenarios, using both an analytically tractable first-order reaction network and a model with a second-order reaction. The results obtained by the mgRDME modelling are compared with the standard RDME model and with the (more detailed) particle-based Brownian dynamics simulations. The dependence of error and numerical cost on the compartment sizes is defined and investigated through a multi-objective optimization problem.}, language = {en} } @inproceedings{VillaniUngerWeiser2024, author = {Villani, Paolo and Unger, J{\"o}rg F. and Weiser, Martin}, title = {Adaptive Gaussian Process Regression for Bayesian inverse problems}, booktitle = {Proceedings of the Conference Algoritmy 2024}, pages = {214 -- 224}, year = {2024}, abstract = {We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on optimizing both the positioning and simulation accuracy of training data in order to reduce the computational cost of simulating training data without compromising the fidelity of the posterior distributions of parameters. The method interleaves a goal-oriented active learning algorithm selecting evaluation points and tolerances based on the expected impact on the Kullback-Leibler divergence of surrogated and true posterior with a Markov Chain Monte Carlo sampling of the posterior. The performance benefit of the adaptive approach is demonstrated for two simple test problems.}, language = {en} } @article{AndresArconesWeiserKoutsourelakisetal.2023, author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Faidon-Stelios and Unger, J{\"o}rg F.}, title = {A Bayesian Framework for Simulation-based Digital Twins of Bridges}, volume = {6}, journal = {EUROSTRUCT 2023:European Association on Quality Control of Bridges and Structures: Digital Transformation in Sustainability}, number = {5}, doi = {10.1002/cepa.2177}, pages = {734 -- 740}, year = {2023}, abstract = {Simulation-based digital twins have emerged as a powerful tool for evaluating the mechanical response of bridges. As virtual representations of physical systems, digital twins can provide a wealth of information that complements traditional inspection and monitoring data. By incorporating virtual sensors and predictive maintenance strategies, they have the potential to improve our understanding of the behavior and performance of bridges over time. However, as bridges age and undergo regular loading and extreme events, their structural characteristics change, often differing from the predictions of their initial design. Digital twins must be continuously adapted to reflect these changes. In this article, we present a Bayesian framework for updating simulation-based digital twins in the context of bridges. Our approach integrates information from measurements to account for inaccuracies in the simulation model and quantify uncertainties. Through its implementation and assessment, this work demonstrates the potential for digital twins to provide a reliable and up-to-date representation of bridge behavior, helping to inform decision-making for maintenance and management.}, language = {en} } @inproceedings{AndresArconesWeiserKoutsourelakisetal.2023, author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Faidon-Stelios and Unger, J{\"o}rg F.}, title = {Evaluation of Model Bias Identification Approaches Based on Bayesian Inference and Applications to Digital Twins}, booktitle = {5th ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering}, pages = {1 -- 15}, year = {2023}, abstract = {In recent years, the use of simulation-based digital twins for monitoring and assessment of complex mechanical systems has greatly expanded. Their potential to increase the information obtained from limited data makes them an invaluable tool for a broad range of real-world applications. Nonetheless, there usually exists a discrepancy between the predicted response and the measurements of the system once built. One of the main contributors to this difference in addition to miscalibrated model parameters is the model error. Quantifying this socalled model bias (as well as proper values for the model parameters) is critical for the reliable performance of digital twins. Model bias identification is ultimately an inverse problem where information from measurements is used to update the original model. Bayesian formulations can tackle this task. Including the model bias as a parameter to be inferred enables the use of a Bayesian framework to obtain a probability distribution that represents the uncertainty between the measurements and the model. Simultaneously, this procedure can be combined with a classic parameter updating scheme to account for the trainable parameters in the original model. This study evaluates the effectiveness of different model bias identification approaches based on Bayesian inference methods. This includes more classical approaches such as direct parameter estimation using MCMC in a Bayesian setup, as well as more recent proposals such as stat-FEM or orthogonal Gaussian Processes. Their potential use in digital twins, generalization capabilities, and computational cost is extensively analyzed.}, language = {en} } @article{MaierWeiserConrad2025, author = {Maier, Kristina and Weiser, Martin and Conrad, Tim}, title = {Hybrid PDE-ODE Models for Efficient Simulation of Infection Spread in Epidemiology}, volume = {481}, journal = {Proceedings of the Royal Society A}, number = {2306}, publisher = {Royal Society}, arxiv = {http://arxiv.org/abs/2405.12938}, doi = {10.1098/rspa.2024.0421}, year = {2025}, abstract = {This paper introduces a novel hybrid model combining Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs) to simulate infectious disease dynamics across geographic regions. By leveraging the spatial detail of PDEs and the computational efficiency of ODEs, the model enables rapid evaluation of public health interventions. Applied to synthetic environments and real-world scenarios in Lombardy, Italy, and Berlin, Germany, the model highlights how interactions between PDE and ODE regions affect infection dynamics, especially in high-density areas. Key findings reveal that the placement of model boundaries in densely populated regions can lead to inaccuracies in infection spread, suggesting that boundaries should be positioned in areas of lower population density to better reflect transmission dynamics. Additionally, regions with low population density hinder infection flow, indicating a need for incorporating, e.g., jumps in the model to enhance its predictive capabilities. Results indicate that the hybrid model achieves a balance between computational speed and accuracy, making it a valuable tool for policymakers in real-time decision-making and scenario analysis in epidemiology and potentially in other fields requiring similar modeling approaches.}, language = {en} } @article{AndresArconesWeiserKoutsourelakisetal.2024, author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Faidon-Stelios and Unger, J{\"o}rg F.}, title = {Model bias identification for Bayesian calibration of stochastic digital twins of bridges}, volume = {41}, journal = {Applied Stochastic Models in Business and Industry}, number = {3}, doi = {10.1002/asmb.2897}, year = {2024}, abstract = {Simulation-based digital twins must provide accurate, robust and reliable digital representations of their physical counterparts. Quantifying the uncertainty in their predictions plays, therefore, a key role in making better-informed decisions that impact the actual system. The update of the simulation model based on data must be then carefully implemented. When applied to complex standing structures such as bridges, discrepancies between the computational model and the real system appear as model bias, which hinders the trustworthiness of the digital twin and increases its uncertainty. Classical Bayesian updating approaches aiming to infer the model parameters often fail at compensating for such model bias, leading to overconfident and unreliable predictions. In this paper, two alternative model bias identification approaches are evaluated in the context of their applicability to digital twins of bridges. A modularized version of Kennedy and O'Hagan's approach and another one based on Orthogonal Gaussian Processes are compared with the classical Bayesian inference framework in a set of representative benchmarks. Additionally, two novel extensions are proposed for such models: the inclusion of noise-aware kernels and the introduction of additional variables not present in the computational model through the bias term. The integration of such approaches in the digital twin corrects the predictions, quantifies their uncertainty, estimates noise from unknown physical sources of error and provides further insight into the system by including additional pre-existing information without modifying the computational model.}, language = {en} } @article{WehlitzSadeghiMontefuscoetal.2025, author = {Wehlitz, Nathalie and Sadeghi, Mohsen and Montefusco, Alberto and Sch{\"u}tte, Christof and Pavliotis, Grigorios A. and Winkelmann, Stefanie}, title = {Approximating particle-based clustering dynamics by stochastic PDEs}, volume = {24}, journal = {SIAM Journal on Applied Dynamical Systems}, number = {2}, arxiv = {http://arxiv.org/abs/2407.18952}, doi = {10.1137/24M1676661}, pages = {1231 -- 1250}, year = {2025}, abstract = {This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane mediated receptor dynamics on cell surfaces, we formulate a stochastic particle-based model for diffusion and pairwise interaction of particles, leading to intriguing clustering phenomena. Employing numerical simulation and cluster detection methods, we explore the approximation of the particle-based clustering dynamics through mean-field approaches. We find that SPDEs successfully reproduce spatiotemporal clustering dynamics, not only in the initial cluster formation period, but also on longer time scales where the successive merging of clusters cannot be tracked by deterministic mean-field models. The computational efficiency of the SPDE approach allows us to generate extensive statistical data for parameter estimation in a simpler model that uses a Markov jump process to capture the temporal evolution of the cluster number.}, language = {en} } @article{HoeflingStraube2025, author = {H{\"o}fling, Felix and Straube, Arthur}, title = {Langevin equations and a geometric integration scheme for the overdamped limit of rotational Brownian motion of axisymmetric particles}, volume = {7}, journal = {Physical Review Research}, arxiv = {http://arxiv.org/abs/2403.04501}, doi = {10.1103/wzdn-29p4}, pages = {043034}, year = {2025}, abstract = {The translational motion of anisotropic or self-propelled colloidal particles is closely linked with the particle's orientation and its rotational Brownian motion. In the overdamped limit, the stochastic evolution of the orientation vector follows a diffusion process on the unit sphere and is characterized by an orientation-dependent ("multiplicative") noise. As a consequence, the corresponding Langevin equation attains different forms depending on whether Itō's or Stratonovich's stochastic calculus is used. We clarify that both forms are equivalent and derive them in a top-down approach from a geometric construction of Brownian motion on the unit sphere, based on infinitesimal random rotations. Our approach suggests further a geometric integration scheme for rotational Brownian motion, which preserves the normalization constraint of the orientation vector exactly. We show that a simple implementation of the scheme, using Gaussian random rotations, converges weakly at order 1 of the integration time step, and we outline an advanced variant of the scheme that is weakly exact for an arbitrarily large time step. Due to a favorable prefactor of the discretization error, already the Gaussian scheme allows for integration time steps that are one order of magnitude larger compared to a commonly used algorithm for rotational Brownian dynamics simulations based on projection on the constraining manifold. For torques originating from constant external fields, we prove by virtue of the Fokker-Planck equation that the constructed diffusion process satisfies detailed balance and converges to the correct equilibrium distribution. The analysis is restricted to time-homogeneous rotational Brownian motion (i.e., a single rotational diffusion constant), which is relevant for axisymmetric particles and also chemically anisotropic spheres, such as self-propelled Janus particles.}, language = {en} } @article{SchaibleWinartoŠkorjancetal.2025, author = {Schaible, Jonas and Winarto, Hanifah and Škorjanc, Viktor and Yoo, Danbi and Zimmermann, Lea and J{\"a}ger, Klaus and Sekulic, Ivan and Schneider, Philipp-Immanuel and Burger, Sven and Wessels, Andreas and Bl{\"a}si, Benedikt and Becker, Christiane}, title = {Optimizing Aesthetic Appearance of Perovskite Solar Cells Using Color Filters}, volume = {9}, journal = {Solar RRL}, publisher = {Wiley}, doi = {10.1002/solr.202400627}, pages = {2400627}, year = {2025}, abstract = {The significance of color aesthetics in photovoltaic (PV) modules gains importance, especially in design-centric applications like building-integrated PVs. Color filters based on distributed Bragg reflectors, consisting of alternating thin-film layers of different refractive indices, can modify the appearance of standard silicon modules. This approach is also extended to optimize the color appearance of emerging PV technologies such as perovskite solar cells, which typically exhibit a less appealing gray-brownish appearance. In this contribution, perovskite solar-cell stacks combined with MorphoColor color filters are presented. Angular-resolved reflectance simulations based on wave optics and ray tracing with experimental data are validated, and the color appearance from various viewing angles is evaluated. Additionally, the impact of individual layers on color appearance and the maximum achievable short-circuit current density in the perovskite solar cell is investigated. By applying Bayesian optimization, the color distance is minimized to the targeted appearance. Tailoring the bridging layers between the color filter and the perovskite solar cell is found to strongly influence the color impression due to the coherently combined color filter and perovskite solar cell. The presented color optimization concept allows to customize the aesthetics of emerging PV thin-film technologies such as perovskite solar cells.}, language = {en} } @misc{RocheBetzYangetal.2024, author = {Roche, L{\´e}o J. and Betz, Fridtjof and Yang, Yuhui and Limame, Imad and Shih, Ching-Wen and Burger, Sven and Reitzenstein, Stephan}, title = {Inside Front Cover: Numerical Investigation of a Coupled Micropillar - Waveguide System for Integrated Quantum Photonic Circuits (Adv. Quantum Technol. 12/2024)}, volume = {7}, journal = {Adv. Quantum Technol.}, doi = {10.1002/qute.202470036}, pages = {2470036}, year = {2024}, language = {en} }