TY - JOUR A1 - Niemann, Jan-Hendrik A1 - Klus, Stefan A1 - Conrad, Natasa Djurdjevac A1 - Schütte, Christof T1 - Koopman-Based Surrogate Models for Multi-Objective Optimization of Agent-Based Systems JF - Physica D: Nonlinear Phenomena N2 - Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics of ABMs, the demand to solve optimization problems to support, for example, decision-making processes naturally arises. Most ABMs, however, are non-deterministic, high-dimensional dynamical systems, so objectives defined in terms of their behavior are computationally expensive. In particular, if the number of agents is large, evaluating the objective functions often becomes prohibitively time-consuming. We consider data-driven reduced models based on the Koopman generator to enable the efficient solution of multi-objective optimization problems involving ABMs. In a first step, we show how to obtain data-driven reduced models of non-deterministic dynamical systems (such as ABMs) that depend on potentially nonlinear control inputs. We then use them in the second step as surrogate models to solve multi-objective optimal control problems. We first illustrate our approach using the example of a voter model, where we compute optimal controls to steer the agents to a predetermined majority, and then using the example of an epidemic ABM, where we compute optimal containment strategies in a prototypical situation. We demonstrate that the surrogate models effectively approximate the Pareto-optimal points of the ABM dynamics by comparing the surrogate-based results with test points, where the objectives are evaluated using the ABM. Our results show that when objectives are defined by the dynamic behavior of ABMs, data-driven surrogate models support or even enable the solution of multi-objective optimization problems. Y1 - 2024 U6 - https://doi.org/https://doi.org/10.1016/j.physd.2024.134052 VL - 460 SP - 134052 ER - TY - JOUR A1 - Lücke, Marvin A1 - Winkelmann, Stefanie A1 - Heitzig, Jobst A1 - Molkenthin, Nora A1 - Koltai, Péter T1 - Learning interpretable collective variables for spreading processes on networks JF - Physical Review E N2 - Collective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes on networks. The relation between CVs and network measures is not well understood and its derivation typically requires detailed knowledge of both the dynamical system and the network topology. In this Letter, we present a data-driven method for algorithmically learning and understanding CVs for binary-state spreading processes on networks of arbitrary topology. We demonstrate our method using four example networks: the stochastic block model, a ring-shaped graph, a random regular graph, and a scale-free network generated by the Albert-Barabási model. Our results deliver evidence for the existence of low-dimensional CVs even in cases that are not yet understood theoretically. Y1 - 2024 U6 - https://doi.org/10.1103/PhysRevE.109.L022301 VL - 109 IS - 2 SP - L022301 ER - TY - JOUR A1 - Binkowski, Felix A1 - Betz, Fridtjof A1 - Colom, Remi A1 - Genevet, Patrice A1 - Burger, Sven T1 - Poles and zeros in non-Hermitian systems: Application to photonics JF - Phys. Rev. B Y1 - 2024 U6 - https://doi.org/10.1103/PhysRevB.109.045414 VL - 109 SP - 045414 ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Chemnitz, Robin A1 - Kostre, Margarita A1 - Schweigart, Fleur A1 - Fless, Friederike A1 - Schütte, Christof A1 - Ducke, Benjamin T1 - A Mathematical perspective on Romanisation: Modelling the Roman road activation process in ancient Tunisia JF - PLoS ONE N2 - Romanisation is a multi-faceted historical phenomenon with profound and lasting cultural impact on the ancient world. In the modern-day territory of Tunisia, this is particularly manifest during the first four centuries AD, under the reign of the Roman Empire. We derive a reduced, operational concept of Romanisation as a cultural diffusion process that is observable in the archaeological remains of the Roman era settlement system. We then introduce a novel mathematical model that computes spatio-temporal approximations for the Romanisation of the settlement system. The model is based on the concept of temporal road activation and makes minimal assumptions regarding input data quality. The results of our study contribute to the understanding of the time dynamics of the region’s road network, under the influence of Romanisation. Our model can be applied in similar archaeological research scenarios, to generate spatio-temporal backbones for the analysis of otherwise intractably complex social processes. Y1 - 2024 U6 - https://doi.org/10.1371/journal.pone.0309752 VL - 19 IS - 9 ER - TY - JOUR A1 - Niemann, Jan-Hendrik A1 - Uram, Samuel A1 - Wolf, Sarah A1 - Conrad, Natasa Djurdjevac A1 - Weiser, Martin T1 - Multilevel Optimization for Policy Design with Agent-Based Epidemic Models JF - Computational Science N2 - Epidemiological models can not only be used to forecast the course of a pandemic like COVID-19, but also to propose and design non-pharmaceutical interventions such as school and work closing. In general, the design of optimal policies leads to nonlinear optimization problems that can be solved by numerical algorithms. Epidemiological models come in different complexities, ranging from systems of simple ordinary differential equations (ODEs) to complex agent-based models (ABMs). The former allow a fast and straightforward optimization, but are limited in accuracy, detail, and parameterization, while the latter can resolve spreading processes in detail, but are extremely expensive to optimize. We consider policy optimization in a prototypical situation modeled as both ODE and ABM, review numerical optimization approaches, and propose a heterogeneous multilevel approach based on combining a fine-resolution ABM and a coarse ODE model. Numerical experiments, in particular with respect to convergence speed, are given for illustrative examples. Y1 - 2024 U6 - https://doi.org/10.1016/j.jocs.2024.102242 VL - 77 SP - 102242 ER - TY - JOUR A1 - Bopp, Julian M. A1 - Plock, Matthias A1 - Turan, Tim A1 - Pieplow, Gregor A1 - Burger, Sven A1 - Schröder, Tim T1 - Sawfish Photonic Crystal Cavity for Near-Unity Emitter-to-Fiber Interfacing in Quantum Network Applications JF - Adv. Opt. Mater. Y1 - 2024 U6 - https://doi.org/10.1002/adom.202301286 VL - 12 SP - 2301286 ER - TY - JOUR A1 - Betz, Fridtjof A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Binkowski, Felix T1 - Efficient rational approximation of optical response functions with the AAA algorithm JF - Laser Photonics Rev. Y1 - 2024 U6 - https://doi.org/10.1002/lpor.202400584 VL - 18 SP - 2400584 ER - TY - GEN A1 - Betz, Fridtjof A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Binkowski, Felix T1 - Source code and simulation results: Efficient rational approximation of optical response functions with the AAA algorithm T2 - Zenodo Y1 - 2024 U6 - https://doi.org/10.5281/zenodo.10853692 SP - doi: 10.5281/zenodo.10853692 ER - TY - JOUR A1 - Betz, Fridtjof A1 - Binkowski, Felix A1 - Kuen, Lilli A1 - Burger, Sven T1 - Version 2 — RPExpand: Software for Riesz projection expansion of resonance phenomena JF - SoftwareX Y1 - 2024 U6 - https://doi.org/10.1016/j.softx.2024.101694 VL - 26 SP - 101694 ER - TY - JOUR A1 - Plock, Matthias A1 - Binkowski, Felix A1 - Zschiedrich, Lin A1 - Schneider, Phillip-Immanuel A1 - Burger, Sven T1 - Fabrication uncertainty guided design optimization of a photonic crystal cavity by using Gaussian processes JF - J. Opt. Soc. Am. B Y1 - 2024 U6 - https://doi.org/10.1364/JOSAB.505767 VL - 41 SP - 850 ER -