@inproceedings{MukherjeeBurgerSiefkeetal.2024, author = {Mukherjee, Deshabrato and Burger, Sven and Siefke, Thomas and Gour, Jeetendra and Bodermann, Bernd and Petrik, Peter}, title = {Modeling of dimensions and sensing properties of gold gratings by spectroscopic ellipsometry and finite element method}, volume = {309}, booktitle = {EPJ Web of Conferences}, doi = {10.1051/epjconf/202430902016}, pages = {02016}, year = {2024}, language = {en} } @article{DjurdjevacConradTonelloZonkeretal.2025, author = {Djurdjevac Conrad, Natasa and Tonello, Elisa and Zonker, Johannes and Siebert, Heike}, title = {Detection of dynamic communities in temporal networks with sparse data}, volume = {10}, journal = {Applied Network Science}, publisher = {Springer International Publishing}, doi = {10.1007/s41109-024-00687-3}, year = {2025}, abstract = {Temporal networks are a powerful tool for studying the dynamic nature of a wide range of real-world complex systems, including social, biological and physical systems. In particular, detection of dynamic communities within these networks can help identify important cohesive structures and fundamental mechanisms driving systems behaviour. However, when working with real-world systems, available data is often limited and sparse, due to missing data on systems entities, their evolution and interactions, as well as uncertainty regarding temporal resolution. This can hinder accurate representation of the system over time and result in incomplete or biased community dynamics. In this paper, we compare established methods for community detection and, using synthetic data experiments and real-world case studies, we evaluate the impact of data sparsity on the quality of identified dynamic communities. Our results give valuable insights on the evolution of systems with sparse data, which are less studied in existing literature, but are frequently encountered in real-world applications.}, language = {en} } @misc{BetzHammerschmidtZschiedrichetal.2024, author = {Betz, Fridtjof and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven and Binkowski, Felix}, title = {Efficient Rational Approximation of Optical Response Functions with the AAA Algorithm (Laser Photonics Rev. 18(11)/2024)}, volume = {18}, journal = {Laser Photonics Rev.}, doi = {10.1002/lpor.202470071}, pages = {2470071}, year = {2024}, language = {en} } @article{KostreDjurdjevacConradSchuetteetal.2024, author = {Kostr{\´e}, Margarita and Djurdjevac Conrad, Natasa and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {Exploration of Particle Swarm Optimisation Algorithm with Divergent Parameters}, journal = {Natural Computing}, year = {2024}, language = {en} } @article{ZimperCornalbaDjurdjevacConradetal.2025, author = {Zimper, Sebastian and Cornalba, Federico and Djurdjevac Conrad, Natasa and Djurdjevac, Ana}, title = {On reduced inertial PDE models for Cucker-Smale flocking dynamics}, volume = {481}, journal = {Proceedings of the Royal Society A}, publisher = {Royal Society}, arxiv = {http://arxiv.org/abs/2407.18717}, doi = {https://doi.org/10.1098/rspa.2024.0675}, year = {2025}, abstract = {In particle systems, flocking refers to the phenomenon where particles' individual velocities eventually align. The Cucker-Smale model is a well-known mathematical framework that describes this behaviour. Many continuous descriptions of the Cucker-Smale model use PDEs with both particle position and velocity as independent variables, thus providing a full description of the particles mean-field limit (MFL) dynamics. In this paper, we introduce a novel reduced inertial PDE model consisting of two equations that depend solely on particle position. In contrast to other reduced models, ours is not derived from the MFL, but directly includes the model reduction at the level of the empirical densities, thus allowing for a straightforward connection to the underlying particle dynamics. We present a thorough analytical investigation of our reduced model, showing that: firstly, our reduced PDE satisfies a natural and interpretable continuous definition of flocking; secondly, in specific cases, we can fully quantify the discrepancy between PDE solution and particle system. Our theoretical results are supported by numerical simulations.}, language = {en} } @article{FischbachBetzAsadovaetal.2025, author = {Fischbach, Jan David and Betz, Fridtjof and Asadova, Nigar and Tassan, Pietro and Urbonas, Darius and St{\"o}ferle, Thilo and Mahrt, Rainer F. and Burger, Sven and Rockstuhl, Carsten and Binkowski, Felix and Sturges, Thomas Jebb}, title = {A framework to compute resonances arising from multiple scattering}, volume = {8}, journal = {Adv. Theory Simul.}, arxiv = {http://arxiv.org/abs/2409.05563}, doi = {10.1002/adts.202400989}, pages = {2400989}, year = {2025}, language = {en} } @article{JaegerTejadaBerwigetal.2025, author = {J{\"a}ger, Klaus and Tejada, Alvarjo and Berwig, Sebastian and Hammerschmidt, Martin and Tockhorn, Philipp and Albrecht, Steve and Becker, Christiane}, title = {Optical Simulations of Nanotextured All-Perovskite Tandem Solar Cells}, volume = {8}, journal = {Adv. Theory Simul.}, doi = {10.1002/adts.202400724}, pages = {2400724}, year = {2025}, language = {en} } @inproceedings{BinkowskiBetzHammerschmidtetal.2024, author = {Binkowski, Felix and Betz, Fridtjof and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven}, title = {Poles and Zeros in Resonant Nano-Photonic Systems}, booktitle = {2024 Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)}, doi = {10.1109/CLEO-PR60912.2024.10676837}, year = {2024}, language = {en} } @inproceedings{JaegerBurgerAeberhardetal.2024, author = {J{\"a}ger, Klaus and Burger, Sven and Aeberhard, Urs and Llado, Esther Alarcon and Bl{\"a}si, Benedikt and Ehrler, Bruno and Favre, Wilfried and Fejfar, Anton{\´i}n and Gageot, Tristan and Gordon, Ivan and Helmers, Henning and H{\"o}hn, Oliver and Isabella, Olindo and Jošt, Marko and Ledinsk{\´y}, Martin and Mandal, Jyotirmoy and Manley, Phillip and Munoz, Delfina and Lizcano, Juan Camilo Ortiz and Paetzold, Ulrich W. and Raman, Aaswath P. and Sai, Hitoshi and Saive, Rebecca and Schmid, Martina and Yablonovitch, Eli and Becker, Christiane}, title = {A Roadmap on Optics for Terawatt Scale Photovoltaics}, booktitle = {Advanced Photonics Congress 2024}, publisher = {Optica Publishing Group}, doi = {10.1364/SELED.2024.STu2G.5}, pages = {STu2G.5}, year = {2024}, language = {en} } @article{ArmasMerbisMeylahnetal.2025, author = {Armas, Jay and Merbis, Wout and Meylahn, Janusz M and Rafiee Rad, Soroush and del Razo, Mauricio J}, title = {Risk aversion can promote cooperation}, volume = {6}, journal = {Journal of Physics: Complexity}, number = {1}, arxiv = {http://arxiv.org/abs/2306.05971}, doi = {10.1088/2632-072X/adb234}, year = {2025}, abstract = {Cooperative dynamics are central to our understanding of many phenomena in living and complex systems. However, we lack a universal mechanism to explain the emergence of cooperation. We present a novel framework for modelling social dilemma games with an arbitrary number of players by combining reaction networks, methods from quantum mechanics applied to stochastic complex systems, game theory and stochastic simulations of molecular reactions. Using this framework, we propose a novel and robust mechanism for cooperation based on risk aversion that leads to cooperative behaviour in population games. Rather than individuals seeking to maximise payouts in the long run, individuals seek to obtain a minimum set of resources with a given level of confidence and in a limited time span. We show that this mechanism can lead to the emergence of new equilibria in a range of social dilemma games.}, language = {en} } @phdthesis{Luecke2024, author = {L{\"u}cke, Marvin}, title = {Concentration effects and collective variables in dynamical systems on networks}, doi = {10.17169/refubium-45325}, year = {2024}, language = {en} } @article{SunBernerRichteretal.2024, author = {Sun, Jingtong and Berner, Julius and Richter, Lorenz and Zeinhofer, Marius and M{\"u}ller, Johannes and Azizzadenesheli, Kamyar and Anandkumar, Anima}, title = {Dynamical Measure Transport and Neural PDE Solvers for Sampling}, arxiv = {http://arxiv.org/abs/2407.07873}, year = {2024}, abstract = {The task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we tackle it through a principled unified framework using deterministic or stochastic evolutions described by partial differential equations (PDEs). This framework incorporates prior trajectory-based sampling methods, such as diffusion models or Schr{\"o}dinger bridges, without relying on the concept of time-reversals. Moreover, it allows us to propose novel numerical methods for solving the transport task and thus sampling from complicated targets without the need for the normalization constant or data samples. We employ physics-informed neural networks (PINNs) to approximate the respective PDE solutions, implying both conceptional and computational advantages. In particular, PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently, leading to significantly better mode coverage in the sampling task compared to alternative methods. Moreover, they can readily be fine-tuned with Gauss-Newton methods to achieve high accuracy in sampling.}, language = {en} } @inproceedings{WinklerRichterOpper2024, author = {Winkler, Ludwig and Richter, Lorenz and Opper, Manfred}, title = {Bridging discrete and continuous state spaces: Exploring the Ehrenfest process in time-continuous diffusion models}, volume = {235}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, arxiv = {http://arxiv.org/abs/2405.03549}, pages = {53017 -- 53038}, year = {2024}, abstract = {Generative modeling via stochastic processes has led to remarkable empirical results as well as to recent advances in their theoretical understanding. In principle, both space and time of the processes can be discrete or continuous. In this work, we study time-continuous Markov jump processes on discrete state spaces and investigate their correspondence to state-continuous diffusion processes given by SDEs. In particular, we revisit the Ehrenfest process, which converges to an Ornstein-Uhlenbeck process in the infinite state space limit. Likewise, we can show that the time-reversal of the Ehrenfest process converges to the time-reversed Ornstein-Uhlenbeck process. This observation bridges discrete and continuous state spaces and allows to carry over methods from one to the respective other setting. Additionally, we suggest an algorithm for training the time-reversal of Markov jump processes which relies on conditional expectations and can thus be directly related to denoising score matching. We demonstrate our methods in multiple convincing numerical experiments.}, language = {en} } @article{AsadovaAchouriArjasetal.2025, author = {Asadova, Nigar and Achouri, Karim and Arjas, Kristian and Ajugui{\´e}, Baptiste and Aydin, Roland and Baron, Alexandre and Beutel, Dominik and Bodermann, Bernd and Boussaoud, Kaoutar and Burger, Sven and Choi, Minseok and Czajkowski, Krzysztof and Evlyukhin, Andrey B. and Fazel-Najafabadi, Atefeh and Fernandez-Corbaton, Ivan and Garg, Puneet and Globosits, David and Hohenester, Ulrich and Kim, Hongyoon and Kim, Seokwoo and Lalanne, Philippe and Le Ru, Eric C. and Meyer, J{\"o}rg and Mun, Jungho and Patelli, Lorenzo and Pflug, Lukas and Rockstuhl, Carsten and Rho, Junsuk and Rotter, Stefan and Stout, Brian and T{\"o}rm{\"a}, P{\"a}ivi and Trigo, Jorge Olmos and Tristram, Frank and Tsitsas, Nikolaos L. and Vall{\´e}e, Renaud and Vynck, Kevin and Weiss, Thomas and Wiecha, Peter and Wriedt, Thomas and Yannopapas, Vassilios and Yurkin, Maxim A. and Zouros, Grigorios P.}, title = {T-matrix representation of optical scattering response: Suggestion for a data format}, volume = {333}, journal = {J. Quant. Spectrosc. Radiat. Transf.}, arxiv = {http://arxiv.org/abs/2408.10727}, doi = {10.1016/j.jqsrt.2024.109310}, pages = {109310}, year = {2025}, language = {en} } @article{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 = {Numerical Investigation of a Coupled Micropillar - Waveguide System for Integrated Quantum Photonic Circuits}, volume = {7}, journal = {Adv. Quantum Technol.}, doi = {10.1002/qute.202400195}, pages = {2400195}, year = {2024}, language = {en} } @article{BinkowskiBurgerKewes2024, author = {Binkowski, Felix and Burger, Sven and Kewes, G{\"u}nter}, title = {A tiny Drude scatterer can accurately model a coherent emitter in nanophotonics}, volume = {13}, journal = {Nanophotonics}, doi = {10.1515/nanoph-2024-0170}, pages = {4537}, year = {2024}, language = {en} } @misc{Sikorski2024, author = {Sikorski, Alexander}, title = {ISOKANN.jl}, doi = {10.5281/zenodo.11519359}, year = {2024}, abstract = {Julia pacarkge implementing the ISOKANN algorithm for the computation of invariant subspaces of Koopman operators}, language = {en} } @article{BernsYildizWinkelmannetal.2025, author = {Berns, Manon and Yildiz, Mirza and Winkelmann, Stefanie and Walter, Alexander}, title = {Independently engaging protein tethers of different length enhance synaptic vesicle trafficking to the plasma membrane}, volume = {603}, journal = {The Journal of Physiology}, number = {20}, doi = {10.1113/JP286651}, pages = {6107 -- 6134}, year = {2025}, abstract = {Synaptic vesicle (SV) trafficking toward the plasma membrane (PM) and subsequent SV maturation are essential for neurotransmitter release. These processes, including SV docking and priming, are coordinated by various proteins, such as SNAREs, Munc13, and Synaptotagmin (Syt), which connect—tether—the SV to the PM. Here, we investigated how tethers of varying lengths mediate SV docking using a simplified mathematical model. The heights of the three tether types—estimated from the structures of the SNARE complex, Munc13, and Syt—defined the SV-to-PM distance ranges for tether formation. Geometric considerations linked SV-to-PM distances to the probability and rate of tether formation. We assumed that SV tethering constrains SV motility and that multiple tethers associate by independent interactions. The model predicted that forming multiple tethers favors shorter SV-to-PM distances. Although tethers acted independently in the model, their geometrical properties often caused sequential assembly, from longer ones (Munc13/Syt), that accelerated SV movement towards the PM, to shorter ones (SNAREs) which stabilized PM-proximal SVs. Modifying tether lengths or numbers affected SV trafficking. The independent implementation of tethering proteins enabled their selective removal to mimic gene knockout situations. This showed that simulated SV-to-PM distance distributions qualitatively aligned with published EM studies upon removal of SNARE and Syt tethers, while Munc13 knockout data were best approximated when assuming additional disruption of SNARE tethers. Thus, while salient features of SV docking can be accounted for by independent tethering alone, our results suggest that functional tether interactions not yet featured in our model are crucial for biological function.}, language = {en} } @misc{BinkowskiBetzHammerschmidtetal.2024, author = {Binkowski, Felix and Betz, Fridtjof and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven}, title = {Source code and simulation results: Resonance modes in microstructured photonic waveguides - Efficient and accurate computation based on AAA rational approximation}, journal = {Zenodo}, doi = {10.5281/zenodo.14202408}, pages = {doi: 10.5281/zenodo.14202408}, year = {2024}, language = {en} } @article{BecksLippoldWinkleretal.2024, author = {Becks, Henrik and Lippold, Lukas and Winkler, Paul and Rohrer, Maximilian and Leusmann, Thorsten and Anton, David and Sprenger, Bjarne and K{\"a}hler, Philipp and Rudenko, Iryna and Andr{\´e}s Arcones, Daniel and Koutsourelakis, Phaedon-Stelios and Unger, J{\"o}rg F. and Weiser, Martin and Petryna, Yuri and Schnellenbach-Held, Martina and Lowke, Dirk and Wessels, Henning and Lenzen, Armin and Zabel, Volkmar and K{\"o}nke, Carsten and Claßen, Martin and Hegger, Josef}, title = {Neuartige Konzepte f{\"u}r die Zustands{\"u}berwachung und -analyse von Br{\"u}ckenbauwerken - Einblicke in das Forschungsvorhaben SPP100+}, volume = {99}, journal = {Bauingenieur}, number = {10}, doi = {10.37544/0005-6650-2024-10-63}, pages = {327 -- 338}, year = {2024}, abstract = {Die Br{\"u}ckeninfrastruktur in Deutschland und Europa steht aufgrund steigender Verkehrslasten und alternder Bauwerke vor erheblichen Herausforderungen. Das DFG-Schwerpunktprogramm 2388 „Hundert plus - Verl{\"a}ngerung der Lebensdauer komplexer Baustrukturen durch intelligente Digitalisierung" (SPP100+) strebt an, durch digitale Innovationen und pr{\"a}diktive Instandhaltungsstrategien die Nutzungsdauer bestehender Br{\"u}ckenbauwerke zu verl{\"a}ngern. Der vorliegende Beitrag fokussiert sich auf das SPP100+ zugeh{\"o}rige Cluster „Monitoring und Simulation", das sieben Teilprojekte umfasst. Die Projekte entwickeln fortschrittliche Methoden zur {\"U}berwachung und Zustandsbewertung von Br{\"u}cken mittels Digitaler Zwillinge, hochaufl{\"o}sender Sensortechnik und numerischer Simulationen. Innovative Ans{\"a}tze wie nichtlineare Modellanpassungen, stochastische Methoden und k{\"u}nstliche Intelligenz erm{\"o}glichen eine pr{\"a}zise und fr{\"u}hzeitige Identifizierung potenzieller Sch{\"a}den. Die Kombination aus kontinuierlichem Bauwerksmonitoring und effizienter Datenauswertung ist entscheidend f{\"u}r die langfristige Sicherheit und Langlebigkeit bestehender Br{\"u}cken und tr{\"a}gt dar{\"u}ber hinaus zur Ressourcenschonung bei.}, language = {de} } @article{GoebelHuynhCheginietal.2025, author = {G{\"o}bel, Fritz and Huynh, Ngoc Mai Monica and Chegini, Fatemeh and Pavarino, Luca and Weiser, Martin and Scacchi, Simone and Anzt, Hartwig}, title = {A BDDC Preconditioner for the Cardiac EMI Model in three Dimensions}, journal = {SIAM J. Sci. Comput.}, arxiv = {http://arxiv.org/abs/2502.07722}, year = {2025}, abstract = {We analyze a Balancing Domain Decomposition by Constraints (BDDC) preconditioner for the solution of three dimensional composite Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models like the Extracellular space, Membrane and Intracellular space (EMI) Model. These microscopic models are essential for the understanding of events in aging and structurally diseased hearts which macroscopic models relying on homogenized descriptions of the cardiac tissue, like Monodomain and Bidomain models, fail to adequately represent. The modeling of each individual cardiac cell results in discontinuous global solutions across cell boundaries, requiring the careful construction of dual and primal spaces for the BDDC preconditioner. We provide a scalable condition number bound for the precondition operator and validate the theoretical results with extensive numerical experiments.}, language = {en} } @article{KlasseWeber2025, author = {Klasse, Sarah Michelle and Weber, Marcus}, title = {A Case Study of the Use of Logical Data Analysis in the Workmen's Village in Tell el-Amarna, Egypt}, volume = {66}, journal = {it - Information Technology}, number = {6}, publisher = {de Gruyter}, doi = {10.1515/itit-2024-0088}, pages = {256 -- 268}, year = {2025}, abstract = {The search for patterns in archaeological contexts is crucial to understanding ancient civilizations, including the organization of their societies and economies. This study focuses on the interdisciplinary application of mathematical logical data analysis to Egyptology, particularly examining food production in the Workmen's Village of Amarna. The introduction provides historical context about Amarna, founded by Pharaoh Akhenaten, and outlines the settlement structure and excavations of the Workmen's Village. The research utilizes archaeobotanical and archaeological data, along with digital humanities tools, to identify activity areas related to food production. The findings reveal spatial patterns in the distribution of tools such as mortars, pestles, and ovens, providing insights into the self-sufficiency and daily life of the villagers. Logical data analysis helps in finding rules and patterns in a dataset which are not visible otherwise, predicting the distribution of unexcavated areas and thus in this case enhancing our understanding of ancient Egyptian food production practices in state- planned settlements.}, language = {en} } @article{BetzBinkowskiFischbachetal.2025, author = {Betz, Fridtjof and Binkowski, Felix and Fischbach, Jan David and Feldman, Nick and Zschiedrich, Lin and Rockstuhl, Carsten and Koenderink, A. Femius and Burger, Sven}, title = {Uncovering hidden resonances in non-Hermitian systems with scattering thresholds}, volume = {19}, journal = {Laser Photonics Rev.}, arxiv = {http://arxiv.org/abs/2503.03549}, doi = {10.1002/lpor.202500811}, pages = {e00811}, year = {2025}, language = {en} } @misc{BetzBinkowskiFischbachetal.2025, author = {Betz, Fridtjof and Binkowski, Felix and Fischbach, Jan David and Feldman, Nick and Rockstuhl, Carsten and Koenderink, A. Femius and Burger, Sven}, title = {Source code and simulation results: Hidden resonances in non-Hermitian systems with scattering thresholds}, journal = {Zenodo}, doi = {10.5281/zenodo.14651612}, pages = {doi: 10.5281/zenodo.14651612}, year = {2025}, language = {en} } @inproceedings{RiberaBorrellRichterSchuette2025, author = {Ribera Borrell, Enric and Richter, Lorenz and Sch{\"u}tte, Christof}, title = {Reinforcement Learning with Random Time Horizons}, volume = {267}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, arxiv = {http://arxiv.org/abs/2506.00962}, pages = {5101 -- 5123}, year = {2025}, language = {en} } @article{MukherjeeBurgerSiefkeetal.2025, author = {Mukherjee, Deshabrato and Burger, Sven and Siefke, Thomas and Gour, Jeetendra and Bodermann, Bernd and Petrik, Peter}, title = {Spectroscopic Ellipsometry of Plasmonic Gratings─Ideal Parameters for Sensing and Subpicometer Measurement Uncertainty}, volume = {10}, journal = {ACS Omega}, number = {14}, doi = {10.1021/acsomega.5c00951}, pages = {14466 -- 14473}, year = {2025}, language = {en} } @article{BlaskovicConradKlusetal.2025, author = {Blaskovic, Filip and Conrad, Tim and Klus, Stefan and Djurdjevac Conrad, Natasa}, title = {Random walk based snapshot clustering for detecting community dynamics in temporal networks}, volume = {15}, journal = {Scientific Reports}, arxiv = {http://arxiv.org/abs/2412.12187}, doi = {10.1038/s41598-025-09340-0}, pages = {24414}, year = {2025}, abstract = {The evolution of many dynamical systems that describe relationships or interactions between objects can be effectively modeled by temporal networks, which are typically represented as a sequence of static network snapshots. In this paper, we introduce a novel random walk based approach that can identify clusters of time-snapshots in which network community structures are stable. This allows to detect significant structural shifts over time, such as the splitting, merging, birth, or death of communities. We also provide a low-dimensional representation of entire snapshots, placing those with similar community structure close to each other in the feature space. To validate our approach, we develop an agent-based algorithm that generates synthetic datasets with the desired characteristic properties, enabling thorough testing and benchmarking. We further demonstrate the effectiveness and broad applicability of our technique by testing it on various social dynamics models and real-world datasets and comparing its performance to several state-of-the-art algorithms. Our findings highlight the strength of our approach to correctly capture and analyze the dynamics of complex systems.}, language = {en} } @phdthesis{Ernst2024, author = {Ernst, Ariane}, title = {Mathematical modeling and analysis of neurotransmission}, year = {2024}, abstract = {Modeling and simulation of neurotransmission plays a central role in the scientific investigation of synaptic functioning and neuronal communication. Understanding the neurotransmission process is crucial due to its fundamental significance in cognitive function, with impairments in this process potentially giving rise to severe pathological conditions. Existing modeling approaches capture the dynamic behavior and the probabilistic properties of the synaptic machinery utilizing results from stochastic chemical kinetics. However, the underlying mathematical theory rarely receives detailed consideration. In this thesis, we explore the neurotransmission process from a mathematical perspective and provide important insights that improve efficiency in its modeling and simulation. We introduce a new method for the direct and exact computation of first- and second-order moments of the postsynaptic current for the case of linear reaction networks, circumventing previously employed stochastic simulations. The approach hinges on the computation of the cross-correlation functions for the associated Markov jump process and their characterization by a partial differential equation. Our method can be applied to efficiently compare coarse-graining strategies for neurotransmission models, which we demonstrate for a significant recent model of synaptic vesicle release. We also numerically analyze the feasibility of reducing this particular model and show that a reduction can preserve the characteristics of the mean output current and its standard deviation to a satisfactory degree under typical stimulation conditions, where the approximation error can even be neglected depending on release site position. As the dependency on the local calcium concentration is preserved in the reduced model, it can be subjected to arbitrary types of signals in future studies. Moreover, we investigate the recovery processes of synaptic vesicles and release sites by introducing a nonlinear model with explicit recovery reactions. A sensitivity analysis provides the novel insight that the widely debated identity of the limiting recovery process during sustained stimulation is time-dependent. For our model, the output current's first-order moment and its deterministic approximation show an exceptionally high level of agreement. We determine this to be an inherent consequence of the model structure due to the independence of the two recovery processes, supporting future use of the deterministic approximation. Parameter estimations confirm our model's capability of reproducing experimental data.}, language = {en} } @article{delRazoDelleSite2025, author = {del Razo, Mauricio and Delle Site, Luigi}, title = {Dynamics of systems with varying number of particles: from Liouville equations to general master equations for open systems}, volume = {18, 001}, journal = {SciPost Physics}, doi = {10.21468/SciPostPhys.18.1.001}, year = {2025}, abstract = {A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number through internal dynamics such as reactions. The physico-mathematical modeling of these systems is extremely challenging, with the major difficulty being the time dependence of the number of degrees of freedom and the additional constraint that the increment or reduction of the number and species of particles must not violate basic physical laws. Theoretical models, in such a case, represent the key tool for the design of computational strategies for numerical studies that deliver trustful results. In this manuscript, we review complementary physico-mathematical approaches of varying number of particles inspired by rather different specific numerical goals. As a result of the analysis on the underlying common structure of these models, we propose a unifying master equation for general dynamical systems with varying number of particles. This equation embeds all the previous models and can potentially model a much larger range of complex systems, ranging from molecular to social agent-based dynamics.}, language = {en} } @article{AndresArconesWeiserKoutsourelakisetal.2024, author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Phaedon-Stelios and Unger, J{\"o}rg F.}, title = {Bias Identification Approaches for Model Updating of Simulation-based Digital Twins of Bridges}, volume = {2}, journal = {Structural Health Monitoring in the Light of Climate Impact and Data Science. Research and Review Journal of Nondestructive Testing}, number = {2}, doi = {10.58286/30524}, year = {2024}, abstract = {Simulation-based digital twins of bridges have the potential not only to serve as monitoring devices of the current state of the structure but also to generate new knowledge through physical predictions that allow for better-informed decisionmaking. For an accurate representation of the bridge, the underlying models must be tuned to reproduce the real system. Nevertheless, the necessary assumptions and simplifications in these models irremediably introduce discrepancies between measurements and model response. We will show that quantifying the extent of the uncertainties introduced through the models that lead to such discrepancies provides a better understanding of the real system, enhances the model updating process, and creates more robust and trustworthy digital twins. The inclusion of an explicit bias term will be applied to a representative demonstrator case based on the thermal response of the Nibelungenbr{\"u}cke of Worms. The findings from this work are englobed in the initiative SPP 100+, whose main aim is the extension of the service life of structures, especially through the implementation of digital twins.}, language = {en} } @article{DonatiChewleStPierreetal.2025, author = {Donati, Luca and Chewle, Surahit and St. Pierre, Dominik and Natarajan, Vijay and Weber, Marcus}, title = {Topological analysis reveals multiple pathways in molecular dynamics}, volume = {21}, journal = {Journal of Chemical Theory and Computation}, number = {20}, address = {J. Chem. Theory Comput.}, arxiv = {http://arxiv.org/abs/2412.20580}, doi = {10.1021/acs.jctc.5c00819}, pages = {10385 -- 10397}, year = {2025}, abstract = {Molecular Dynamics simulations are indispensable tools for comprehending the dynamic behavior of biomolecules, yet extracting meaningful molecular pathways from these simulations remains challenging due to the vast amount of high dimensional data. In this work, we present Molecular Kinetics via Topology (MoKiTo), a novel approach that combines the ISOKANN algorithm to determine the membership function of a molecular system with a topological analysis tool inspired by the Mapper algorithm. Our strategy efficiently identifies and characterizes distinct molecular pathways, enabling the detection and visualization of critical conformational transitions and rare events. This method offers deeper insights into molecular mechanisms, facilitating the design of targeted interventions in drug discovery and protein engineering.}, language = {en} } @article{BinkowskiBetzHammerschmidtetal.2025, author = {Binkowski, Felix and Betz, Fridtjof and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven}, title = {Resonance modes in microstructured photonic waveguides: Efficient and accurate computation based on AAA rational approximation}, volume = {14}, journal = {Nanophotonics}, arxiv = {http://arxiv.org/abs/2412.13826}, doi = {10.1515/nanoph-2024-0755}, pages = {1665}, year = {2025}, language = {en} } @inproceedings{SchaibleWinartoSkorjancetal.2025, author = {Schaible, Jonas and Winarto, Hanifah and Skorjanc, Victor and Yoo, Danbi and Zimmermann, Lea and Wessels, Andreas and J{\"a}ger, Klaus and Sekulic, Ivan and Schneider, Philipp-Immanuel and Bl{\"a}si, Benedikt and Burger, Sven and Becker, Christiane}, title = {Optimization strategies for colorful thin film solar cells}, volume = {PC13361}, booktitle = {Proc. SPIE}, doi = {10.1117/12.3041408}, pages = {PC133610E}, year = {2025}, language = {en} } @article{JaegerAeberhardAlarconLladoetal.2025, author = {J{\"a}ger, Klaus and Aeberhard, Urs and Alarcon Llado, Esther and Bl{\"a}si, Benedikt and Burger, Sven and Ehrler, Bruno and Favre, Wilfried and Fejfar, Anton{\´i}n and Gageot, Tristan and Gordon, Ivan and Helmers, Henning and H{\"o}hn, Oliver and Isabella, Olindo and Jošt, Marko and Ledinsk{\´y}, Martin and Mandal, Jyotirmoy and Manley, Phillip and Mu{\~n}oz, Delfina and Omair, Zunaid and Ortiz Lizcano, Juan Camilo and Paetzold, Ulrich W. and Raman, Aaswath P. and Sai, Hitoshi and Saive, Rebecca and Schmid, Martina and Yablonovitch, Eli and Becker, Christiane}, title = {Optics for terawatt-scale photovoltaics: review and perspectives}, volume = {17}, journal = {Adv. Opt. Photonics}, number = {1}, publisher = {Optica Publishing Group}, issn = {1943-8206}, doi = {10.1364/AOP.530556}, pages = {185 -- 294}, year = {2025}, abstract = {Photovoltaics, a mature technology, is set to play a vital role in achieving a carbon-free energy system. This article examines the pivotal role of optics in advancing photovoltaics. We identify key scientific research areas where the optics community can make significant contributions. We are guided by the central question: How can optics facilitate the large-scale deployment of photovoltaics necessary for decarbonizing our societies?}, language = {en} } @article{delRazoKostre2025, author = {del Razo, Mauricio and Kostr{\´e}, Margarita}, title = {Open reaction-diffusion systems: bridging probabilistic theory and simulations across scales}, volume = {58}, journal = {Journal of Physics A: Mathematical and Theoretical}, number = {14}, doi = {10.1088/1751-8121/adc520}, year = {2025}, abstract = {Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual particle/agent level, and in realistic applications, they often display interaction with their environment through energy or material exchange with a reservoir. This requires intricate mathematical considerations, especially in the case of material exchange since the varying number of particles/agents results in ``on-the-fly'' modification of the system dimension. In this work, we first overview the probabilistic description of reaction-diffusion processes at the particle level, which readily handles varying number of particles. We then extend this model to consistently incorporate interactions with macroscopic material reservoirs. Based on the resulting expressions, we bridge the probabilistic description with macroscopic concentration-based descriptions for linear and nonlinear reaction-diffusion systems, as well as for an archetypal open reaction-diffusion system. Using these mathematical bridges across scales, we finally develop numerical schemes for open reaction-diffusion systems, which we implement in two illustrative examples. This work establishes a methodological workflow to bridge particle-based probabilistic descriptions with macroscopic concentration-based descriptions of reaction-diffusion in open settings, laying the foundations for a multiscale theoretical framework upon which to construct theory and simulation schemes that are consistent across scales.}, language = {en} } @article{BauerWeberDiehlWieseneckeretal.2021, author = {Bauer, Wolfgang and Weber, Marcus and Diehl-Wiesenecker, Eva and Galtung, Noa and Prpic, Monika and Somasundaram, Rajan and Tauber, Rudolf and Schwenk, Jochen and Micke, Patrick and Kappert, Kai}, title = {Plasma Proteome Fingerprints Reveal Distinctiveness and Clinical Outcome of SARS-CoV-2 Infection}, volume = {13}, journal = {Viruses}, number = {12}, doi = {10.3390/v13122456}, pages = {2456}, year = {2021}, abstract = {We evaluated how plasma proteomic signatures in patients with suspected COVID-19 can unravel the pathophysiology, and determine kinetics and clinical outcome of the infection. We identified distinct plasma proteins linked to the presence and course of COVID-19. These plasma proteomic findings may translate to a protein fingerprint, helping to assist clinical management decisions.}, language = {en} } @misc{RiberaBorrellQuerRichteretal.2021, author = {Ribera Borrell, Enric and Quer, Jannes and Richter, Lorenz and Sch{\"u}tte, Christof}, title = {Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics}, issn = {1438-0064}, year = {2021}, abstract = {Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal importance sampling controls as a stochastic optimization problem, this then brings additional numerical challenges and the convergence of corresponding algorithms might as well suffer from metastabilty. In this article we address this issue by combining systematic control approaches with the heuristic adaptive metadynamics method. Crucially, we approximate the importance sampling control by a neural network, which makes the algorithm in principle feasible for high dimensional applications. We can numerically demonstrate in relevant metastable problems that our algorithm is more effective than previous attempts and that only the combination of the two approaches leads to a satisfying convergence and therefore to an efficient sampling in certain metastable settings.}, language = {en} } @article{BetzBinkowskiHammerschmidtetal.2023, author = {Betz, Fridtjof and Binkowski, Felix and Hammerschmidt, Martin and Zschiedrich, Lin and Burger, Sven}, title = {Cover Picture: Resonance Expansion of Quadratic Quantities with Regularized Quasinormal Modes}, volume = {220}, journal = {Phys. Status Solidi A}, doi = {10.1002/pssa.202370013}, pages = {2370013}, year = {2023}, language = {en} } @article{SchuetteKlusHartmann2023, author = {Sch{\"u}tte, Christof and Klus, Stefan and Hartmann, Carsten}, title = {Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning}, volume = {32}, journal = {Acta Numerica}, doi = {10.1017/S0962492923000016}, pages = {517 -- 673}, year = {2023}, abstract = {One of the main challenges in molecular dynamics is overcoming the 'timescale barrier': in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based techniques that have emerged from dynamical systems theory, numerical mathematics and machine learning over the last two decades. We will focus on how transfer operators can be used to approximate the dynamical behaviour on long timescales, review the introduction of this approach into molecular dynamics, and outline the respective theory, as well as the algorithmic development, from the early numerics-based methods, via variational reformulations, to modern data-based techniques utilizing and improving concepts from machine learning. Furthermore, its relation to rare event simulation techniques will be explained, revealing a broad equivalence of variational principles for long-time quantities in molecular dynamics. The article will mainly take a mathematical perspective and will leave the application to real-world molecular systems to the more than 1000 research articles already written on this subject.}, language = {en} } @inproceedings{KuenBetzBinkowskietal.2023, author = {Kuen, Lilli and Betz, Fridtjof and Binkowski, Felix and Schneider, Philipp-Immanuel and Hammerschmidt, Martin and Heermeier, Niels and Rodt, Sven and Reitzenstein, Stephan and Burger, Sven}, title = {Applying a Riesz-projection-based contour integral eigenvalue solver to compute resonance modes of a VCSEL}, volume = {12575}, booktitle = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/2306.02926}, doi = {10.1117/12.2665490}, pages = {125750J}, year = {2023}, language = {en} } @misc{Sikorski2023, author = {Sikorski, Alexander}, title = {VoronoiGraph.jl}, doi = {10.5281/zenodo.6417636}, year = {2023}, abstract = {This Package implements a variation of the Voronoi Graph Traversal algorithm by Polianskii and Pokorny [1]. It constructs a Voronoi Diagram from a set of points by performing a random walk on the graph of the vertices of the diagram. Unlike many other Voronoi implementations this algorithm is not limited to 2 or 3 dimensions and promises good performance even in higher dimensions.}, language = {en} } @article{MikheevaColomAchourietal.2023, author = {Mikheeva, Elena and Colom, R{\´e}mi and Achouri, Karim and Overvig, Adam and Binkowski, Felix and Duboz, Jean-Yves and Cueff, S{\´e}bastien and Fan, Shanhui and Burger, Sven and Al{\`u}, Andrea and Genevet, Patrice}, title = {Asymmetric phase modulation with light with parity-symmetry broken metasurfaces}, volume = {10}, journal = {Optica}, doi = {10.1364/OPTICA.495681}, pages = {1287}, year = {2023}, language = {en} } @book{TernesBauerBraueretal.2023, author = {Ternes, Thomas and Bauer, Karl-Heinz and Brauer, Frank and Drewes, J{\"o}rg and Joss, Adriano and Hiller, Georg and Jewell, Kevin and Oehlmann, J{\"o}rg and Radke, Michael and Schulte-Oehlmann, Ulrike and Schwartz, Thomas and Seel, Peter and V{\"o}lker, Jeanette and Weber, Lilo and Weber, Marcus}, title = {Handlungsempfehlung zur integrativen Bewertung der weitergehenden Abwasserbehandlung von kommunalen Kl{\"a}ranlagen}, volume = {T1/2023}, editor = {Wilhelm, Christian}, publisher = {DWA / GDCh}, isbn = {978-3-96862-563-8}, year = {2023}, abstract = {Das vorliegende Statuspapier beschreibt ein Konzept zur weitergehenden Abwasserbehandlung f{\"u}r die Bewertung von Aufbereitungsverfahren, sowohl in einer Pilotphase zur Auswahl von Verfah- rensoptionen als auch f{\"u}r die Bewertung großtechnischer Anlagen.}, language = {de} } @misc{SikorskiSechiHelfmann2021, author = {Sikorski, Alexander and Sechi, Renata and Helfmann, Luzie}, title = {cmdtools}, doi = {https://doi.org/10.5281/zenodo.4749331}, year = {2021}, abstract = {Python implementation of severals tools (PCCA, AJC, SQRA, P/Q estimation) for the analysis of dynamical systems from the transfer operator perspective.}, language = {en} } @article{WeilandtBehlingGoncalvesetal.2023, author = {Weilandt, Frank and Behling, Robert and Goncalves, Romulo and Madadi, Arash and Richter, Lorenz and Sanona, Tiago and Spengler, Daniel and Welsch, Jona}, title = {Early Crop Classification via Multi-Modal Satellite Data Fusion and Temporal Attention}, volume = {15}, journal = {Remote Sensing}, number = {3}, doi = {10.3390/rs15030799}, pages = {799}, year = {2023}, abstract = {In this article, we propose a deep learning-based algorithm for the classification of crop types from Sentinel-1 and Sentinel-2 time series data which is based on the celebrated transformer architecture. Crucially, we enable our algorithm to do early classification, i.e., predict crop types at arbitrary time points early in the year with a single trained model (progressive intra-season classification). Such early season predictions are of practical relevance for instance for yield forecasts or the modeling of agricultural water balances, therefore being important for the public as well as the private sector. Furthermore, we improve the mechanism of combining different data sources for the prediction task, allowing for both optical and radar data as inputs (multi-modal data fusion) without the need for temporal interpolation. We can demonstrate the effectiveness of our approach on an extensive data set from three federal states of Germany reaching an average F1 score of 0.92 using data of a complete growing season to predict the eight most important crop types and an F1 score above 0.8 when doing early classification at least one month before harvest time. In carefully chosen experiments, we can show that our model generalizes well in time and space.}, language = {en} } @inproceedings{ZinkEkteraiMartinetal.2023, author = {Zink, Christof and Ekterai, Michael and Martin, Dominik and Clemens, William and Maennel, Angela and Mundinger, Konrad and Richter, Lorenz and Crump, Paul and Knigge, Andrea}, title = {Deep-learning-based visual inspection of facets and p-sides for efficient quality control of diode lasers}, volume = {12403}, booktitle = {High-Power Diode Laser Technology XXI}, publisher = {SPIE}, doi = {10.1117/12.2648691}, pages = {94 -- 112}, year = {2023}, abstract = {The optical inspection of the surfaces of diode lasers, especially the p-sides and facets, is an essential part of the quality control in the laser fabrication procedure. With reliable, fast, and flexible optical inspection processes, it is possible to identify and eliminate defects, accelerate device selection, reduce production costs, and shorten the cycle time for product development. Due to a vast range of rapidly changing designs, structures, and coatings, however, it is impossible to realize a practical inspection with conventional software. In this work, we therefore suggest a deep learning based defect detection algorithm that builds on a Faster Regional Convolutional Neural Network (Faster R-CNN) as a core component. While for related, more general object detection problems, the application of such models is straightforward, it turns out that our task exhibits some additional challenges. On the one hand, a sophisticated pre- and postprocessing of the data has to be deployed to make the application of the deep learning model feasible. On the other hand, we find that creating labeled training data is not a trivial task in our scenario, and one has to be extra careful with model evaluation. We can demonstrate in multiple empirical assessments that our algorithm can detect defects in diode lasers accurately and reliably in most cases. We analyze the results of our production-ready pipeline in detail, discuss its limitations and provide some proposals for further improvements.}, language = {en} } @inproceedings{RichterBerner2024, author = {Richter, Lorenz and Berner, Julius}, title = {Improved sampling via learned diffusions}, booktitle = {International Conference on Learning Representations 2024}, arxiv = {http://arxiv.org/abs/2307.01198}, year = {2024}, abstract = {Recently, a series of papers proposed deep learning-based approaches to sample from unnormalized target densities using controlled diffusion processes. In this work, we identify these approaches as special cases of the Schr{\"o}dinger bridge problem, seeking the most likely stochastic evolution between a given prior distribution and the specified target. We further generalize this framework by introducing a variational formulation based on divergences between path space measures of time-reversed diffusion processes. This abstract perspective leads to practical losses that can be optimized by gradient-based algorithms and includes previous objectives as special cases. At the same time, it allows us to consider divergences other than the reverse Kullback-Leibler divergence that is known to suffer from mode collapse. In particular, we propose the so-called log-variance loss, which exhibits favorable numerical properties and leads to significantly improved performance across all considered approaches.}, language = {en} } @incollection{HartmannRichter2023, author = {Hartmann, Carsten and Richter, Lorenz}, title = {Transgressing the Boundaries: Towards a Rigorous Understanding of Deep Learning and Its (Non )Robustness}, volume = {4}, booktitle = {AI - Limits and Prospects of Artificial Intelligence}, editor = {Klimczak, Peter and Petersen, Christer}, publisher = {transcript Verlag}, arxiv = {http://arxiv.org/abs/2307.02454}, doi = {10.1515/9783839457320}, pages = {43 -- 82}, year = {2023}, abstract = {The recent advances in machine learning in various fields of applications can be largely attributed to the rise of deep learning (DL) methods and architectures. Despite being a key technology behind autonomous cars, image processing, speech recognition, etc., a notorious problem remains the lack of theoretical understanding of DL and related interpretability and (adversarial) robustness issues. Understanding the specifics of DL, as compared to, say, other forms of nonlinear regression methods or statistical learning, is interesting from a mathematical perspective, but at the same time it is of crucial importance in practice: treating neural networks as mere black boxes might be sufficient in certain cases, but many applications require waterproof performance guarantees and a deeper understanding of what could go wrong and why it could go wrong. It is probably fair to say that, despite being mathematically well founded as a method to approximate complicated functions, DL is mostly still more like modern alchemy that is firmly in the hands of engineers and computer scientists. Nevertheless, it is evident that certain specifics of DL that could explain its success in applications demands systematic mathematical approaches. In this work, we review robustness issues of DL and particularly bridge concerns and attempts from approximation theory to statistical learning theory. Further, we review Bayesian Deep Learning as a means for uncertainty quantification and rigorous explainability.}, language = {en} } @article{StraubeHoefling2024, author = {Straube, Arthur and H{\"o}fling, Felix}, title = {Depinning transition of self-propelled particles}, volume = {110}, journal = {Physical Review E}, number = {6}, arxiv = {http://arxiv.org/abs/2306.09150}, doi = {10.1103/PhysRevE.110.L062601}, pages = {L062601}, year = {2024}, abstract = {For self-propelled particles in a corrugated potential landscape, we describe a discontinuous change of the classical depinning transition and a host of unique behaviors sensitive to the persistence of the propulsion direction. Exact and semianalytic results for active Brownian particles corroborate a creep regime with a superexponentially suppressed drift velocity upon lowering the force towards the threshold value. This unusual nonlinear response emerges from the competition of two critical scaling laws with exponents of 1/2 for rapidly reorienting particles and 𝑑/2 for particles with a persistent orientation; the latter case depends on the dimensionality 𝑑 of rotational motion and also includes run-and-tumble particles. Additionally, different giant diffusion phenomena occur in the two regimes. Our findings extend to random dynamics with bounded noise near a saddle-node bifurcation and have potential applications in various nonequilibrium problems, including arrested active matter and cell migration.}, language = {en} } @article{MontefuscoHelfmannOkunolaetal.2024, author = {Montefusco, Alberto and Helfmann, Luzie and Okunola, Toluwani and Winkelmann, Stefanie and Sch{\"u}tte, Christof}, title = {Partial mean-field model for neurotransmission dynamics}, volume = {369}, journal = {Mathematical Biosciences}, arxiv = {http://arxiv.org/abs/2307.01737}, doi = {10.1016/j.mbs.2024.109143}, year = {2024}, abstract = {This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the stochastic-spatial particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios.}, language = {en} }