TY - JOUR A1 - Reuss, Joana A1 - Macdonald, Jan A1 - Becker, Simon A1 - Schultka, Konrad A1 - Richter, Lorenz A1 - Körner, Marco T1 - Meta-learning For Few-Shot Time Series Crop Type Classification: A Benchmark On The EuroCropsML Dataset N2 - Spatial imbalances in crop type data pose significant challenges for accurate classification in remote sensing applications. Algorithms aiming at transferring knowledge from data-rich to data-scarce tasks have thus surged in popularity. However, despite their effectiveness in previous evaluations, their performance in challenging real-world applications is unclear and needs to be evaluated. This study benchmarks transfer learning and several meta-learning algorithms, including (First-Order) Model-Agnostic Meta-Learning ((FO)-MAML), Almost No Inner Loop (ANIL), and Task-Informed Meta-Learning (TIML), on the real-world EuroCropsML time series dataset, which combines farmer-reported crop data with Sentinel-2 satellite observations from Estonia, Latvia, and Portugal. Our findings indicate that MAML-based meta-learning algorithms achieve slightly higher accuracy compared to simpler transfer learning methods when applied to crop type classification tasks in Estonia after pre-training on data from Latvia. However, this improvement comes at the cost of increased computational demands and training time. Moreover, we find that the transfer of knowledge between geographically disparate regions, such as Estonia and Portugal, poses significant challenges to all investigated algorithms. These insights underscore the trade-offs between accuracy and computational resource requirements in selecting machine learning methods for real-world crop type classification tasks and highlight the difficulties of transferring knowledge between different regions of the Earth. To facilitate future research in this domain, we present the first comprehensive benchmark for evaluating transfer and meta-learning methods for crop type classification under real-world conditions. The corresponding code is publicly available at this https URL. Y1 - 2025 ER - TY - GEN ED - Fackeldey, Konstantin ED - Kannan, Aswin ED - Pokutta, Sebastian ED - Sharma, Kartikey ED - Walter, Daniel ED - Walter, Andrea ED - Weiser, Martin T1 - Mathematical Optimization for Machine Learning N2 - Mathematical optimization and machine learning are closely related. This proceedings volume of the Thematic Einstein Semester 2023 of the Berlin Mathematics Research Center MATH+ collects recent progress on their interplay in topics such as discrete optimization, nonlinear programming, optimal control, first-order methods, multilevel optimization, machine learning in optimization, physics-informed learning, and fairness in machine learning. Y1 - 2025 SN - 9783111376776 U6 - https://doi.org/10.1515/9783111376776 PB - De Gruyter ER - TY - CHAP A1 - Schneider, Philipp-Immanuel A1 - Sekulic, Ivan A1 - Plock, Matthias A1 - Hammerschmidt, Martin A1 - Rodt, Sven A1 - Reitzenstein, Stephan A1 - Burger, Sven T1 - Physics-informed Bayesian optimization of nanophotonic devices T2 - Advanced Photonics Congress Y1 - 2025 U6 - https://doi.org/10.1364/IPRSN.2025.ITu1A.2 VL - IPRSN SP - ITu1A.2 ER - TY - CHAP A1 - Jäger, Klaus A1 - Mandal, Jyotirmoy A1 - Rand, Barry P. A1 - Meggers, Forrest A1 - Becker, Christiane T1 - Thermal Management of Solar Modules with Infrared-Antireflective Coatings T2 - Advanced Photonics Congress Y1 - 2025 U6 - https://doi.org/10.1364/SOLITH.2025.SM4E.2 VL - SOLITH SP - SM4E.2 ER - TY - JOUR A1 - Tillmann, Peter A1 - Bläsi, Benedikt A1 - Burger, Sven A1 - Hammerschmidt, Martin A1 - Höhn, Oliver A1 - Becker, Christiane A1 - Jäger, Klaus T1 - Optimizing metal grating back reflectors for III-V-on-silicon multijunction solar cells JF - Opt. Express Y1 - 2021 U6 - https://doi.org/10.1364/OE.426761 VL - 29 SP - 22517 ER - TY - GEN A1 - Raharinirina, N. Alexia A1 - Weber, Marcus A1 - Birk, Ralph A1 - Fackeldey, Konstantin A1 - Klasse, Sarah M. A1 - Richter, Tonio Sebastian T1 - Different Tools and Results for Correspondence Analysis N2 - This is a list of codes generated from ancient egyptian texts. The codes are used for a correspondence analysis (CA). Codes and CA software are available from the linked webpage. Y1 - 2021 U6 - https://doi.org/10.12752/8257 N1 - A detailed description of the software can be found in the code repository at https://github.com/AlexiaNomena/Correspondence_Analysis_User_Friendly (repository version of CA software might include updates). ER - TY - GEN A1 - Jäger, Klaus A1 - Sutter, Johannes A1 - Schneider, Philipp-Immanuel A1 - Hammerschmidt, Martin A1 - Becker, Christiane T1 - Optical simulations of nanotextured perovskite/silicon tandem solar cell T2 - HZB Data Service Y1 - 2021 U6 - https://doi.org/10.5442/ND000005 ER - TY - JOUR A1 - Plock, Matthias A1 - Burger, Sven A1 - Schneider, Philipp-Immanuel T1 - Recent advances in Bayesian optimization with applications to parameter reconstruction in optical nano-metrology JF - Proc. SPIE Y1 - 2021 U6 - https://doi.org/10.1117/12.2592266 VL - 11783 SP - 117830J ER - TY - JOUR A1 - Winkelmann, Stefanie A1 - Zonker, Johannes A1 - Schütte, Christof A1 - Djurdjevac Conrad, Natasa T1 - Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading JF - Mathematical Biosciences N2 - Agent based models (ABMs) are a useful tool for modeling spatio-temporal population dynamics, where many details can be included in the model description. Their computational cost though is very high and for stochastic ABMs a lot of individual simulations are required to sample quantities of interest. Especially, large numbers of agents render the sampling infeasible. Model reduction to a metapopulation model leads to a significant gain in computational efficiency, while preserving important dynamical properties. Based on a precise mathematical description of spatio-temporal ABMs, we present two different metapopulation approaches (stochastic and piecewise deterministic) and discuss the approximation steps between the different models within this framework. Especially, we show how the stochastic metapopulation model results from a Galerkin projection of the underlying ABM onto a finite-dimensional ansatz space. Finally, we utilize our modeling framework to provide a conceptual model for the spreading of COVID-19 that can be scaled to real-world scenarios. Y1 - 2021 U6 - https://doi.org/10.1016/j.mbs.2021.108619 VL - 336 PB - Elsevier ER - TY - JOUR A1 - Andrle, Anna A1 - Hönicke, Philipp A1 - Gwalt, Grzegorz A1 - Schneider, Philipp-Immanuel A1 - Kayser, Yves A1 - Siewert, Frank A1 - Soltwisch, Victor T1 - GIXRF and machine learning as metrological tools for shape and element sensitive reconstructions of periodic nanostructures JF - Proc. SPIE Y1 - 2021 U6 - https://doi.org/10.1117/12.2586082 VL - 11611 SP - 116110R ER - TY - JOUR A1 - Nitzke, Isabel A1 - Fackeldey, Konstantin A1 - Vrabec, Jadran T1 - Long range corrections for inhomogeneous fluids containing a droplet or a bubble JF - Molecular Simulation N2 - Long range corrections for molecular simulations of inhomogeneous fluids with a spherical interface are presented. Correction terms for potential energy, force and virial are derived for the monatomic Lennard–Jones fluid. The method is generalised to the Mie potential and arbitrary molecular structures, employing a numerically efficient centre of mass cut-off scheme. The results are validated by a series of droplet simulations for one-centre and two-centre Lennard–Jones fluids with different cut-off radii rc. Systems with rc=8σ provide a check of self-consistence. Further, a system containing a bubble is investigated for the one-centre Lennard–Jones fluid. The equilibrium properties are almost completely independent on the cut-off radius. In comparison with vapour–liquid equilibrium data for systems without a curved interface, all properties show the expected behaviour. Simulation data are used to approximate the surface tension, which is in good agreement with the findings for planar interfaces, thus verifying the present corrections. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1080/08927022.2021.1954639 SP - 1 EP - 14 ER - TY - JOUR A1 - Andrle, Anna A1 - Hönicke, Philipp A1 - Gwalt, Grzegorz A1 - Schneider, Philipp-Immanuel A1 - Kayser, Yves A1 - Siewert, Frank A1 - Soltwisch, Victor T1 - Shape- and Element-Sensitive Reconstruction of Periodic Nanostructures with Grazing Incidence X-ray Fluorescence Analysis and Machine Learning JF - Nanomaterials Y1 - 2021 U6 - https://doi.org/10.3390/nano11071647 VL - 11 SP - 1647 ER - TY - CHAP A1 - Chegini, Fatemeh A1 - Kopanicakova, Alena A1 - Weiser, Martin A1 - Krause, Rolf T1 - Quantitative Analysis of Nonlinear MultifidelityOptimization for Inverse Electrophysiology T2 - Domain Decomposition Methods in Science and Engineering XXVI N2 - The electric conductivity of cardiac tissue determines excitation propagation and is important for quantifying ischemia and scar tissue and for building personalized models. Estimating conductivity distributions from endocardial mapping data is a challenging inverse problem due to the computational complexity of the monodomain equation, which describes the cardiac excitation. For computing a maximum posterior estimate, we investigate different optimization approaches based on adjoint gradient computation: steepest descent, limited memory BFGS, and recursive multilevel trust region methods, which are using mesh hierarchies or heterogeneous model hierarchies. We compare overall performance, asymptotic convergence rate, and pre-asymptotic progress on selected examples in order to assess the benefit of our multifidelity acceleration. Y1 - 2022 SP - 65 EP - 76 PB - Springer ER - TY - JOUR A1 - Alhaddad, Samer A1 - Förstner, Jens A1 - Groth, Stefan A1 - Grünewald, Daniel A1 - Grynko, Yevgen A1 - Hannig, Frank A1 - Kenter, Tobias A1 - Pfreundt, F.J. A1 - Plessl, Christian A1 - Schotte, Merlind A1 - Steinke, Thomas A1 - Teich, J. A1 - Weiser, Martin A1 - Wende, Florian T1 - The HighPerMeshes Framework for Numerical Algorithms on Unstructured Grids JF - Concurrency and Computation: Practice and Experience N2 - Solving PDEs on unstructured grids is a cornerstone of engineering and scientific computing. Heterogeneous parallel platforms, including CPUs, GPUs, and FPGAs, enable energy-efficient and computationally demanding simulations. In this article, we introduce the HPM C++-embedded DSL that bridges the abstraction gap between the mathematical formulation of mesh-based algorithms for PDE problems on the one hand and an increasing number of heterogeneous platforms with their different programming models on the other hand. Thus, the HPM DSL aims at higher productivity in the code development process for multiple target platforms. We introduce the concepts as well as the basic structure of the HPM DSL, and demonstrate its usage with three examples. The mapping of the abstract algorithmic description onto parallel hardware, including distributed memory compute clusters, is presented. A code generator and a matching back end allow the acceleration of HPM code with GPUs. Finally, the achievable performance and scalability are demonstrated for different example problems. Y1 - 2022 U6 - https://doi.org/10.1002/cpe.6616 VL - 34 IS - 14 ER - TY - JOUR A1 - Ayanbayev, Birzhan A1 - Klebanov, Ilja A1 - Lie, Han Cheng A1 - Sullivan, T. J. T1 - Γ-convergence of Onsager–Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems JF - Inverse Problems Y1 - 2022 U6 - https://doi.org/10.1088/1361-6420/ac3f81 VL - 38 IS - 2 ER - TY - JOUR A1 - Ayanbayev, Birzhan A1 - Klebanov, Ilja A1 - Lie, Han Cheng A1 - Sullivan, T. J. T1 - Γ-convergence of Onsager–Machlup functionals: II. Infinite product measures on Banach spaces JF - Inverse Problems Y1 - 2022 U6 - https://doi.org/10.1088/1361-6420/ac3f82 VL - 38 IS - 2 ER - TY - JOUR A1 - Tierno, Pietro A1 - Johansen, Tom H. A1 - Straube, Arthur T1 - Thermally active nanoparticle clusters enslaved by engineered domain wall traps JF - Nature Commun. N2 - The stable assembly of fluctuating nanoparticle clusters on a surface represents a technological challenge of widespread interest for both fundamental and applied research. Here we demonstrate a technique to stably confine in two dimensions clusters of interacting nanoparticles via size-tunable, virtual magnetic traps. We use cylindrical Bloch walls arranged to form a triangular lattice of ferromagnetic domains within an epitaxially grown ferrite garnet film. At each domain, the magnetic stray field generates an effective harmonic potential with a field tunable stifness. The experiments are combined with theory to show that the magnetic confinement is effectively harmonic and pairwise interactions are of dipolar nature, leading to central, strictly repulsive forces. For clusters of magnetic nanoparticles, the stationary collective states arise from the competition between repulsion, confinement and the tendency to fill the central potential well. Using a numerical simulation model as a quantitative map between the experiment and theory we explore the field-induced crystallization process for larger clusters and unveil the existence of three different dynamical regimes. The present method provides a model platform for investigations of the collective phenomena emerging when strongly confined nanoparticle clusters are forced to move in an idealized, harmonic-like potential. Y1 - 2021 U6 - https://doi.org/10.1038/s41467-021-25931-7 VL - 12 SP - 5813 ER - TY - JOUR A1 - Oehme, Stephan A1 - Moewis, Philippe A1 - Boeth, Heide A1 - Bartek, Benjamin A1 - Lippert, Annika A1 - von Tycowicz, Christoph A1 - Ehrig, Rainald A1 - Duda, Georg A1 - Jung, Tobias T1 - PCL insufficient patients with increased translational and rotational passive knee joint laxity have no increased range of anterior–posterior and rotational tibiofemoral motion during level walking JF - Scientific Reports Y1 - 2022 U6 - https://doi.org/10.1038/s41598-022-17328-3 VL - 12 IS - 1 SP - 1 EP - 11 ER - TY - GEN A1 - Niemann, Jan-Hendrik A1 - Schütte, Christof A1 - Klus, Stefan T1 - Simulation data: Data-driven model reduction of agent-based systems using the Koopman generator T2 - PLOS ONE Y1 - 2021 U6 - https://doi.org/http://doi.org/10.5281/zenodo.4522119 N1 - This repository contains the simulation data for the article "Data-driven model reduction of agent-based systems using the Koopman generator" by Jan-Hendrik Niemann, Stefan Klus and Christof Schütte. The archive complete_voter_model.zip contains the simulation results for the extended voter model on a complete graph for the parameters given in the corresponding txt-files to learn a reduced SDE model. The files are of the form [types, time steps, samples, training points].The archive dependency.zip contains additional simulation results of the form [types, time steps, samples, training points] to learn a reduced SDE model. The parameters used are given in the corresponding txt-files.The archive random_voter_model.zip contains the simulation results to learn a reduced SDE model for the given adjacency matrix within the archive. The file aggregate_state is of the form [training points, types, time steps, samples]. The file full_state is of the form [training points, agents, time steps, samples].The archive predator_prey_model.zip contains the simulation results to learn a reduced SDE model and calculation of the mean value of the agent-based model. The data is of the form [types, time steps, samples, training points] and [samples, time steps, types].The archive two_clustered_voter_model.zip contains the simulation results for the extended voter model on a graph with two clusters for the given adjacency matrices to learn a reduced SDE model. The file aggregate_state is of the form [training points, types, time steps, samples]. The file full_state is of the form [training points, agents, time steps, samples]. VL - 16 IS - 5 ER - TY - CHAP A1 - Tillmann, Peter A1 - Jäger, Klaus A1 - Katz, Eugene A1 - Becker, Christiane T1 - Relaxed current-matching constraints by bifacial operation and luminescent coupling in perovskite/silicon tandem solar cells T2 - 2021 IEEE 48th Photovoltaic Specialists Conference (PVSC) Y1 - 2021 U6 - https://doi.org/10.1109/PVSC43889.2021.9518891 SP - 1086 ER - TY - GEN A1 - Betz, Fridtjof A1 - Binkowski, Felix A1 - Burger, Sven T1 - RPExpand: Software for Riesz projection expansion of resonance phenomena [Source Code] Y1 - 2021 U6 - https://doi.org/10.24433/CO.2372084.v1 ER - TY - JOUR A1 - Wu, Tong A1 - Arrivault, Denis A1 - Duruflé, Marc A1 - Gras, Alexandre A1 - Binkowski, Felix A1 - Burger, Sven A1 - Yan, Wei A1 - Lalanne, Philippe T1 - Efficient hybrid method for the modal analysis of optical microcavities and nanoresonators JF - J. Opt. Soc. Am. A Y1 - 2021 U6 - https://doi.org/10.1364/JOSAA.428224 VL - 38 SP - 1224 ER - TY - JOUR A1 - Betz, Fridtjof A1 - Binkowski, Felix A1 - Burger, Sven T1 - RPExpand: Software for Riesz projection expansion of resonance phenomena JF - SoftwareX Y1 - 2021 U6 - https://doi.org/10.1016/j.softx.2021.100763 VL - 15 SP - 100763 ER - TY - JOUR A1 - Negrin-Montecelo, Yoel A1 - Movsesyan, Artur A1 - Gao, Jie A1 - Burger, Sven A1 - Wang, Zhiming A1 - Nlate, Sylvain A1 - Pouget, Emilie A1 - Oda, Reiko A1 - Comesana-Hermo, Miguel A1 - Govorov, Alexander O. A1 - Correa-Duarte, Miguel T1 - Chiral Generation of Hot Carriers for Polarization-Sensitive Plasmonic Photocatalysis with Hybrid Nanostructures JF - J. Am. Chem. Soc. Y1 - 2022 U6 - https://doi.org/10.1021/jacs.1c10526 VL - 144 SP - 1663 ER - TY - JOUR A1 - Wang, Junyang A1 - Cockayne, Jon A1 - Chkrebtii, Oksana A1 - Sullivan, T. J. A1 - Oates, Chris T1 - Bayesian numerical methods for nonlinear partial differential equations JF - Statistics and Computing Y1 - 2021 U6 - https://doi.org/10.1007/s11222-021-10030-w VL - 31 IS - 5 ER - TY - CHAP A1 - Schnauber, Peter A1 - Schall, Johannes A1 - Bounouar, Samir A1 - Srinivasan, Kartik A1 - Davanco, Marcelo A1 - Song, Jin-Dong A1 - Burger, Sven A1 - Rodt, Sven A1 - Reitzenstein, Stephan T1 - Deterministically fabricated quantum dot – waveguide systems for on-chip quantum optics T2 - Proc. SPIE Y1 - 2021 U6 - https://doi.org/10.1117/12.2596042 VL - 11806 SP - 118060G ER - TY - CHAP A1 - Perevoznik, Dmitrii A1 - Bose, Surajit A1 - Burger, Sven A1 - Demircan, Ayhan A1 - Morgner, Uwe T1 - Writing Photonic Components in Polymers Using Femtosecond Pulses T2 - Conference on Lasers and Electro-Optics (CLEO) Y1 - 2021 U6 - https://doi.org/10.1364/CLEO_AT.2021.ATh4P.4 SP - ATh4P.4 ER - TY - JOUR A1 - del Razo, Mauricio A1 - Frömberg, Daniela A1 - Straube, Arthur A1 - Schütte, Christof A1 - Höfling, Felix A1 - Winkelmann, Stefanie T1 - A probabilistic framework for particle-based reaction–diffusion dynamics using classical Fock space representations JF - Letters in Mathematical Physics Y1 - 2022 U6 - https://doi.org/10.1007/s11005-022-01539-w VL - 112 IS - 49 ER - TY - JOUR A1 - Straube, Arthur A1 - Winkelmann, Stefanie A1 - Schütte, Christof A1 - Höfling, Felix T1 - Stochastic pH oscillations in a model of the urea–urease reaction confined to lipid vesicles JF - J. Phys. Chem. Lett. N2 - The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We numerically study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules. For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller. The mean period, however, is found to be remarkably robust for vesicle sizes down to approximately 200 nm, but the periodicity of the rhythm is gradually destroyed for smaller vesicles. The observed oscillations are explained as a canard-like limit cycle that differs from the wide class of conventional feedback oscillators. Y1 - 2021 U6 - https://doi.org/10.1021/acs.jpclett.1c03016 VL - 12 SP - 9888 EP - 9893 ER - TY - JOUR A1 - Betz, Fridtjof A1 - Binkowski, Felix A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Resonance expansion of quadratic quantities with regularized quasinormal modes JF - Phys. Status Solidi A Y1 - 2023 U6 - https://doi.org/10.1002/pssa.202200892 VL - 220 SP - 2200892 ER - TY - JOUR A1 - Ben Soltane, Isam A1 - Colom, Rémi A1 - Stout, Brian A1 - Bonod, Nicolas T1 - Derivation of the Transient and Steady Optical States from the Poles of the S-Matrix JF - Laser Photon. Rev. Y1 - 2023 U6 - https://doi.org/10.1002/lpor.202200141 VL - 17 SP - 2200141 ER - TY - JOUR A1 - Ribera Borrell, Enric A1 - Quer, Jannes A1 - Richter, Lorenz A1 - Schütte, Christof T1 - Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics JF - SIAM Journal on Scientific Computing (SISC) N2 - 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. KW - importance sampling KW - stochastic optimal control KW - rare event simulation KW - metastability KW - neural networks KW - metadynamics Y1 - 2023 U6 - https://doi.org/10.1137/22M1503464 VL - 89 IS - 1 ER - TY - GEN A1 - Weiser, Martin A1 - Chegini, Fatemeh T1 - Higher-order time integration using spectral deferred correction method (SDC) in a cell by cell discretization of cardiac excitation N2 - This C++ code implements a cell-by-cell model of cardiac excitation using a piecewise-continuous finite element discretization and spectral deferred correction time stepping. The code is based on the Kaskade 7 finite element toolbox and forms a prototype for the µCarp code to be implemented in the Microcard project. Y1 - 2022 U6 - https://doi.org/10.35097/716 ER - TY - JOUR A1 - Montefusco, Alberto A1 - Sharma, Upanshu A1 - Tse, Oliver T1 - Fourier-Cattaneo equation: stochastic origin, variational formulation, and asymptotic limits N2 - We introduce a variational structure for the Fourier-Cattaneo (FC) system which is a second-order hyperbolic system. This variational structure is inspired by the large-deviation rate functional for the Kac process which is closely linked to the FC system. Using this variational formulation we introduce appropriate solution concepts for the FC equation and prove an a priori estimate which connects this variational structure to an appropriate Lyapunov function and Fisher information, the so-called FIR inequality. Finally, we use this formulation and estimate to study the diffusive and hyperbolic limits for the FC system. Y1 - 2022 ER - TY - JOUR A1 - Helfmann, Luzie A1 - Conrad, Natasa Djurdjevac A1 - Lorenz-Spreen, Philipp A1 - Schütte, Christof T1 - Modelling opinion dynamics under the impact of influencer and media strategies JF - Scientific Reports N2 - Digital communication has made the public discourse considerably more complex, and new actors and strategies have emerged as a result of this seismic shift. Aside from the often-studied interactions among individuals during opinion formation, which have been facilitated on a large scale by social media platforms, the changing role of traditional media and the emerging role of "influencers" are not well understood, and the implications of their engagement strategies arising from the incentive structure of the attention economy even less so. Here we propose a novel opinion dynamics model that accounts for these different roles, namely that media and influencers change their own positions on slower time scales than individuals, while influencers dynamically gain and lose followers. Numerical simulations show the importance of their relative influence in creating qualitatively different opinion formation dynamics: with influencers, fragmented but short-lived clusters emerge, which are then counteracted by more stable media positions. Mean-field approximations by partial differential equations reproduce this dynamic. Based on the mean-field model, we study how strategies of influencers to gain more followers can influence the overall opinion distribution. We show that moving towards extreme positions can be a beneficial strategy for influencers to gain followers. Finally, we demonstrate that optimal control strategies allow other influencers or media to counteract such attempts and prevent further fragmentation of the opinion landscape. Our modelling framework contributes to better understanding the different roles and strategies in the increasingly complex information ecosystem and their impact on public opinion formation. Y1 - 2023 U6 - https://doi.org/10.1038/s41598-023-46187-9 VL - 13 SP - 19375 ER - TY - JOUR A1 - Wolf, Sarah A1 - Fürst, Steffen A1 - Geiges, Andreas A1 - Laublichler, Manfred A1 - Mielke, Jahel A1 - Steudle, Gesine A1 - Winter, Konstantin A1 - Jaeger, Carlo T1 - The Decision Theatre Triangle for societal challenges – an example case and research needs JF - Journal of Cleaner Production N2 - Tackling societal challenges relating to sustainability requires both an understanding of the underlying complex socio-ecological systems and participation of scientists as well as relevant stakeholders, such as practice experts, decision makers, and citizens. This paper introduces the Decision Theatre Triangle, a method which combines empirical information, mathematical modelling and simulation, and a format for dialogue between scientists and stakeholders. While it builds on previous Decision Theatre work, the new structuring into these three elements emphasizes what is needed for setting up a Decision Theatre for a given challenge. Based on experience with a specific example – sustainable mobility in Germany – it is argued that agent-based models are particularly suitable for Decision Theatres and that the method is useful not only for decision support but also for science communication and co-creation of a deeper knowledge of the system under discussion. As a step towards facilitating a broader use of the Decision Theatre Triangle method, the paper then sketches research needs for each of its three elements, with a focus on mathematical modelling and simulation. Y1 - 2023 U6 - https://doi.org/10.1016/j.jclepro.2023.136299 VL - 394 SP - 136299 ER - TY - THES A1 - Chegini, Fatemeh T1 - Multilevel optimization algorithm for Inverse Problem in Electrocardiography N2 - The electric conductivity of cardiac tissue determines excitation propagation and is vital for quantifying ischemia and scar tissue and building personalized models. As scar tissue is generally characterized by different conduction of electrical excitation, we aim to estimate conductivity-related parameters in mathematical excitation models from endocardial mapping data, particularly the anisotropic conductivity tensor in the monodomain equation, which describes the cardiac excitation. Yet, estimating the distributed and anisotropic conductivity tensors reliably and efficiently from endocardial mapping data or electrocardiograms is a challenging inverse problem due to the computational complexity of the monodomain equation; Many expensive high-resolution computations for the monodomain equation on very fine space and time discretizations are involved. Thus, we aim at building an efficient multilevel method for accelerating the estimation procedure combining electrophysiology models of different complex- ity, which uses a computationally cheap eikonal model in addition to the more accurate monodomain model. Distributed parameter estimation, well-known as an ill-posed inverse problem, can be performed by minimizing the misfit between simulated and measured electrical activity on the endocardial surface subject to the monodomain model and some regularization, leading to a partial differential equation constrained optimization problem. We formulate this optimization problem, including scar tissue modeling and different regularizations, and design an efficient iterative solver. To this aim, we consider monodomain grid hi- erarchies, monodomain-eikonal model hierarchies, and the combination of both hierarchies in a recursive multilevel trust-region (RMTR) method. On the one hand, both the trust region method’s estimation quality and efficiency, independent of the data, are investigated from several numerical exam- ples. Endocardial mapping data of realistic density appears to be sufficient to provide quantitatively reasonable estimates of the location, size, and shape of scars close to the endocardial surface. In several situations, scar reconstruction based on eikonal and monodomain models differ significantly, suggesting the use of the more involved monodomain model for this purpose. Moreover, Eikonal models can accelerate the computations considerably, enabling the use of complex electrophysiology models for estimating myocardial scars from endocardial mapping data. In many situations, eikonal models approximate monodomain models well but are orders of magnitude faster to solve. Thus, eikonal models can utilize them to provide an RMTR acceleration with negligible overhead per iteration, resulting in a practical approach to estimating myocardial scars from endocardial mapping data. In addition, the multilevel solver is faster than a comparable single-level solver. On the other hand, we investigate different optimization approaches based on adjoint gradient computation for computing a maximum posterior estimate: steepest descent, limited memory BFGS, and recursive multilevel trust region methods using mesh hierarchies or heterogeneous model hierarchies. We compare overall performance, asymptotic convergence rate, and pre-asymptotic progress on selected examples in order to assess the benefit of our multifidelity acceleration. Y1 - 2022 ER - TY - JOUR A1 - Fischer-Holzhausen, Sophie A1 - Röblitz, Susanna T1 - Hormonal regulation of ovarian follicle growth in humans: Model-based exploration of cycle variability and parameter sensitivities JF - Journal of Theoretical Biology N2 - We present a modelling and simulation framework for the dynamics of ovarian follicles and key hormones along the hypothalamic-pituitary-gonadal axis throughout consecutive human menstrual cycles. All simulation results (hormone concentrations and ovarian follicle sizes) are in biological units and can easily be compared to clinical data. The model takes into account variability in follicles' response to stimulating hormones, which introduces variability between cycles. The growth of ovarian follicles in waves is an emergent property in our model simulations and further supports the hypothesis that follicular waves are also present in humans. We use Approximate Bayesian Computation and cluster analysis to construct a population of virtual subjects and to study parameter distributions and sensitivities. The model can be used to compare and optimize treatment protocols for ovarian hyperstimulation, thus potentially forming the integral part of a clinical decision support system in reproductive endocrinology. Y1 - 2022 U6 - https://doi.org/https://doi.org/10.1016/j.jtbi.2022.111150 ER - TY - JOUR A1 - Fischer-Holzhausen, Sophie A1 - Röblitz, Susanna T1 - Mathematical modelling of follicular growth and ovarian stimulation JF - Current Opinion in Endocrine and Metabolic Research Y1 - 2022 U6 - https://doi.org/https://doi.org/10.1016/j.coemr.2022.100385 ER - TY - JOUR A1 - Krüger, Tillmann A1 - Leeners, Brigitte A1 - Tronci, Enrico A1 - Mancini, Toni A1 - Ille, Fabian A1 - Egli, Marcel A1 - Engler, Harald A1 - Röblitz, Susanna A1 - Frieling, Helge A1 - Sinke, Christopher A1 - Jahn, Kirsten T1 - The androgen system across the menstrual cycle: Hormonal, (epi-)genetic and psychometric alterations JF - Physiology and Behavior Y1 - 2022 U6 - https://doi.org/https://doi.org/10.1016/j.physbeh.2022.114034 ER - TY - CHAP A1 - Binkowski, Felix A1 - Betz, Fridtjof A1 - Hammerschmidt, Martin A1 - Schneider, Philipp-Immanuel A1 - Zschiedrich, Lin A1 - Burger, Sven ED - Zouhdi, S. T1 - Numerical methods for the investigation of resonances in nanophotonics T2 - The 12th International Conference on Metamaterials, Photonic Crystals and Plasmonics (META 2022) Y1 - 2022 SN - 2429-1390 SP - 247 ER - TY - CHAP A1 - Movsesyan, Artur A1 - Santiago, Eva Yazmin A1 - Burger, Sven A1 - Correa-Duarte, Miguel A1 - Besteiro, Lucas V. A1 - Wang, Zhiming A1 - Govorov, Alexander O. ED - Zouhdi, S. T1 - The anisotropy of hot carriers’ spatial distribution contrasts the isotropy of photothermal effects in complex and small plasmonic nanocrystals with complex shapes T2 - The 12th International Conference on Metamaterials, Photonic Crystals and Plasmonics (META 2022) Y1 - 2022 SN - 2429-1390 SP - 285 ER - TY - CHAP A1 - Binkowski, Felix A1 - Betz, Fridtjof A1 - Colom, Remi A1 - Hammerschmidt, Martin A1 - Schneider, Philipp-Immanuel A1 - Zschiedrich, Lin A1 - Burger, Sven ED - Zouhdi, S. ED - Pawlak, D. ED - Kudelski, A. T1 - Contour integral methods for resonance phenomena in nano-optics T2 - The 11th International Conference on Metamaterials, Photonic Crystals and Plasmonics (META 2021) Y1 - 2021 SN - 2429-1390 SP - 523 ER - TY - JOUR A1 - Ernst, Ariane A1 - Unger, Nathalie A1 - Schütte, Christof A1 - Walter, Alexander A1 - Winkelmann, Stefanie T1 - Rate-limiting recovery processes in neurotransmission under sustained stimulation JF - Mathematical Biosciences N2 - At chemical synapses, an arriving electric signal induces the fusion of vesicles with the presynaptic membrane, thereby releasing neurotransmitters into the synaptic cleft. After a fusion event, both the release site and the vesicle undergo a recovery process before becoming available for reuse again. Of central interest is the question which of the two restoration steps acts as the limiting factor during neurotrans-mission under high-frequency sustained stimulation. In order to investigate this question, we introduce a novel non-linear reaction network which involves explicit recovery steps for both the vesicles and the release sites, and includes the induced time-dependent output current. The associated reaction dynamics are formulated by means of ordinary differential equations (ODEs), as well as via the associated stochastic jump process. While the stochastic jump model describes a single release site, the average over many release sites is close to the ODE solution and shares its periodic structure. The reason for this can be traced back to the insight that recovery dynamics of vesicles and release sites are statistically almost independent. A sensitivity analysis on the recovery rates based on the ODE formulation reveals that neither the vesicle nor the release site recovery step can be identified as the essential rate-limiting step but that the rate- limiting feature changes over the course of stimulation. Under sustained stimulation the dynamics given by the ODEs exhibit transient dynamics leading from an initial depression of the postsynaptic response to an asymptotic periodic orbit, while the individual trajectories of the stochastic jump model lack the oscillatory behavior an asymptotic periodicity of the ODE-solution. Y1 - 2023 U6 - https://doi.org/10.1016/j.mbs.2023.109023 VL - 362 ER - TY - JOUR A1 - Fernandes, Rita A1 - Chaowdhary, Suvrat A1 - Saleh, Noureldin A1 - Mikula, Natalia A1 - Kanevche, Katerina A1 - Berlepsch, Hans A1 - Hosogi, Naoki A1 - Heberle, Joachim A1 - Weber, Marcus A1 - Böttcher, Christoph A1 - Koksch, Beate T1 - Cyanine Dye Coupling Mediates Self-assembly of a pH Sensitive Peptide into Novel 3D Architectures JF - Angewandte Chemie N2 - A conjugated Cy5 dye-peptide system reveals the formation of two novel and structurally distinct supramolecular assemblies with photo-physical characteristics of H-type dimers or tetramers, respectively. The molecular ultrastructures are triggered by the complementary interplay of mutual chromophore coupling and pH induced changes in the peptide charge pattern. Y1 - 2022 VL - 61 IS - 48 SP - e202208647 ER - TY - THES A1 - Rabben, Robert Julian T1 - Ein holistischer Ansatz zur Analyse molekularer Konformationen auf der Basis von ISOKANN Y1 - 2022 ER - TY - JOUR A1 - Secker, Christopher A1 - Fackeldey, Konstantin A1 - Weber, Marcus A1 - Ray, Sourav A1 - Gorgulla, Christoph A1 - Schütte, Christof T1 - Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists JF - Journal of Cheminformatics N2 - Opioids are essential pharmaceuticals due to their analgesic properties, however, lethal side effects, addiction, and opioid tolerance are extremely challenging. The development of novel molecules targeting the μ-opioid receptor (MOR) in inflamed, but not in healthy tissue, could significantly reduce these unwanted effects. Finding such novel molecules can be achieved by maximizing the binding affinity to the MOR at acidic pH while minimizing it at neutral pH, thus combining two conflicting objectives. Here, this multi-objective optimal affinity approach is presented, together with a virtual drug discovery pipeline for its practical implementation. When applied to finding pH-specific drug candidates, it combines protonation state-dependent structure and ligand preparation with high-throughput virtual screening. We employ this pipeline to characterize a set of MOR agonists identifying a morphine-like opioid derivative with higher predicted binding affinities to the MOR at low pH compared to neutral pH. Our results also confirm existing experimental evidence that NFEPP, a previously described fentanyl derivative with reduced side effects, and recently reported β-fluorofentanyls and -morphines show an increased specificity for the MOR at acidic pH when compared to fentanyl and morphine. We further applied our approach to screen a >50K ligand library identifying novel molecules with pH-specific predicted binding affinities to the MOR. The presented differential docking pipeline can be applied to perform multi-objective affinity optimization to identify safer and more specific drug candidates at large scale. Y1 - 2023 U6 - https://doi.org/10.1186/s13321-023-00746-4 VL - 15 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 - CHAP A1 - Gander, Lia A1 - Krause, Rolf A1 - Weiser, Martin A1 - Costabal, Francisco A1 - Pezzuto, Simone T1 - On the Accuracy of Eikonal Approximations in Cardiac Electrophysiology in the Presence of Fibrosis T2 - Functional Imaging and Modeling of the Heart. FIMH 2023. N2 - Fibrotic tissue is one of the main risk factors for cardiac arrhythmias. It is therefore a key component in computational studies. In this work, we compare the monodomain equation to two eikonal models for cardiac electrophysiology in the presence of fibrosis. We show that discontinuities in the conductivity field, due to the presence of fibrosis, introduce a delay in the activation times. The monodomain equation and eikonal-diffusion model correctly capture these delays, contrarily to the classical eikonal equation. Importantly, a coarse space discretization of the monodomain equation amplifies these delays, even after accounting for numerical error in conduction velocity. The numerical discretization may also introduce artificial conduction blocks and hence increase propagation complexity. Therefore, some care is required when comparing eikonal models to the discretized monodomain equation. Y1 - 2023 U6 - https://doi.org/10.1007/978-3-031-35302-4_14 VL - 13958 PB - Springer, Cham ER - TY - JOUR A1 - Subramaniam, Jayant S. A1 - Hubig, Michael A1 - Muggenthaler, Holger A1 - Schenkl, Sebastian A1 - Ullrich, Julia A1 - Pourtier, Grégroire A1 - Weiser, Martin A1 - Mall, Gita T1 - Sensitivity of temperature-based time since death estimation on measurement location JF - International Journal of Legal Medicine N2 - Rectal temperature measurement (RTM) from crime scenes is an important parameter for temperature-based time of death estimation (TDE). Various influential variables exist in TDE methods like the uncertainty in thermal and environmental parameters. Although RTM depends in particular on the location of measurement position, this relationship has never been investigated separately. The presented study fills this gap using Finite Element (FE) simulations of body cooling. A manually meshed coarse human FE model and an FE geometry model developed from the CT scan of a male corpse are used for TDE sensitivity analysis. The coarse model is considered with and without a support structure of moist soil. As there is no clear definition of ideal rectal temperature measurement location for TDE, possible variations in RTM location (RTML) are considered based on anatomy and forensic practice. The maximum variation of TDE caused by RTML changes is investigated via FE simulation. Moreover, the influence of ambient temperature, of FE model change and of the models positioning on a wet soil underground are also discussed. As a general outcome, we notice that maximum TDE deviations of up to ca. 2-3 h due to RTML deviations have to be expected. The direction of maximum influence of RTML change on TDE generally was on the line caudal to cranial. Y1 - 2023 U6 - https://doi.org/10.1007/s00414-023-03040-y VL - 137 SP - 1815 EP - 1837 ER - TY - CHAP A1 - Tockhorn, Philipp A1 - Sutter, Johannes A1 - Cruz, Alexandros A1 - Wagner, Philipp A1 - Jäger, Klaus A1 - Yoo, Danbi A1 - Lang, Felix A1 - Grischek, Max A1 - Li, Bor A1 - Al-Ashouri, Amran A1 - Köhnen, Eike A1 - Stolterfoht, Martin A1 - Neher, Dieter A1 - Schlatmann, Rutger A1 - Rech, Bernd A1 - Stannowski, Bernd A1 - Albrecht, Steve A1 - Becker, Christiane T1 - Nanooptically Enhanced Perovskite/Silicon Tandem Solar Cells with 29.80% Power Conversion Efficiency T2 - OSA Adv. Photonics Y1 - 2022 U6 - https://doi.org/10.1364/NOMA.2022.JTu4H.2 SP - JTu4H.2 ER - TY - JOUR A1 - Semler, Phillip A1 - Weiser, Martin T1 - Adaptive Gaussian Process Regression for Efficient Building of Surrogate Models in Inverse Problems JF - Inverse Problems N2 - In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model y with a surrogate model y(s) that can be evaluated quickly leads to a significant speedup. The approximation quality of the surrogate model depends strongly on the number, position, and accuracy of the sample points. With an additional finite computational budget, this leads to a problem of (computer) experimental design. In contrast to the selection of sample points, the trade-off between accuracy and effort has hardly been studied systematically. We therefore propose an adaptive algorithm to find an optimal design in terms of position and accuracy. Pursuing a sequential design by incrementally appending the computational budget leads to a convex and constrained optimization problem. As a surrogate, we construct a Gaussian process regression model. We measure the global approximation error in terms of its impact on the accuracy of the identified parameter and aim for a uniform absolute tolerance, assuming that y(s) is computed by finite element calculations. A priori error estimates and a coarse estimate of computational effort relate the expected improvement of the surrogate model error to computational effort, resulting in the most efficient combination of sample point and evaluation tolerance. We also allow for improving the accuracy of already existing sample points by continuing previously truncated finite element solution procedures. Y1 - 2023 U6 - https://doi.org/10.1088/1361-6420/ad0028 VL - 39 IS - 12 SP - 125003 ER - TY - JOUR A1 - Ullrich, Julia A1 - Weiser, Martin A1 - Subramaniam, Jayant A1 - Schenkl, Sebastian A1 - Muggenthaler, Holger A1 - Hubig, Michael A1 - Mall, Gita T1 - The impact of anatomy variation on temperature based time of death estimation JF - International Journal of Legal Medicine N2 - Temperature-based time of death estimation (TTDE) using simulation methods such as the finite element (FE) method promises higher accuracy and broader applicability in nonstandard cooling scenarios than established phenomenological methods. Their accuracy depends crucially on the simulation model to capture the actual situation. The model fidelity in turn hinges on the representation of the corpse’s anatomy in form of computational meshes as well as on the thermodynamic parameters. While inaccuracies in anatomy representation due to coarse mesh resolution are known to have a minor impact on the estimated time of death, the sensitivity with respect to larger differences in the anatomy has so far not been studied. We assess this sensitivity by comparing four independently generated and vastly different anatomical models in terms of the estimated time of death in an identical cooling scenario. In order to isolate the impact of shape variation, the models are scaled to a reference size, and the possible impact of measurement location variation is excluded explicitly, which gives a lower bound on the impact of anatomy on the estimated time of death. Y1 - 2023 U6 - https://doi.org/10.1007/s00414-023-03026-w VL - 137 SP - 1615 EP - 1627 ER - TY - THES A1 - Tillmann, Peter T1 - Optimizing bifacial tandem solar cells for realistic operation conditions Y1 - 2023 U6 - https://doi.org/10.17169/refubium-39571 ER - TY - CHAP A1 - Mukherjee, Deshabrato A1 - Kalas, Benjámin A1 - Burger, Sven A1 - Sáfrán, György A1 - Serényi, Miklós A1 - Fried, Miklós A1 - Petrik, Péter T1 - Nanostructures for in-situ surface-enhanced Kretschmann-Raether ellipsometry T2 - Proc. SPIE Y1 - 2023 U6 - https://doi.org/10.1117/12.2649080 VL - 12428 SP - 124280S ER - TY - GEN A1 - Betz, Fridtjof A1 - Binkowski, Felix A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Source code and simulation results for computing resonance expansions of quadratic quantities with regularized quasinormal modes T2 - Zenodo Y1 - 2022 U6 - https://doi.org/10.5281/zenodo.7376556 ER - TY - GEN A1 - Ternes, Thomas A1 - Bauer, Karl-Heinz A1 - Brauer, Frank A1 - Drewes, Jürgen A1 - Jewell, Kevin A1 - Joss, Adriano A1 - Oehlmann, Jörg A1 - Radtke, Michael A1 - Schulte-Oehlmann, Ulrike A1 - Schwartz, Thomas A1 - Seel, Peter A1 - Völker, Jeanette A1 - Weber, Lilo A1 - Weber, Marcus T1 - Handlungsempfehlung zur integrativen Bewertung der weitergehenden Abwasserbehandlung von kommunalen Kläranlagen T2 - DWA-Themen N2 - Der DWA-Themenband beschreibt ein Konzept zur weitergehenden Abwasserbehandlung für die Bewertung von Aufbereitungsverfahren, sowohl in einer Pilotphase zur Auswahl von Verfahrensoptionen als auch für die Bewertung großtechnischer Anlagen. Emissionsseitig basiert das Konzept auf bereits regulatorisch definierten Parametern wie anorganischen Stickstoff-Verbindungen oder Phosphat sowie auf neuen noch nicht in der Abwasserverordnung regulierten Parametern. Die immissionsseitige Betrachtung erfolgt auf Basis der rechtlich durch die Europäische Wasserrahmenrichtlinie und andere Anforderungen bindenden Instrumente. Hierfür werden spezifische Vorgehensweisen vorgeschlagen. Anhand zweier ausgewählter Praxisbeispiele wird deutlich, dass es zur Bewertung der Verfahrensoptionen an einem Standort dienlich ist, ausgewählte Reduktionen bzw. Entfernungen von Stoffen, Organismen und Effekten zu bestimmen. Y1 - 2023 VL - T1/2023 PB - DWA ER - TY - CHAP A1 - Chegini, Fatemeh A1 - Steinke, Thomas A1 - Weiser, Martin T1 - Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods N2 - The locality of solution features in cardiac electrophysiology simulations calls for adaptive methods. Due to the overhead incurred by established mesh refinement and coarsening, however, such approaches failed in accelerating the computations. Here we investigate a different route to spatial adaptivity that is based on nested subset selection for algebraic degrees of freedom in spectral deferred correction methods. This combination of algebraic adaptivity and iterative solvers for higher order collocation time stepping realizes a multirate integration with minimal overhead. This leads to moderate but significant speedups in both monodomain and cell-by-cell models of cardiac excitation, as demonstrated at four numerical examples. Y1 - 2022 ER - TY - JOUR A1 - Straube, Arthur A1 - Winkelmann, Stefanie A1 - Höfling, Felix T1 - Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles JF - The Journal of Physical Chemistry B N2 - This theoretical study concerns a pH oscillator based on the urea-urease reaction confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyse the structure of the phase flow and of the limit cycle, which controls the dynamics for giant vesicles and dominates the pronouncedly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, which are amenable to analytic treatments that are complemented by numerical solutions, and obtain the period and amplitude of the oscillations as well as the parameter domain, where oscillatory behavior persists. We show that the accuracy of these predictions is highly sensitive to the employed reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The faithful modeling of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms. Y1 - 2023 U6 - https://doi.org/10.1021/acs.jpcb.2c09092 VL - 127 IS - 13 SP - 2955 EP - 2967 ER - TY - JOUR A1 - Sikorski, Alexander A1 - Ribera Borrell, Enric A1 - Weber, Marcus T1 - Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN JF - Journal of Mathematical Physics N2 - The dominant eigenfunctions of the Koopman operator characterize the metastabilities and slow-timescale dynamics of stochastic diffusion processes. In the context of molecular dynamics and Markov state modeling, they allow for a description of the location and frequencies of rare transitions, which are hard to obtain by direct simulation alone. In this article, we reformulate the eigenproblem in terms of the ISOKANN framework, an iterative algorithm that learns the eigenfunctions by alternating between short burst simulations and a mixture of machine learning and classical numerics, which naturally leads to a proof of convergence. We furthermore show how the intermediate iterates can be used to reduce the sampling variance by importance sampling and optimal control (enhanced sampling), as well as to select locations for further training (adaptive sampling). We demonstrate the usage of our proposed method in experiments, increasing the approximation accuracy by several orders of magnitude. Y1 - 2024 U6 - https://doi.org/10.1063/5.0140764 VL - 65 SP - 013502 ER - TY - JOUR A1 - Huynh, Ngoc A1 - Chegini, Fatemeh A1 - Pavarino, Luca A1 - Weiser, Martin A1 - Scacchi, Simone T1 - Convergence analysis of BDDC preconditioners for hybrid DG discretizations of the cardiac cell-by-cell model JF - SIAM Journal on Scientific Computing N2 - A Balancing Domain Decomposition by Constraints (BDDC) preconditioner is constructed and analyzed for the solution of hybrid Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models. The latter are different from the classical Bidomain and Monodomain cardiac models based on homogenized descriptions of the cardiac tissue at the macroscopic level, and therefore they allow the representation of individual cardiac cells, cell aggregates, damaged tissues and nonuniform distributions of ion channels on the cell membrane. The resulting discrete cell-by-cell models have discontinuous global solutions across the cell boundaries, hence the proposed BDDC preconditioner is based on appropriate dual and primal spaces with additional constraints which transfer information between cells (subdomains) without influencing the overall discontinuity of the global solution. A scalable convergence rate bound is proved for the resulting BDDC cell-by-cell preconditioned operator, while numerical tests validate this bound and investigate its dependence on the discretization parameters. Y1 - 2023 VL - 45 IS - 6 SP - A2836 EP - A2857 ER - TY - JOUR A1 - Boltz, Horst-Holger A1 - Kurchan, Jorge A1 - Liu, Andrea J. T1 - Fluctuation distributions of energy minima in complex landscapes JF - Physical Review Research N2 - We discuss the properties of the distributions of energies of minima obtained by gradient descent in complex energy landscapes. We find strikingly similar phenomenology across several prototypical models. We particularly focus on the distribution of energies of minima in the analytically well-understood p-spin-interaction spin-glass model. We numerically find non-Gaussian distributions that resemble the Tracy-Widom distributions often found in problems of random correlated variables, and nontrivial finite-size scaling. Based on this, we propose a picture of gradient-descent dynamics that highlights the importance of a first-passage process in the eigenvalues of the Hessian. This picture provides a concrete link to problems in which the Tracy-Widom distribution is established. Aspects of this first-passage view of gradient-descent dynamics are generic for nonconvex complex landscapes, rationalizing the commonality that we find across models. Y1 - 2020 U6 - https://doi.org/10.1103/PhysRevResearch.3.013061 VL - 3 IS - 1 SP - 013061 ER - TY - JOUR A1 - Carderera, Alejandro A1 - Pokutta, Sebastian A1 - Schütte, Christof A1 - Weiser, Martin T1 - An efficient first-order conditional gradient algorithm in data-driven sparse identification of nonlinear dynamics to solve sparse recovery problems under noise JF - Journal of Computational and Applied Mathematics N2 - Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the potential to transform data-rich fields where well-established dynamical models remain unknown. This work contributes to the recent trend in data-driven sparse identification of nonlinear dynamics of finding the best sparse fit to observational data in a large library of potential nonlinear models. We propose an efficient first-order Conditional Gradient algorithm for solving the underlying optimization problem. In comparison to the most prominent alternative algorithms, the new algorithm shows significantly improved performance on several essential issues like sparsity-induction, structure-preservation, noise robustness, and sample efficiency. We demonstrate these advantages on several dynamics from the field of synchronization, particle dynamics, and enzyme chemistry. Y1 - 2021 ER - TY - JOUR A1 - Wulkow, Niklas A1 - Telgmann, Regina A1 - Hungenberg, Klaus-Dieter A1 - Schütte, Christof A1 - Wulkow, Michael T1 - Deterministic and Stochastic Parameter Estimation for Polymer Reaction Kinetics I: Theory and Simple Examples JF - Macromolecular Theory and Simulations N2 - Two different approaches to parameter estimation (PE) in the context of polymerization are introduced, refined, combined, and applied. The first is classical PE where one is interested in finding parameters which minimize the distance between the output of a chemical model and experimental data. The second is Bayesian PE allowing for quantifying parameter uncertainty caused by experimental measurement error and model imperfection. Based on detailed descriptions of motivation, theoretical background, and methodological aspects for both approaches, their relation are outlined. The main aim of this article is to show how the two approaches complement each other and can be used together to generate strong information gain regarding the model and its parameters. Both approaches and their interplay in application to polymerization reaction systems are illustrated. This is the first part in a two-article series on parameter estimation for polymer reaction kinetics with a focus on theory and methodology while in the second part a more complex example will be considered. Y1 - 2021 U6 - https://doi.org/10.1002/mats.202100017 VL - 30 ER - TY - JOUR A1 - del Razo, Mauricio J. A1 - Dibak, Manuel A1 - Schütte, Christof A1 - Noé, Frank T1 - Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics JF - The Journal of Chemical Physics Y1 - 2021 U6 - https://doi.org/10.1063/5.0060314 VL - 155 IS - 12 ER - TY - JOUR A1 - Gelss, Patrick A1 - Klus, Stefan A1 - Schuster, Ingmar A1 - Schütte, Christof T1 - Feature space approximation for kernel-based supervised learning JF - Knowledge-Based Sytems Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1016/j.knosys.2021.106935 VL - 221 PB - Elsevier ER - TY - JOUR A1 - Jäger, Klaus A1 - Sutter, Johannes A1 - Hammerschmidt, Martin A1 - Schneider, Philipp-Immanuel A1 - Becker, Christiane T1 - Prospects of light management in perovskite/silicon tandem solar cells JF - Nanophotonics Y1 - 2021 U6 - https://doi.org/10.1515/nanoph-2020-0674 VL - 10 SP - 1991 ER - TY - JOUR A1 - Liu, Yongtao A1 - Zhou, Zhiguang A1 - Wang, Fan A1 - Kewes, Günter A1 - Wen, Shihui A1 - Burger, Sven A1 - Wakiani, Majid Ebrahimi A1 - Xi, Peng A1 - Yang, Jiong A1 - Yang, Xusan A1 - Benson, Oliver A1 - Jin, Dayong T1 - Axial localization and tracking of self-interference nanoparticles by lateral point spread functions JF - Nat. Commun. Y1 - 2021 U6 - https://doi.org/10.1038/s41467-021-22283-0 VL - 12 SP - 2019 ER - TY - JOUR A1 - Bittracher, Andreas A1 - Moschner, Johann A1 - Koksch, Beate A1 - Netz, Roland A1 - Schütte, Christof T1 - Exploring the locking stage of NFGAILS amyloid fibrillation via transition manifold analysis JF - The European Physical Journal B Y1 - 2021 U6 - https://doi.org/10.1140/epjb/s10051-021-00200-0 VL - 94 ER - TY - JOUR A1 - Lücke, Marvin A1 - Lu, Jingyi A1 - Quevedo, Daniel E. T1 - Coding for secrecy in remote state estimation with an adversary JF - IEEE Transactions on Automatic Control N2 - We study the problem of remote state estimation in the presence of an eavesdropper. A sensor transmits state information over a packet-dropping link to a legitimate user. This information is randomly overheard by an eavesdropper. To reduce information leakage to the eavesdropper, previous studies have shown that by encoding the estimate with the acknowledgments (Acks), perfect secrecy can be achieved. However, this strategy greatly relies on the accuracy of the Acks and may easily fail if the Acks are compromised by cyberattacks. In this article, we tackle this issue by proposing to switch between sending an encoded state and sending the plain state to stay resilient against fake Acks. Specifically, we assume the Acks to be randomly attacked and derive recursive expressions for the minimum-mean-squared error estimates and error covariance matrices at the legitimate user and at the eavesdropper. Based upon this, we propose a transmission policy that depends on the probability of synchronization. We formulate a partially observable Markov decision process to model the evolution of the synchronization status and derive associated optimal transmission policies. Numerical examples are provided to verify the theoretical results. Y1 - 2022 U6 - https://doi.org/10.1109/TAC.2022.3169839 VL - 67 IS - 9 SP - 4955 EP - 4962 ER - TY - JOUR A1 - Chegini, Fatemeh A1 - Kopanicakova, Alena A1 - Krause, Rolf A1 - Weiser, Martin T1 - Efficient Identification of Scars using Heterogeneous Model Hierarchies JF - EP Europace N2 - Aims. Detection and quantification of myocardial scars are helpful both for diagnosis of heart diseases and for building personalized simulation models. Scar tissue is generally charac­terized by a different conduction of electrical excitation. We aim at estimating conductivity-related parameters from endocardial mapping data, in particular the conductivity tensor. Solving this inverse problem requires computationally expensive monodomain simulations on fine discretizations. Therefore, we aim at accelerating the estimation using a multilevel method combining electrophysiology models of different complexity, namely the mono­domain and the eikonal model. Methods. Distributed parameter estimation is performed by minimizing the misfit between simulated and measured electrical activity on the endocardial surface, subject to the mono­domain model and regularization, leading to a constrained optimization problem. We formulate this optimization problem, including the modeling of scar tissue and different regularizations, and design an efficient iterative solver. We consider monodomain grid hierarchies and monodomain-eikonal model hierarchies in a recursive multilevel trust-region method. Results. From several numerical examples, both the efficiency of the method and the estimation quality, depending on the data, are investigated. The multilevel solver is significantly faster than a comparable single level solver. Endocardial mapping data of realistic density appears to be just sufficient to provide quantitatively reasonable estimates of location, size, and shape of scars close to the endocardial surface. Conclusion. In several situations, scar reconstruction based on eikonal and monodomain models differ significantly, suggesting the use of the more accurate but more expensive monodomain model for this purpose. Still, eikonal models can be utilized to accelerate the computations considerably, enabling the use of complex electrophysiology models for estimating myocardial scars from endocardial mapping data. Y1 - 2021 U6 - https://doi.org/10.1093/europace/euaa402 VL - 23 SP - i113 EP - i122 ER - TY - CHAP A1 - Jäger, Klaus A1 - Tillmann, Peter A1 - Katz, Eugene A. A1 - Becker, Christiane T1 - Simulating bifacial perovskite/silicon tandem solar cells in large PV fields T2 - OSA Advanced Photonics Congress Y1 - 2020 U6 - https://doi.org/10.1364/PVLED.2020.PvTh1G.3 SP - PvTh1G.3 ER - TY - JOUR A1 - Jäger, Klaus A1 - Tillmann, Peter A1 - Katz, Eugene A. A1 - Becker, Christiane T1 - Perovskite/silicon tandem solar cells: Effect of luminescent coupling and bifaciality JF - Sol. RRL Y1 - 2021 U6 - https://doi.org/10.1002/solr.202000628 VL - 5 SP - 2000628 ER - TY - JOUR A1 - Helfmann, Luzie A1 - Heitzig, Jobst A1 - Koltai, Péter A1 - Kurths, Jürgen A1 - Schütte, Christof T1 - Statistical analysis of tipping pathways in agent-based models JF - Eur. Phys. J. Spec. Top. N2 - Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals on the microscopic scale can lead to emergent dynamics on the macroscopic scale, for instance a sudden shift of majority opinion or behavior. Here we are introducing a methodology for studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations. Due to a large number of interacting individuals, agent-based models are high-dimensional, though usually a lower-dimensional structure of the emerging collective behaviour exists. We therefore apply Diffusion Maps, a non-linear dimension reduction technique, to reveal the intrinsic low-dimensional structure. We characterize the tipping behaviour by means of Transition Path Theory, which helps gaining a statistical understanding of the tipping paths such as their distribution, flux and rate. By systematically studying two agent-based models that exhibit a multitude of tipping pathways and cascading effects, we illustrate the practicability of our approach. Y1 - 2021 U6 - https://doi.org/10.1140/epjs/s11734-021-00191-0 VL - 230 SP - 3249 EP - 3271 ER - TY - JOUR A1 - Manley, Phillip A1 - Segantini, Michele A1 - Ahiboz, Doguscan A1 - Hammerschmidt, Martin A1 - Arnaoutakis, Georgios A1 - MacQueen, Rowan W. A1 - Burger, Sven A1 - Becker, Christiane T1 - Double-layer metasurface for enhanced photon up-conversion JF - APL Photon. Y1 - 2021 U6 - https://doi.org/10.1063/5.0040839 VL - 6 SP - 036103 ER - TY - JOUR A1 - Pakhomov, Anton V. A1 - Hammerschmidt, Martin A1 - Burger, Sven A1 - Pertsch, Thomas A1 - Setzpfand, Frank T1 - Modeling of surface-induced second-harmonic generation from multilayer structures by the transfer matrix method JF - Opt. Express Y1 - 2021 U6 - https://doi.org/10.1364/OE.417066 VL - 29 SP - 9098 ER - TY - JOUR A1 - Binkowski, Felix A1 - Wu, Tong A1 - Lalanne, Philippe A1 - Burger, Sven A1 - Govorov, Alexander O. T1 - Hot Electron Generation through Near-Field Excitation of Plasmonic Nanoresonators JF - ACS Photonics Y1 - 2021 U6 - https://doi.org/10.1021/acsphotonics.1c00231 VL - 8 SP - 1243 ER - TY - JOUR A1 - Cvetkovic, Nada A1 - Conrad, Tim A1 - Lie, Han Cheng T1 - A Convergent Discretisation Method for Transition Path Theory for Diffusion Processes JF - Multiscale Modeling & Simulation Y1 - 2021 U6 - https://doi.org/10.1137/20M1329354 VL - 19 IS - 1 SP - 242 EP - 266 PB - Society for Industrial and Applied Mathematics ER - TY - BOOK A1 - Deuflhard, Peter A1 - Weiser, Martin T1 - Numerische Mathematik 3. Adaptive Lösung partieller Differentialgleichungen Y1 - 2020 SN - 978-3-11-069168-9 U6 - https://doi.org/10.1515/9783110689655 PB - de Gruyter ET - 2 ER - TY - JOUR A1 - Sikorski, Alexander A1 - Weber, Marcus A1 - Schütte, Christof T1 - The Augmented Jump Chain JF - Advanced Theory and Simulations N2 - Modern methods of simulating molecular systems are based on the mathematical theory of Markov operators with a focus on autonomous equilibrated systems. However, non-autonomous physical systems or non-autonomous simulation processes are becoming more and more important. A representation of non-autonomous Markov jump processes is presented as autonomous Markov chains on space-time. Augmenting the spatial information of the embedded Markov chain by the temporal information of the associated jump times, the so-called augmented jump chain is derived. The augmented jump chain inherits the sparseness of the infinitesimal generator of the original process and therefore provides a useful tool for studying time-dependent dynamics even in high dimensions. Furthermore, possible generalizations and applications to the computation of committor functions and coherent sets in the non-autonomous setting are discussed. After deriving the theoretical foundations, the concepts with a proof-of-concept Galerkin discretization of the transfer operator of the augmented jump chain applied to simple examples are illustrated. Y1 - 2021 U6 - https://doi.org/10.1002/adts.202000274 VL - 4 IS - 4 PB - Wiley-VCH ER - TY - JOUR A1 - Sechi, Renata A1 - Sikorski, Alexander A1 - Weber, Marcus T1 - Estimation of the Koopman Generator by Newton's Extrapolation JF - Multiscale Modeling and Simulation N2 - This article addresses the problem of estimating the Koopman generator of a Markov process. The direct computation of the infinitesimal generator is not easy because of the discretization of the state space, in particular because of the trade-off inherent in the choice of the best lag time to study the process. Short lag times implies a strong discretization of the state space and a consequent loss of Markovianity. Large lag times bypass events on fast timescales. We propose a method to approximate the generator with the computation of the Newton polynomial extrapolation. This technique is a multistep approach which uses as its input Koopman transfer operators evaluated for a series of lag times. Thus, the estimated infinitesimal generator combines information from different time resolutions and does not bias only fast- or slow-decaying dynamics. We show that the multi-scale Newton method can improve the estimation of the generator in comparison to the computation using finite difference or matrix logarithm methods. Y1 - 2020 U6 - https://doi.org/10.1137/20M1333006 VL - 19 IS - 2 SP - 758 EP - 774 PB - SIAM ER - TY - THES A1 - Venkatareddy, Narendra Lagumaddepalli T1 - Revealing secrets of mussel-glue mimetic peptides - From advanced NMR to computational process modelling Y1 - 2020 ER - TY - THES A1 - Eshtewy, Neveen Ali Salem T1 - Mathematical Modeling of Metabolic-Genetic Networks Y1 - 2020 ER - TY - JOUR A1 - Öttinger, Hans Christian A1 - Montefusco, Alberto A1 - Peletier, Mark A. T1 - A Framework of Nonequilibrium Statistical Mechanics. I. Role and Types of Fluctuations JF - Journal of Non-Equilibrium Thermodynamics N2 - Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized representation of microscopic details. We consider fluctuation-enhanced equations associated with Markov processes and elaborate the general recipes for evaluating dynamic material properties, which characterize force-flux constitutive laws, by statistical mechanics. Markov processes with continuous trajectories are conveniently characterized by stochastic differential equations and lead to Green–Kubo-type formulas for dynamic material properties. Markov processes with discontinuous jumps include transitions over energy barriers with the rates calculated by Kramers. We describe a unified approach to Markovian fluctuations and demonstrate how the appropriate type of fluctuations (continuous versus discontinuous) is reflected in the mathematical structure of the phenomenological equations. Y1 - 2021 U6 - https://doi.org/10.1515/jnet-2020-0068 VL - 46 IS - 1 SP - 1 EP - 13 PB - De Gruyter ER - TY - JOUR A1 - Montefusco, Alberto A1 - Peletier, Mark A. A1 - Öttinger, Hans Christian T1 - A Framework of Nonequilibrium Statistical Mechanics. II. Coarse-Graining JF - Journal of Non-Equilibrium Thermodynamics N2 - For a given thermodynamic system, and a given choice of coarse-grained state variables, the knowledge of a force-flux constitutive law is the basis for any nonequilibrium modeling. In the first paper of this series we established how, by a generalization of the classical fluctuation-dissipation theorem (FDT), the structure of a constitutive law is directly related to the distribution of the fluctuations of the state variables. When these fluctuations can be expressed in terms of diffusion processes, one may use Green–Kubo-type coarse-graining schemes to find the constitutive laws. In this paper we propose a coarse-graining method that is valid when the fluctuations are described by means of general Markov processes, which include diffusions as a special case. We prove the success of the method by numerically computing the constitutive law for a simple chemical reaction A⇄B. Furthermore, we show that, for such a system, one cannot find a consistent constitutive law by any Green–Kubo-like scheme. Y1 - 2021 U6 - https://doi.org/10.1515/jnet-2020-0069 VL - 46 IS - 1 SP - 15 EP - 33 PB - De Gruyter ER - TY - JOUR A1 - Sunkara, Vikram A1 - Heinz, Gitta A. A1 - Heinrich, Frederik F. A1 - Durek, Pawel A1 - Mobasheri, Ali A1 - Mashreghi, Mir-Farzin A1 - Lang, Annemarie T1 - Combining segmental bulk- and single-cell RNA-sequencing to define the chondrocyte gene expression signature in the murine knee joint JF - bioarxiv (Accepted in Osteoarthr. Cartil.) Y1 - 2020 U6 - https://doi.org/10.1101/2020.06.13.148056 ER - TY - JOUR A1 - Lang, Annemarie A1 - Helfmeier, Sarah A1 - Stefanowski, Jonathan A1 - Kuppe, Aditi A1 - Sunkara, Vikram A1 - Pfeiffenberger, Moritz A1 - Wolter, Angelique A1 - Damerau, Alexandra A1 - Hemmati-Sadeghi, Shabnam A1 - Ringe, Jochen A1 - Haag, Rainer A1 - Hauser, Anja E. A1 - Löhning, Max A1 - Perka, Carsten A1 - Duda, Georg A1 - Hoff, Paula A1 - Schmidt-Bleek, Katharina A1 - Gaber, Timo A1 - Buttgereit, Frank T1 - HIF-stabilization prevents delayed fracture healing JF - bioarxiv Y1 - 2020 U6 - https://doi.org/10.1101/2020.07.02.182832 ER - TY - JOUR A1 - Laydon, Daniel J. A1 - Sunkara, Vikram A1 - Boelen, Lies A1 - Bangham, Charles R. M. A1 - Asquith, Becca T1 - The relative contributions of infectious and mitotic spread to HTLV-1 persistence JF - PLOS Computational Biology Y1 - 2020 U6 - https://doi.org/10.1371/journal.pcbi.1007470 ER - TY - JOUR A1 - Schiela, Anton A1 - Stöcklein, Matthias A1 - Weiser, Martin T1 - A primal dual projection algorithm for efficient constraint preconditioning JF - SIAM Journal on Scientific Computing N2 - We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and analysed as a gradient method on a quotient space, the given problem can be solved by computing sulutions for a sequence of constrained surrogate problems, projections onto the feasible subspaces, and Lagrange multiplier updates. As a major application we consider a class of optimization problems with PDEs, where PDP can be applied together with a projected cg method using a block triangular constraint preconditioner. Numerical experiments show reliable and competitive performance for an optimal control problem in elasticity. Y1 - 2021 U6 - https://doi.org/10.1137/20M1380739 VL - 43 IS - 6 SP - A4095 EP - A4120 ER - TY - JOUR A1 - Mielke, Alexander A1 - Montefusco, Alberto A1 - Peletier, Mark A. T1 - Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence JF - Continuum Mechanics and Thermodynamics N2 - This paper revolves around a subtle distinction between two concepts: passing to the limit in a family of gradient systems, on one hand, and deriving effective kinetic relations on the other. The two concepts are strongly related, and in many examples they even appear to be the same. Our main contributions are to show that they are different, to show that well-known techniques developed for the former may give incorrect results for the latter, and to introduce new tools to remedy this. The approach is based on the Energy-Dissipation Principle that provides a variational formulation to gradient-flow equations that allows one to apply techniques from Γ-convergence of functional on states and functionals on trajectories. Y1 - 2021 U6 - https://doi.org/10.1007/s00161-020-00932-x VL - 33 SP - 611 EP - 637 PB - Springer ER - TY - THES A1 - Santiago, Xavier Garcia T1 - Numerical methods for shape optimization of photonic nanostructures Y1 - 2021 U6 - https://doi.org/10.5445/IR/1000131006 ER - TY - JOUR A1 - Raharinirina, N. Alexia A1 - Acevedo-Trejos, Esteban A1 - Merico, Agostino T1 - Modelling the acclimation capacity of coral reefs to a warming ocean JF - PLOS COMPUTATIONAL BIOLOGY N2 - The symbiotic relationship between corals and photosynthetic algae is the foundation of coral reef ecosystems. This relationship breaks down, leading to coral death, when sea temperature exceeds the thermal tolerance of the coral-algae complex. While acclimation via phenotypic plasticity at the organismal level is an important mechanism for corals to cope with global warming, community-based shifts in response to acclimating capacities may give valuable indications about the future of corals at a regional scale. Reliable regional-scale predictions, however, are hampered by uncertainties on the speed with which coral communities will be able to acclimate. Here we present a trait-based, acclimation dynamics model, which we use in combination with observational data, to provide a first, crude estimate of the speed of coral acclimation at the community level and to investigate the effects of different global warming scenarios on three iconic reef ecosystems of the tropics: Great Barrier Reef, South East Asia, and Caribbean. The model predicts that coral acclimation may confer some level of protection by delaying the decline of some reefs such as the Great Barrier Reef. However, the current rates of acclimation will not be sufficient to rescue corals from global warming. Based on our estimates of coral acclimation capacities, the model results suggest substantial declines in coral abundances in all three regions, ranging from 12% to 55%, depending on the region and on the climate change scenario considered. Our results highlight the importance and urgency of precise assessments and quantitative estimates, for example through laboratory experiments, of the natural acclimation capacity of corals and of the speed with which corals may be able to acclimate to global warming. Y1 - 2022 U6 - https://doi.org/10.1371/journal.pcbi.1010099 ER - TY - GEN A1 - Schütte, Christof A1 - Klus, Stefan A1 - Hartmann, Carsten T1 - Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning N2 - One of the main challenges in molecular dynamics is overcoming the “timescale barrier”, a phrase used to describe that in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, not 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 behavior 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 MD. 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. T3 - ZIB-Report - 22-25 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-88637 SN - 1438-0064 ER - TY - JOUR A1 - Ramos Leite, Tiago A1 - Zschiedrich, Lin A1 - Kizilkaya, Orhan A1 - McPeak, Kevin M. T1 - Resonant Plasmonic–Biomolecular Chiral Interactions in the Far-Ultraviolet: Enantiomeric Discrimination of sub-10 nm Amino Acid Films JF - Nano Lett. Y1 - 2022 UR - https://digitalcommons.lsu.edu/chem_engineering_pubs/34/ U6 - https://doi.org/10.1021/acs.nanolett.2c01724 VL - 22 SP - 7343 ER - TY - JOUR A1 - Rej, Sourav A1 - Santiago, Eva Yazmin A1 - Baturina, Olga A1 - Zhang, Yu A1 - Burger, Sven A1 - Kment, Stepan A1 - Govorov, Alexander O. A1 - Naldoni, Alberto T1 - Colloidal Titanium Nitride Nanobars for Broadband Inexpensive Plasmonics and Photochemistry from Visible to Mid-IR Wavelengths JF - Nano Energy Y1 - 2022 U6 - https://doi.org/10.1016/j.nanoen.2022.107989 VL - 104 SP - 107989 ER - TY - CHAP A1 - Berner, Julius A1 - Richter, Lorenz A1 - Ullrich, Karen T1 - An optimal control perspective on diffusion-based generative modeling T2 - Transactions on Machine Learning Research N2 - We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs) such as recently developed diffusion probabilistic models. In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals. This perspective allows to transfer methods from optimal control theory to generative modeling. First, we show that the evidence lower bound is a direct consequence of the well-known verification theorem from control theory. Further, we develop a novel diffusion-based method for sampling from unnormalized densities -- a problem frequently occurring in statistics and computational sciences. Y1 - 2024 UR - https://openreview.net/forum?id=oYIjw37pTP ER - TY - JOUR A1 - Nüsken, Nikolas A1 - Richter, Lorenz T1 - Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems JF - Journal of Machine Learning N2 - Solving high-dimensional partial differential equations is a recurrent challenge in economics, science and engineering. In recent years, a great number of computational approaches have been developed, most of them relying on a combination of Monte Carlo sampling and deep learning based approximation. For elliptic and parabolic problems, existing methods can broadly be classified into those resting on reformulations in terms of backward stochastic differential equations (BSDEs) and those aiming to minimize a regression-type L2-error (physics-informed neural networks, PINNs). In this paper, we review the literature and suggest a methodology based on the novel diffusion loss that interpolates between BSDEs and PINNs. Our contribution opens the door towards a unified understanding of numerical approaches for high-dimensional PDEs, as well as for implementations that combine the strengths of BSDEs and PINNs. The diffusion loss furthermore bears close similarities to (least squares) temporal difference objectives found in reinforcement learning. We also discuss eigenvalue problems and perform extensive numerical studies, including calculations of the ground state for nonlinear Schr ¨odinger operators and committor functions relevant in molecular dynamics. Y1 - 2023 U6 - https://doi.org/0.4208/jml.220416 VL - 2 IS - 1 SP - 31 EP - 64 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Richter, Lorenz T1 - Nonasymptotic bounds for suboptimal importance sampling JF - SIAM/ASA Journal on Uncertainty Quantification N2 - Importance sampling is a popular variance reduction method for Monte Carlo estimation, where an evident question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically possible, in practice only suboptimal proposal distributions are available and it can often be observed numerically that those can reduce statistical performance significantly, leading to large relative errors and therefore counteracting the original intention. Previous analysis on importance sampling has often focused on asymptotic arguments that work well in a large deviations regime. In this article, we provide lower and upper bounds on the relative error in a nonasymptotic setting. They depend on the deviation of the actual proposal from optimality, and we thus identify potential robustness issues that importance sampling may have, especially in high dimensions. We particularly focus on path sampling problems for diffusion processes with nonvanishing noise, for which generating good proposals comes with additional technical challenges. We provide numerous numerical examples that support our findings and demonstrate the applicability of the derived bounds. Y1 - 2024 U6 - https://doi.org/10.1137/21M1427760 VL - 12 IS - 2 SP - 309 EP - 346 ER - TY - JOUR A1 - Rickert, Lucas A1 - Betz, Fridtjof A1 - Plock, Matthias A1 - Burger, Sven A1 - Heindel, Tobias T1 - High-performance designs for fiber-pigtailed quantum-light sources based on quantum dots in electrically-controlled circular Bragg gratings JF - Opt. Express Y1 - 2023 U6 - https://doi.org/10.1364/OE.486060 VL - 31 SP - 14750 ER - TY - GEN A1 - Rickert, Lucas A1 - Betz, Fridtjof A1 - Plock, Matthias A1 - Burger, Sven A1 - Heindel, Tobias T1 - Data publication for "High-performance designs for fiber-pigtailed quantum-light sources based on quantum dots in electrically-controlled circular Bragg gratings" T2 - Zenodo Y1 - 2022 U6 - https://doi.org/10.5281/zenodo.7360516 SP - 7360516 ER -