TY - JOUR A1 - Wang, Yujing A1 - Vannucci, Luca A1 - Burger, Sven A1 - Gregersen, Niels T1 - Near-unity efficiency in ridge waveguide-based, on-chip single-photon sources JF - Mater. Quantum Technol. Y1 - 2022 U6 - https://doi.org/10.1088/2633-4356/aca8e8 VL - 2 SP - 045004 ER - TY - JOUR A1 - Lopez-Fraguas, Eduardo A1 - Binkowski, Felix A1 - Burger, Sven A1 - Hagedorn, Sylvia A1 - Garcia-Camara, Braulio A1 - Vergaz, Ricardo A1 - Becker, Christiane A1 - Manley, Phillip T1 - Tripling the light extraction efficiency of a deep ultraviolet LED using a nanostructured p-contact JF - Sci. Rep. Y1 - 2022 U6 - https://doi.org/10.1038/s41598-022-15499-7 VL - 12 SP - 11480 ER - TY - GEN A1 - Betz, Fridtjof A1 - Colom, Remi A1 - Burger, Sven A1 - Naydenov, Boris T1 - Scripts for quantifying the effect of diamond nano-pillars on the fluorescence of NV centers T2 - Zenodo Y1 - 2022 U6 - https://doi.org/10.5281/zenodo.6558815 ER - TY - THES A1 - Niemann, Jan-Hendrik T1 - Learning Reduced Models for Large-Scale Agent-Based Systems N2 - Modeling social systems and studying their dynamical behavior plays an important role in many fields of research. Agent-based modeling provides a high degree of detail into artificial societies by describing the model from the perspective of the agents. The interactions of agents, often characterized by simple rules, lead to complex, time-evolving patterns. Their understanding is of great importance, e.g., for predicting and influencing epidemics. Analysis and simulation, however, often becomes prohibitively time-consuming when the number of agents or the time scale of interest is large. Therefore, this thesis is devoted to learn significantly reduced models of large-scale agent-based systems from simulation data. We show how data-driven methods based on transfer operators can be used to find reduced models represented by ordinary or stochastic differential equations that describe the dynamical behavior of larger groups or entire populations and thus enable the analysis and prediction of agent-based systems. To this end, we first present an extension of EDMD (extended dynamic mode decomposition) called gEDMD to approximate the Koopman generator from data. This method can be used to compute eigenfunctions, eigenvalues, and modes of the generator, as well as for system identification and model reduction of both deterministic and non-deterministic dynamical systems. Secondly, we analyze the long-term behavior of certain agent-based models and their pathwise approximations by stochastic differential equations for large numbers of agents using transfer operators. We show that, under certain conditions, the transfer operator approach connects the pathwise approximations on finite time scales with methods for describing the behavior on possibly exponentially long time scales. As a consequence, we can use the finite-time, pathwise approximations to characterize metastable behavior on long time scales using transfer operators. This can significantly reduce the computational cost. The third part addresses the data-driven model reduction since in many cases no analytical limit models are known or existent. We show how the Koopman operator theory can be used to infer the governing equations of agent-based systems directly from simulation data. Using benchmark problems, we demonstrate that for sufficiently large population sizes the data-driven models agree well with analytical limit equations and, moreover, that the reduced models allow predictions even in cases far from the limit or when no limit equations are known. Lastly, we demonstrate the potential of the presented approach. We present an ansatz for the multi-objective optimization of agent-based systems with the help of data-driven surrogate models based on the Koopman generator. In particular, when limit models are unknown or non-existent, this approach makes multi-objective optimization problems solvable that would otherwise be computationally infeasible due to very expensive objective functions. Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:188-refubium-35530-6 UR - https://refubium.fu-berlin.de/handle/fub188/35530 ER - TY - JOUR A1 - Beron-Vera, Francisco Javier A1 - Olascoaga, Maria Josefina A1 - Helfmann, Luzie A1 - Miron, Philippe T1 - Sampling-Dependent Transition Paths of Iceland-Scotland Overflow Water JF - Journal of Physical Oceanography N2 - In this note, we apply Transition Path Theory (TPT) from Markov chains to shed light on the problem of Iceland-Scotland Overflow Water (ISOW) equatorward export. A recent analysis of observed trajectories of submerged floats demanded revision of the traditional abyssal circulation theory, which postulates that ISOW should steadily flow along a deep boundary current (DBC) around the subpolar North Atlantic prior to exiting it. The TPT analyses carried out here allow to focus the attention on the portions of flow from the origin of ISOW to the region where ISOW exits the subpolar North Atlantic and suggest that insufficient sampling may be biasing the aforementioned demand. The analyses, appropriately adapted to represent a continuous input of ISOW, are carried out on three time-homogeneous Markov chains modeling the ISOW flow. One is constructed using a high number of simulated trajectories homogeneously covering the flow domain. The other two use much fewer trajectories which heterogeneously cover the domain. The trajectories in the latter two chains are observed trajectories or simulated trajectories subsampled at the observed frequency. While the densely sampled chain supports a well-defined DBC, the more heterogeneously sampled chains do not, irrespective of whether observed or simulated trajectories are used. Studying the sampling sensitivity of the Markov chains, we can give recommendations for enlarging the existing float dataset to improve the significance of conclusions about time-asymptotic aspects of the ISOW circulation. Y1 - 2023 U6 - https://doi.org/10.1175/JPO-D-22-0172.1 VL - 53 IS - 4 SP - 1151 EP - 1160 ER - TY - JOUR A1 - Bartels, Tinko A1 - Fisikopoulos, Vissarion A1 - Weiser, Martin T1 - Fast Floating-Point Filters for Robust Predicates JF - BIT Numerical Mathematics N2 - Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information systems and computer-aided design. With floating-point arithmetic, these geometric predicates can incur round-off errors that may lead to incorrect results and inconsistencies, causing computations to fail. This issue has been addressed using a combination of exact arithmetic for robustness and floating-point filters to mitigate the computational cost of exact computations. The implementation of exact computations and floating-point filters can be a difficult task, and code generation tools have been proposed to address this. We present a new C++ meta-programming framework for the generation of fast, robust predicates for arbitrary geometric predicates based on polynomial expressions. We combine and extend different approaches to filtering, branch reduction, and overflow avoidance that have previously been proposed. We show examples of how this approach produces correct results for data sets that could lead to incorrect predicate results with naive implementations. Our benchmark results demonstrate that our implementation surpasses state-of-the-art implementations. Y1 - 2023 U6 - https://doi.org/10.1007/s10543-023-00975-x VL - 63 ER - TY - CHAP A1 - Dhanakoti, Siva Prasad Chakri A1 - Maddocks, John A1 - Weiser, Martin T1 - Navigation of Concentric Tube Continuum Robots using Optimal Control T2 - Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics N2 - Recently developed Concentric Tube Continuum Robots (CTCRs) are widely exploited in, for example in minimally invasive surgeries which involve navigating inside narrow body cavities close to sensitive regions. These CTCRs can be controlled by extending and rotating the tubes in order to reach a target point or perform some task. The robot must deviate as little as possible from this narrow space and avoid damaging neighbouring tissue. We consider \emph{open-loop} optimal control of CTCRs parameterized over pseudo-time, primarily aiming at minimizing the robot's working volume during its motion. External loads acting on the system like tip loads or contact with tissues are not considered here. We also discussed the inclusion of tip's orientation in the optimal framework to perform some tasks. We recall a quaternion-based formulation of the robot configuration, discuss discretization, develop optimization objectives addressing different criteria, and investigate their impact on robot path planning for several numerical examples. This optimal framework can be applied to any backbone based continuum robots. Y1 - 2022 U6 - https://doi.org/10.5220/0011271000003271 SP - 146 EP - 154 ER - TY - JOUR A1 - Binkowski, Felix A1 - Betz, Fridtjof A1 - Hammerschmidt, Martin A1 - Schneider, Philipp-Immanuel A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators JF - Commun. Phys. Y1 - 2022 U6 - https://doi.org/10.1038/s42005-022-00977-1 VL - 5 SP - 202 ER - TY - JOUR 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 - Li, Jinzhao A1 - Shargaieva, Oleksandra A1 - Unger, Eva A1 - Al-Ashouri, Amran A1 - Köhnen, Eike A1 - Stolterfoth, Martin A1 - Neher, Dieter A1 - Schlatmann, Rutger A1 - Rech, Bernd A1 - Stannowski, Bernd A1 - Albrecht, Steve A1 - Becker, Christiane T1 - Nano-optical designs for high-efficiency monolithic perovskite–silicon tandem solar cells JF - Nat. Nanotechnol. Y1 - 2022 U6 - https://doi.org/10.1038/s41565-022-01228-8 VL - 17 SP - 1214 ER - TY - JOUR 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. T1 - Plasmonic nanocrystals with complex shapes for photocatalysis and growth: Contrasting anisotropic hot-electron generation with the photothermal effect JF - Adv. Opt. Mater. Y1 - 2022 U6 - https://doi.org/10.1002/adom.202102663 VL - 10 SP - 2102663 ER - TY - GEN A1 - Colom, Remi A1 - Binkowski, Felix A1 - Betz, Fridtjof A1 - Kivshar, Yuri A1 - Burger, Sven T1 - Source code and simulation results for nanoantennas supporting an enhanced Purcell factor due to interfering resonances T2 - Zenodo Y1 - 2022 U6 - https://doi.org/10.5281/zenodo.6565850 ER - TY - JOUR A1 - Klus, Stefan A1 - Djurdjevac Conrad, Natasa T1 - Koopman-based spectral clustering of directed and time-evolving graphs JF - Journal of Nonlinear Science N2 - While spectral clustering algorithms for undirected graphs are well established and have been successfully applied to unsupervised machine learning problems ranging from image segmentation and genome sequencing to signal processing and social network analysis, clustering directed graphs remains notoriously difficult. Two of the main challenges are that the eigenvalues and eigenvectors of graph Laplacians associated with directed graphs are in general complex-valued and that there is no universally accepted definition of clusters in directed graphs. We first exploit relationships between the graph Laplacian and transfer operators and in particular between clusters in undirected graphs and metastable sets in stochastic dynamical systems and then use a generalization of the notion of metastability to derive clustering algorithms for directed and time-evolving graphs. The resulting clusters can be interpreted as coherent sets, which play an important role in the analysis of transport and mixing processes in fluid flows. Y1 - 2022 U6 - https://doi.org/10.1007/s00332-022-09863-0 VL - 33 ER - TY - JOUR A1 - Benner, Peter A1 - Burger, Michael A1 - Göddeke, Dominik A1 - Görgen, Christiane A1 - Himpe, Christian A1 - Heiland, Jan A1 - Koprucki, Thomas A1 - Ohlberger, Mario A1 - Rave, Stephan A1 - Reidelbach, Marco A1 - Saak, Jens A1 - Schöbel, Anita A1 - Tabelow, Karsten A1 - Weber, Marcus T1 - Die mathematische Forschungsdateninitiative in der NFDI: MaRDI (Mathematical Research Data Initiative) JF - GAMM Rundbrief Y1 - 2022 IS - 1 SP - 40 EP - 43 ER - TY - JOUR A1 - Tillmann, Peter A1 - Jäger, Klaus A1 - Karsenti, Asher A1 - Kreinin, Lev A1 - Becker, Christiane T1 - Model-Chain Validation for Estimating the Energy Yield of Bifacial Perovskite/Silicon Tandem Solar Cells JF - Sol. RRL Y1 - 2022 U6 - https://doi.org/10.1002/solr.202200079 VL - 6 SP - 2200079 ER - TY - JOUR A1 - Engel, Maximilian A1 - Olicón-Méndez, Guillermo A1 - Wehlitz, Nathalie A1 - Winkelmann, Stefanie T1 - Synchronization and random attractors in reaction jump processes JF - Journal of Dynamics and Differential Equations N2 - This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. Based on Gillespie’s stochastic simulation algorithm, a corresponding random dynamical system is formulated in a two-step procedure, at first for the states of the embedded discrete-time Markov chain and then for the augmented Markov chain including random jump times. We uncover a time-shifted synchronization in the sense that—after some initial waiting time—one trajectory exactly replicates another one with a certain time delay. Whether or not such a synchronization behavior occurs depends on the combination of the initial states. We prove this partial time-shifted synchronization for the special setting of a birth-death process by analyzing the corresponding two-point motion of the embedded Markov chain and determine the structure of the associated random attractor. In this context, we also provide general results on existence and form of random attractors for discrete-time, discrete-space random dynamical systems. Y1 - 2024 U6 - https://doi.org/10.1007/s10884-023-10345-4 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization N2 - The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition. T3 - ZIB-Report - 23-19 KW - shortest path KW - flight planning KW - free flight KW - optimal control KW - global optimization KW - Newton's method Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91309 SN - 1438-0064 ER - TY - THES A1 - Danecker, Fabian T1 - A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization N2 - This thesis introduces the novel hybrid algorithm DisCOptER for globally optimal flight planning. DisCOptER (Discrete-Continuous Optimization for Enhanced Resolution) com- bines discrete and continuous optimization in a two-stage approach to find optimal trajectories up to arbitrary precision in finite time. In the discrete phase, a directed auxiliary graph is created in order to define a set of candidate paths that densely covers the relevant part of the trajectory space. Then, Yen’s algorithm is employed to identify a set of promising candidate paths. These are used as starting points for the subsequent stage in which they are refined with a locally convergent optimal control method. The correctness, accuracy, and complexity of DisCOptER are intricately linked to the choice of the switch-over point, defined by the discretization coarseness. Only a sufficiently dense graph enables the algorithm to find a path within the convex domain surrounding the global minimizer. Initialized with such a path, the second stage rapidly converges to the optimum. Conversely, an excessively dense graph poses the risk of overly costly and redundant computations. The determination of the optimal switch-over point necessitates a profound understanding of the local behavior of the problem, the approximation properties of the graph, and the convergence characteristics of the employed optimal control method. These topics are explored extensively in this thesis. Crucially, the density of the auxiliary graph is solely dependent on the en- vironmental conditions, yet independent of the desired solution accuracy. As a consequence, the algorithm inherits the superior asymptotic convergence properties of the optimal control stage. The practical implications of this computational efficiency are demonstrated in realistic environments, where the DisCOptER algorithm consistently delivers highly accurate globally optimal trajectories with exceptional computational efficiency. This notable improvement upon existing approaches underscores the algorithm’s significance. Beyond its technical prowess, the DisCOptER algorithm stands as a valuable tool contributing to the reduction of costs and the overall enhancement of flight operations efficiency. Y1 - 2023 UR - http://dx.doi.org/10.17169/refubium-43526 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - A Discrete-Continuous Algorithm for Free Flight Planning JF - Algorithms N2 - We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach. KW - shortest path KW - flight planning KW - free flight KW - discrete-continuous algorithm KW - optimal control KW - discrete optimization Y1 - 2020 U6 - https://doi.org/10.3390/a14010004 SN - 1438-0064 VL - 14 IS - 1 SP - 4 PB - MDPI ER - TY - GEN A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Newton's Method for Global Free Flight Trajectory Optimization N2 - Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case. T3 - ZIB-Report - 23-08 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-89876 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Convergence Properties of Newton’s Method for Globally Optimal Free Flight Trajectory Optimization T2 - 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023) N2 - The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition. Y1 - 2023 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2023.3 VL - 115 SP - 3:1 EP - 3:6 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Newton's Method for Global Free Flight Trajectory Optimization JF - Operations Research Forum N2 - Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case. Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-91846 VL - 4 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - Error Bounds for Discrete-Continuous Free Flight Trajectory Optimization JF - Journal of Optimization Theory and Applications N2 - Flight planning, the computation of optimal routes in view of flight time and fuel consumption under given weather conditions, is traditionally done by finding globally shortest paths in a predefined airway network. Free flight trajectories, not restricted to a network, have the potential to reduce the costs significantly, and can be computed using locally convergent continuous optimal control methods. Hybrid methods that start with a discrete global search and refine with a fast continuous local optimization combine the best properties of both approaches, but rely on a good switchover, which requires error estimates for discrete paths relative to continuous trajectories. Based on vertex density and local complete connectivity, we derive localized and a priori bounds for the flight time of discrete paths relative to the optimal continuous trajectory, and illustrate their properties on a set of benchmark problems. It turns out that localization improves the error bound by four orders of magnitude, but still leaves ample opportunities for tighter bounds using a posteriori error estimators. Y1 - 2023 U6 - https://doi.org/10.1007/s10957-023-02264-7 VL - 198 SP - 830 EP - 856 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization T2 - 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022) N2 - We present an efficient algorithm that finds a globally optimal solution to the 2D Free Flight Trajectory Optimization Problem (aka Zermelo Navigation Problem) up to arbitrary precision in finite time. The algorithm combines a discrete and a continuous optimization phase. In the discrete phase, a set of candidate paths that densely covers the trajectory space is created on a directed auxiliary graph. Then Yen’s algorithm provides a promising set of discrete candidate paths which subsequently undergo a locally convergent refinement stage. Provided that the auxiliary graph is sufficiently dense, the method finds a path that lies within the convex domain around the global minimizer. From this starting point, the second stage will converge rapidly to the optimum. The density of the auxiliary graph depends solely on the wind field, and not on the accuracy of the solution, such that the method inherits the superior asymptotic convergence properties of the optimal control stage. Y1 - 2022 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2022.2 VL - 106 SP - 1 EP - 13 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Danecker, Fabian A1 - Weiser, Martin T1 - A Discrete-Continuous Algorithm for Free Flight Planning N2 - We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach. T3 - ZIB-Report - 20-33 KW - shortest path KW - flight planning KW - free flight KW - discrete-continuous algorithm KW - optimal control KW - discrete optimization Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81343 SN - 1438-0064 ER - TY - JOUR A1 - Widler, Valeria A1 - Kaminska, Barbara A1 - Martins, Andre C. R. A1 - Puga-Gonzalez, Ivan T1 - An Investigation into the Causal Mechanism of Political Opinion Dynamics: A Model of Hierarchical Coarse-Graining with Community-Bounded Social Influence JF - Computational Social Science of Social Cohesion and Polarization N2 - The increasing polarization in democratic societies is an emergent outcome of political opinion dynamics. Yet, the fundamental mechanisms behind the formation of political opinions, from individual beliefs to collective consensus, remain unknown. Understanding that a causal mechanism must account for both bottom-up and top-down influences, we conceptualize political opinion dynamics as hierarchical coarse-graining, where microscale opinions integrate into a macro-scale state variable. Using the CODA (Continuous Opinions Discrete Actions) model, we simulate Bayesian opinion updating, social identity-based information integration, and migration between social identity groups to represent higher-level connectivity. This results in coarse-graining across micro, meso, and macro levels. Our findings show that higher-level connectivity shapes information integration, yielding three regimes: independent (disconnected, local convergence), parallel (fast, global convergence), and iterative (slow, stepwise convergence). In the iterative regime, low connectivity fosters transient diversity, indicating an informed consensus. In all regimes, time-scale separation leads to downward causation, where agents converge on the aggregate majority choice, driving consensus. Critically, any degree of coherent higher-level information integration can overcome misalignment via global downward causation. The results highlight how emergent properties of the causal mechanism, such as downward causation, are essential for consensus and may inform more precise investigations into polarized political discourse. Y1 - 2026 U6 - https://doi.org/10.1007/978-3-032-01373-6_10 SP - 225 EP - 256 PB - Springer, Cham. ET - Computational Social Science of Social Cohesion and Polarization ER - TY - JOUR A1 - Marco, Reidelbach T1 - MaRDMO: Future Gateway to FAIR Mathematical Data JF - E-Science-Tage 2025: Research Data Management: Challenges in a Changing World N2 - Mathematical research data plays a crucial role across scientific disciplines, yet its documentation and dissemination remain challenging due to the lack of standardized research data management practices. The MaRDMO Plugin addresses these challenges by integrating mathematical models, algorithms, and interdisciplinary workflows into the established framework of the Research Data Management Organiser (RDMO). Built on FAIR principles, MaRDMO enables structured documentation and retrieval of mathematical research data through guided questionnaires. It connects to multiple knowledge graphs, including MathModDB, MathAlgoDB, and the MaRDI Portal. Users can document and search for models, algorithms, and workflows via dynamic selection interfaces that also leverage other sources such as Wikidata. The plugin facilitates the export to the individual MaRDI services, ensuring data quality through automated validation. By embedding mathematical research data management into the widely adopted RDMO platform, MaRDMO represents a significant step toward making mathematical research data more findable, accessible, and reusable. Y1 - 2025 U6 - https://doi.org/10.11588/heibooks.1652.c23913 SP - 40 EP - 53 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 framework, the new framework 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 - 2025 U6 - https://doi.org/10.1016/j.cam.2025.116675 VL - 470 ER - TY - JOUR A1 - Schembera, Björn A1 - Wübbeling, Frank A1 - Shehu, Aurela A1 - Biedinger, Christine A1 - Fiedler, Jochen A1 - Reidelbach, Marco A1 - Schmidt, Burkhard A1 - Ferrer, Eloi A1 - Koprucki, Thomas T1 - FAIR Representation of Mathematical Research Data: MathModDB and MathAlgoDB as Knowledge Graphs for Mathematical Models and Numerical Algorithms JF - 2nd Conference on Research Data Infrastructure (CoRDI) Y1 - 2025 U6 - https://doi.org/10.5281/zenodo.16735911 ER - TY - THES A1 - Villani, Paolo T1 - Regression Techniques for Surrogate Modelling in Bayesian Inverse Problems N2 - For many real-world applications, a system of interest can be represented via a mathematical model which depends on a set of parameters. In order to identify the parameters, a set of observations is available and an Inverse Problem is formulated. Identifying the parameters from the observations is often a challenging task, especially when the model is expensive to evaluate. This is the case for Partial Differential Equations models, where numerical simulations which are both inexact and computationally expensive are required to obtain the model output. To ease the computational costs, surrogate models can be used to approximate the forward model. In this work, we present two different regression techniques, Gaussian Process Regression and Lipschitz Regression. After reformulating the Inverse Problem to account for the surrogate model, we develope an adaptive training strategy to train the surrogate model. The proposed training strategy aims at optimizing not only the training points’ positions but also their evaluation accuracies. Moreover, interleaved sampling of the posterior distribution of the unknown parameters is performed while the surrogate model is trained, providing a solution for the Inverse Problem. The quality of the surrogating techniques as well as the effectiveness of the adaptive training strategy are tested through different numerical experiments. Y1 - 2025 ER - TY - JOUR A1 - Sikeler, Christoph A1 - Kempter, Susanne A1 - Sekulic, Ivan A1 - Burger, Sven A1 - Liedl, Tim T1 - Chiral Plasmonic Crystals Self-Assembled by DNA Origami JF - J. Phys. Chem. C Y1 - 2025 U6 - https://doi.org/10.1021/acs.jpcc.4c08768 VL - 129 IS - 10 SP - 5116 EP - 5121 ER - TY - GEN A1 - Zhang, Wei A1 - Schütte, Christof T1 - Reliable approximation of long relaxation timescales in molecular dynamics N2 - Many interesting rare events in molecular systems like ligand association, protein folding or con- formational changes happen on timescales that often are not accessible by direct numerical simulation. Therefore rare event approximation approaches like interface sampling, Markov state model building or advanced reaction coordinate based free energy estimation have attracted huge attention recently. In this article we analyze the reliability of such approaches: How precise is an estimate of long relaxation timescales of molecular systems resulting from various forms of rare event approximation methods? Our results give a theoretical answer to this question by relating it with the transfer operator approach to molecular dynamics. By doing so they also allow for understanding deep connections between the different approaches. T3 - ZIB-Report - 17-19 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63718 SN - 1438-0064 ER - TY - JOUR A1 - Gonnermann-Müller, Jana A1 - Haase, Jennifer A1 - Leins, Nicolas A1 - Igel, Moritz A1 - Fackeldey, Konstantin A1 - Pokutta, Sebastian T1 - FACET: Multi-Agent AI Supporting Teachers in Scaling Differentiated Learning for Diverse Students JF - arXiv N2 - Classrooms are becoming increasingly heterogeneous, comprising learners with diverse performance and motivation levels, language proficiencies, and learning differences such as dyslexia and ADHD. While teachers recognize the need for differentiated instruction, growing workloads create substantial barriers, making differentiated instruction an ideal that is often unrealized in practice. Current AI educational tools, which promise differentiated materials, are predominantly student-facing and performance-centric, ignoring other aspects that shape learning outcomes. We introduce FACET, a teacher-facing multi-agent framework designed to address these gaps by supporting differentiation that accounts for motivation, performance, and learning differences. Developed with educational stakeholders from the outset, the framework coordinates four specialized agents, including learner simulation, diagnostic assessment, material generation, and evaluation within a teacher-in-the-loop design. School principals (N = 30) shaped system requirements through participatory workshops, while in-service K-12 teachers (N = 70) evaluated material quality. Mixed-methods evaluation demonstrates strong perceived value for inclusive differentiation. Practitioners emphasized both the urgent need arising from classroom heterogeneity and the importance of maintaining pedagogical autonomy as a prerequisite for adoption. We discuss implications for future school deployment and outline partnerships for longitudinal classroom implementation. Y1 - 2026 U6 - https://doi.org/https://arxiv.org/abs/2601.22788 ER - TY - JOUR A1 - Andrés Arcones, Daniel A1 - Weiser, Martin A1 - Koutsourelakis, Phaedon-Stelios A1 - Unger, Jörg F. T1 - Embedded Model Form Uncertainty Quantification with Measurement Noise for Bayesian Model Calibration JF - Data-Centric Engineering N2 - A key factor in ensuring the accuracy of computer simulations that model physical systems is the proper calibration of their parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian methods provide a robust framework for quantifying and propagating these uncertainties to model predictions. Nevertheless, Bayesian methods paired with inexact models usually produce predictions unable to represent the observed datapoints. Additionally, the quantified uncertainties of these overconfident models cannot be propagated to other Quantities of Interest (QoIs) reliably. A promising solution involves embedding a model inadequacy term in the inference parameters, allowing the quantified model form uncertainty to influence non-observed QoIs. This paper introduces a more interpretable framework for embedding the model inadequacy compared to existing methods. To overcome the limitations of current approaches, we adapt the existing likelihood models to properly account for noise in the measurements and propose two new formulations designed to address their shortcomings. Moreover, we evaluate the performance of this inadequacy-embedding approach in the presence of discrepancies between measurements and model predictions, including noise and outliers. Particular attention is given to how the uncertainty associated with the model inadequacy term propagates to the QoIs, enabling a more comprehensive statistical analysis of prediction’s reliability. Finally, the proposed approach is applied to estimate the uncertainty in the predicted heat flux from a transient thermal simulation using temperature bservations. Y1 - 2026 U6 - https://doi.org/10.1017/dce.2025.10035 VL - 7 ER - TY - JOUR A1 - Mehrmann, Carolin A1 - Johny, Jacob A1 - Ebbinghaus, Petra A1 - Hammerschmidt, Martin A1 - Das, Ankita A1 - Wei, Xin A1 - Tesch, Marc F. A1 - Rabe, Martin T1 - Nano IR spectroscopy on Silicon-Supported Organic–Inorganic Hybrid Materials JF - Phys. Chem. Chem. Phys. Y1 - 2026 U6 - https://doi.org/10.1039/D5CP03815D PB - Royal Society of Chemistry (RSC) ER - TY - JOUR A1 - Farias-Basulto, Guillermo A1 - Mehlhop, Thede A1 - Otto, Nicolas J. A1 - Bertram, Tobias A1 - Jäger, Klaus A1 - Gall, Stefan A1 - Weinberger, Nikolaus A1 - Schlatmann, Rutger A1 - Lauermann, Iver A1 - Klenk, Reiner A1 - List-Kratochvil, Emil A1 - Kaufmann, Christian A. T1 - Improving Perovskite/CIGS Tandem Solar Cells for Higher Power Conversion Efficiency through Light Management and Bandgap Engineering JF - ACS Appl. Mater. Interfaces Y1 - 2025 U6 - https://doi.org/10.1021/acsami.5c15458 VL - 17 SP - 56250 ER - TY - JOUR A1 - Lelièvre, Tony A1 - Zhang, Wei T1 - Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates JF - Multiscale Modeling and Simulation N2 - Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Lelièvre, Nonlinearity, 2010] to approximate the essential dynamics of high-dimensional diffusion processes along a given reaction coordinate. The approximation error of the effective dynamics when it is used to approximate the behavior of the original dynamics has been considered in recent years. As a continuation of the previous work [F. Legoll, T. Lelièvre, and S. Olla, Stoch. Process. Appl, 2017], in this paper we obtain pathwise estimates for effective dynamics when the reaction coordinate function is either nonlinear or vector-valued. Y1 - 2018 U6 - https://doi.org/10.1137/18M1186034 IS - 17 SP - 1019 EP - 1051 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Schütte, Christof A1 - Zhang, Wei T1 - Jarzynski's equality, fluctuation theorems, and variance reduction: Mathematical analysis and numerical algorithms JF - Journal of Statistical Physics N2 - In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski's equality. Y1 - 2018 U6 - https://doi.org/10.1007/s10955-019-02286-4 VL - 175 IS - 6 SP - 1214 EP - 1261 ER - TY - JOUR A1 - Zhang, Wei T1 - Some new results on relative entropy production, time reversal, and optimal control of time-inhomogeneous diffusion processes JF - Journal of Mathematical Physics N2 - This paper studies time-inhomogeneous nonequilibrium diffusion processes, including both Brownian dynamics and Langevin dynamics. We derive upper bounds of the relative entropy production of the time-inhomogeneous process with respect to the transient invariant probability measures. We also study the time reversal of the reverse process in Crooks' fluctuation theorem. We show that the time reversal of the reverse process coincides with the optimally controlled forward process that leads to zero variance importance sampling estimator based on Jarzynski's equality. Y1 - 2021 U6 - https://doi.org/10.1063/5.0038740 VL - 62 IS - 4 ER - TY - JOUR A1 - Lelievre, Tony A1 - Stoltz, Gabriel A1 - Zhang, Wei T1 - Multiple projection MCMC algorithms on submanifolds JF - IMA Journal of Numerical Analysis N2 - We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for this generalization is that the numerical solvers used to project proposed moves to the submanifold of interest may find several solutions. We show that the new algorithms indeed sample the target probability measure correctly, thanks to some carefully enforced reversibility property. We demonstrate the interest of the new MCMC algorithms on illustrative numerical examples. Y1 - 2022 U6 - https://doi.org/10.1093/imanum/drac006 ER - TY - JOUR A1 - Zhang, Wei A1 - Li, Tiejun A1 - Schütte, Christof T1 - Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks JF - Journal of Computational Physics N2 - In this paper, we consider the eigenvalue PDE problem of the infinitesimal generators of metastable diffusion processes. We propose a numerical algorithm based on training artificial neural networks for solving the leading eigenvalues and eigenfunctions of such high-dimensional eigenvalue problem. The algorithm is useful in understanding the dynamical behaviors of metastable processes on large timescales. We demonstrate the capability of our algorithm on a high-dimensional model problem, and on the simple molecular system alanine dipeptide. Y1 - 2021 U6 - https://doi.org/10.1016/j.jcp.2022.111377 VL - 465 ER - TY - JOUR A1 - Zhang, Wei A1 - Klus, Stefan A1 - Conrad, Tim A1 - Schütte, Christof T1 - Learning chemical reaction networks from trajectory data JF - SIAM Journal on Applied Dynamical Systems (SIADS) N2 - We develop a data-driven method to learn chemical reaction networks from trajectory data. Modeling the reaction system as a continuous-time Markov chain and assuming the system is fully observed,our method learns the propensity functions of the system with predetermined basis functions by maximizing the likelihood function of the trajectory data under l^1 sparse regularization. We demonstrate our method with numerical examples using synthetic data and carry out an asymptotic analysis of the proposed learning procedure in the infinite-data limit. Y1 - 2019 U6 - https://doi.org/10.1137/19M1265880 VL - 18 IS - 4 SP - 2000 EP - 2046 ER - TY - JOUR A1 - Zhao, Yue A1 - Zhang, Wei A1 - Li, Tiejun T1 - EPR-Net: Constructing non-equilibrium potential landscape via a variational force projection formulation JF - National Science Review N2 - We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state (NESS) systems. EPR-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product space. Remarkably, our loss function has an intimate connection with the steady entropy production rate (EPR), enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness, and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an 8D limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics. Y1 - 2024 U6 - https://doi.org/10.1093/nsr/nwae052 VL - 11 IS - 7 ER - TY - JOUR A1 - Akhyar, Fatima-Zahrae A1 - Zhang, Wei A1 - Stoltz, Gabriel A1 - Schütte, Christof T1 - Generative modeling of conditional probability distributions on the level-sets of collective variables N2 - Given a probability distribution $\mu$ in $\mathbb{R}^d$ represented by data, we study in this paper the generative modeling of its conditional probability distributions on the level-sets of a collective variable $\xi: \mathbb{R}^d \rightarrow \mathbb{R}^k$, where $1 \le k t0. We obtain promising results assuming Newtonian cooling for boxes filled with air, heaps of clothes, or books in two different experimental scenarios. Two different parameter estimators, (TA0^, t0^) based on four temperature measurements and (TA0*, t0*) for 4N measurements were tested. Our results in a climate chamber were partially appropriate for TTDE input. A decline at time t0 from TA0 = 22.5°C ↓ TA1 = 14°C was reconstructed at t = t0 + 95min with relative deviations ρt0^ = 27% and ρTA0^ = 19% relative to t - t0 and TA0 – TA1 respectively, for N = 1 with span Δt = 50min. For N = 200 in a time interval [t0 + 95min, t0 + 295min] we found ρt0^ = 5% and ρTA0^ = 11% with the same Δt. Further research is necessary to guarantee applicability in routine casework, in particular with respect to more elaborate cooling models, estimation algorithms, and evaluation localization. Y1 - 2026 ER - TY - JOUR A1 - Villani, Paolo A1 - Andrés Arcones, Daniel A1 - Unger, Jörg F. A1 - Weiser, Martin T1 - Gaussian mixture models for model improvement N2 - Modeling complex physical systems such as they arise in civil engineering applications requires finding a trade-off between physical fidelity and practicality. Consequently, deviations of simulation from measurements are ubiquitous even after model calibration due to the model discrepancy, which may result from deliberate modeling decisions, ignorance, or lack of knowledge. If the mismatch between simulation and measurements are deemed unacceptable, the model has to be improved. Targeted model improvement is challenging due to a non-local impact of model discrepancies on measurements and the dependence on sensor configurations. Many approaches to model improvement, such as Bayesian calibration with additive mismatch terms, gray-box models, symbolic regression, or stochastic model updating, often lack interpretability, generalizability, physical consistency, or practical applicability. This paper introduces a non-intrusive approach to model discrepancy analysis using mixture models. Instead of directly modifying the model structure, the method maps sensor readings to clusters of physically meaningful parameters, automatically assigning sensor readings to parameter vector clusters. This mapping can reveal systematic discrepancies and model biases, guiding targeted, physics-based refinements by the modeler. The approach is formulated within a Bayesian framework, enabling the identification of parameter clusters and their assignments via the Expectation-Maximization (EM) algorithm. The methodology is demonstrated through numerical experiments, including an illustrative example and a real-world case study of heat transfer in a concrete bridge. Y1 - 2026 ER - TY - JOUR A1 - Kresse, Jakob A1 - Sikorski, Alexander A1 - Chewle, Surahit A1 - Sunkara, Vikram A1 - Weber, Marcus T1 - Revealing the Atomistic Mechanism of Rare Events in Molecular Dynamics JF - Journal of Chemical Theory and Computation N2 - Interpretable reaction coordinates are essential for understanding rare conformational transitions in molecular dynamics. The Atomistic Mechanism Of Rare Events in Molecular Dynamics (AMORE-MD) framework enhances interpretability of deep-learned reaction coordinates by connecting them to atomistic mechanisms, without requiring any a priori knowledge of collective variables, pathways, or endpoints. Here, AMORE-MD employs the ISOKANN algorithm to learn a neural membership function χ representing the dominant slow process, from which transition pathways are reconstructed as minimum-energy paths aligned with the gradient of χ, and atomic contributions are quantified through gradient-based sensitivity analysis. Iterative enhanced sampling further enriches transition regions and improves coverage of rare events enabling recovery of known mechanisms and chemically interpretable structural rearrangements at atomic resolution for the Müller-Brown potential, alanine dipeptide, and the elastin-derived hexapeptide VGVAPG. Y1 - 2026 U6 - https://doi.org/10.1021/acs.jctc.5c01906 VL - 22 IS - 5 SP - 2380 EP - 2389 ER - TY - GEN A1 - Baumann, Felix A1 - Duda, Georg A1 - Schiela, Anton A1 - Weiser, Martin ED - Hintermüller, Michael ED - Herzog, Roland ED - Kanzow, Christian ED - Ulbrich, Michael ED - Ulbrich, Stefan T1 - Identification of Stress in Heterogeneous Contact Models BT - Simulation and Hierarchical Optimization, Part II T2 - Non-Smooth and Complementarity-Based Distributed Parameter Systems N2 - We develop a heterogeneous model of the lower limb system to simulate muscle forces and stresses acting on the knee joint. The modelling of the bone dynamics leads to an index-3 DAE, which we discretize by higher order collocation methods. Furthermore, we present an elastomechanical contact knee joint model of the articular cartilage. For the solution of the contact problem we develop an efficient multigrid solver, based on an Augmented-Lagrangian relaxation of the contact constraints. We formulate the identification of joint forces and resulting stresses with respect to different knee joint models as an inverse problem based on medical gait data. Y1 - 2026 VL - 173 PB - Springer Nature ER - TY - JOUR A1 - Fischbach, Jan David A1 - Betz, Fridtjof A1 - Rebholz, Lukas A1 - Garg, Puneet A1 - Frizyuk, Kristina A1 - Binkowski, Felix A1 - Burger, Sven A1 - Hammerschmidt, Martin A1 - Rockstuhl, Carsten T1 - Pole-Expansion of the T-Matrix Based on a Matrix-Valued AAA-Algorithm JF - ArXiV Y1 - 2026 U6 - https://doi.org/10.48550/arXiv.2602.18414 SP - arXiv:2602.18414 ER - TY - JOUR A1 - Lücke, Marvin A1 - Winkelmann, Stefanie A1 - Koltai, Peter T1 - Accurate mean-field equation for voter model dynamics on scale-free networks JF - Physical Review E N2 - Understanding the emergent macroscopic behavior of dynamical systems on networks is a crucial but challenging task. One of the simplest and most effective methods to construct a reduced macroscopic model is given by mean-field theory. The resulting approximations perform well on dense and homogeneous networks but poorly on scale-free networks, which, however, are more realistic in many applications. In this paper, we introduce a modified version of the mean-field approximation for voter model dynamics on scale-free networks. The two main deviations from classical theory are that we use degree-weighted shares as coarse variables and that we introduce a correlation factor that can be interpreted as slowing down dynamics induced by interactions. We observe that the correlation factor is only a property of the network and not of the state or of parameters of the process. This approach achieves a significantly smaller approximation error than standard methods without increasing dimensionality. Y1 - 2026 U6 - https://doi.org/10.1103/vkpx-5cvt VL - 113 ER - TY - JOUR A1 - Wehlitz, Nathalie A1 - Pavliotis, Grigorios A1 - Schütte, Christof A1 - Winkelmann, Stefanie T1 - Data-driven Reduction of Transfer Operators for Particle Clustering Dynamics N2 - We develop an operator-based framework to coarse-grain interacting particle systems that exhibit clustering dynamics. Starting from the particle-based transfer operator, we first construct a sequence of reduced representations: the operator is projected onto concentrations and then further reduced by representing the concentration dynamics on a geometric low-dimensional manifold and an adapted finite-state discretization. The resulting coarse-grained transfer operator is finally estimated from dynamical simulation data by inferring the transition probabilities between the Markov states. Applied to systems with multichromatic and Morse interaction potentials, the reduced model reproduces key features of the clustering process, including transitions between cluster configurations and the emergence of metastable states. Spectral analysis and transition-path analysis of the estimated operator reveal implied time scales and dominant transition pathways, providing an interpretable and efficient description of particle-clustering dynamics. Y1 - 2026 ER - TY - JOUR A1 - Schütte, Christof A1 - Sikorski, Alexander A1 - Kresse, Jakob A1 - Weber, Marcus T1 - On-the-Fly Lifting of Coarse Reaction-Coordinate Paths to Full-Dimensional Transition Path Ensembles N2 - Effective dynamics on a low-dimensional collective-variable (CV) or latent space can be simulated far more cheaply than the underlying high-dimensional stochastic system, but exploiting such coarse predictions requires lifting: turning a coarse CV trajectory into dynamically consistent full-dimensional states and path ensembles, without relying on global sampling of invariant or conditional fiber measures. We present a local, on-the-fly lifting strategy based on guided full-system trajectories. First an effective model in CV space is used to obtain a coarse reference trajectory. Then, an ensemble of full-dimensional trajectories is generated from a guided version of the original dynamics, where the guidance steers the trajectory to track the CV reference path. Because guidance biases the path distribution, we correct it via pathwise Girsanov reweighting, yielding a correct-by-construction importance-sampling approximation of the conditional law of the uncontrolled dynamics. We further connect the approach to stochastic optimal control, clarifying how coarse models can inform variance-reducing guidance for rare-event quantities. Numerical experiments demonstrate that inexpensive coarse transition paths can be converted into realistic full-system transition pathways (including barrier crossings and detours) and can accelerate estimation of transition pathways and statistics while providing minimal bias through weighted ensembles. Y1 - 2026 U6 - https://doi.org/10.48550/arXiv.2603.23266 ER -