TY - CHAP A1 - Zschiedrich, Lin A1 - Betz, Fridtjof A1 - Binkowski, Felix A1 - Kuen, Lilli A1 - Hammerschmidt, Martin A1 - Burger, Sven T1 - Efficient Photonic Component Analysis via AAA Rational Approximation T2 - 2025 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD) Y1 - 2025 U6 - https://doi.org/10.1109/NUSOD64393.2025.11199710 SP - 115 EP - 116 ER - TY - CHAP A1 - Schembera, Björn A1 - Wübbeling, Frank A1 - Kleikamp, Hendrik A1 - Biedinger, Christine A1 - Fiedler, Jochen A1 - Reidelbach, Marco A1 - Shehu, Aurela A1 - Schmidt, Burkhard A1 - Koprucki, Thomas A1 - Iglezakis, Dotothea A1 - Göddeke, Dominik T1 - Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines T2 - Metadata and Semantic Research - MTSR 2023 N2 - In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data, the Mathematical Research Data Initiative has developed, merged and implemented ontologies and knowledge graphs. This contributes to making mathematical research data FAIR by introducing semantic technology and documenting the mathematical foundations accordingly. Using the concrete example of microfracture analysis of porous media, it is shown how the knowledge of the underlying mathematical model and the corresponding numerical algorithms for its solution can be represented by the ontologies. Y1 - 2023 U6 - https://doi.org/10.1007/978-3-031-65990-4_14 SP - 161 EP - 168 PB - Springer Nature Switzerland CY - Cham ET - Communications in Computer and Information Science ER - TY - CHAP A1 - Reidelbach, Marco A1 - Schembera, Björn A1 - Weber, Marcus T1 - Towards a FAIR Documentation of Workflows and Models in Applied Mathematics T2 - Mathematical Software – ICMS 2024 N2 - Modeling-Simulation-Optimization workflows play a fundamental role in applied mathematics. The Mathematical Research Data Initiative, MaRDI, responded to this by developing a FAIR and machine-interpretable template for a comprehensive documentation of such workflows. MaRDMO, a Plugin for the Research Data Management Organiser, enables scientists from diverse fields to document and publish their workflows on the MaRDI Portal seamlessly using the MaRDI template. Central to these workflows are mathematical models. MaRDI addresses them with the MathModDB ontology, offering a structured formal model description. Here, we showcase the interaction between MaRDMO and the MathModDB Knowledge Graph through an algebraic modeling workflow from the Digital Humanities. This demonstration underscores the versatility of both services beyond their original numerical domain. Y1 - 2024 U6 - https://doi.org/10.1007/978-3-031-64529-7_27 VL - 14749 SP - 254 EP - 262 PB - Springer Nature Switzerland CY - Cham ET - Lecture Notes in Computer Science ER - TY - CHAP A1 - Vaitl, Lorenz A1 - Winkler, Ludwig A1 - Richter, Lorenz A1 - Kessel, Pan T1 - Fast and unified path gradient estimators for normalizing flows T2 - International Conference on Learning Representations 2024 N2 - Recent work shows that path gradient estimators for normalizing flows have lower variance compared to standard estimators for variational inference, resulting in improved training. However, they are often prohibitively more expensive from a computational point of view and cannot be applied to maximum likelihood train- ing in a scalable manner, which severely hinders their widespread adoption. In this work, we overcome these crucial limitations. Specifically, we propose a fast path gradient estimator which improves computational efficiency significantly and works for all normalizing flow architectures of practical relevance. We then show that this estimator can also be applied to maximum likelihood training for which it has a regularizing effect as it can take the form of a given target energy func- tion into account. We empirically establish its superior performance and reduced variance for several natural sciences applications. Y1 - 2024 UR - https://openreview.net/pdf?id=zlkXLb3wpF ER - TY - CHAP A1 - Lücke, Marvin A1 - Koltai, Peter A1 - Winkelmann, Stefanie A1 - Molkethin, Nora A1 - Heitzig, Jobst T1 - Discovering collective variable dynamics of agent-based models T2 - 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022 N2 - Analytical approximations of the macroscopic behavior of agent-based models (e.g. via mean-field theory) often introduce a significant error, especially in the transient phase. For an example model called continuous-time noisy voter model, we use two data-driven approaches to learn the evolution of collective variables instead. The first approach utilizes the SINDy method to approximate the macroscopic dynamics without prior knowledge, but has proven itself to be not particularly robust. The second approach employs an informed learning strategy which includes knowledge about the agent-based model. Both approaches exhibit a considerably smaller error than the conventional analytical approximation. Y1 - 2022 U6 - https://doi.org/https://doi.org/10.15495/EPub_UBT_00006809 ER - TY - CHAP A1 - Schaible, Jonas A1 - Yoo, Danbi A1 - Winarto, Hanifa A1 - Miaskiewicz, Alexandra A1 - Albrecht, Steve A1 - Wessels, Andreas A1 - Bläsi, Benedikt A1 - Burger, Sven A1 - Jaeger, Klaus A1 - Becker, Christiane T1 - On aesthetical appearance of colored perovskite solar modules T2 - Proc. SPIE Y1 - 2024 U6 - https://doi.org/10.1117/12.3017427 VL - PC13014 SP - PC1301406 PB - SPIE ER - TY - CHAP A1 - Becker, Christiane A1 - Bläsi, Benedikt A1 - Burger, Sven A1 - Ehrler, Bruno A1 - Gordon, Ivan A1 - Isabella, Olindo A1 - Jäger, Klaus A1 - Jost, Marko A1 - Manley, Phillip A1 - Muñoz, Delfina A1 - Paetzold, Ulrich W. A1 - Sai, Hitoshi A1 - Yablonovitch, Eli T1 - Optical challenges for terawatt-scale photovoltaics T2 - Proc. SPIE Y1 - 2024 U6 - https://doi.org/10.1117/12.3016415 VL - PC13014 SP - PC1301401 PB - SPIE ER - TY - CHAP A1 - Semler, Phillip A1 - Weiser, Martin ED - Fackeldey, Konstantin ED - Kannan, Aswin ED - Pokutta, Sebastian ED - Sharma, Kartikey ED - Walter, Daniel ED - Walther, Andrea ED - Weiser, Martin T1 - Adaptive gradient-enhanced Gaussian process surrogates for inverse problems T2 - Mathematical Optimization for Machine Learning: Proceedings of the MATH+ Thematic Einstein Semester 2023 N2 - Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a fully adaptive greedy approach to the computational design of experiments problem using gradient-enhanced Gaussian process regression as surrogates. Designs are incrementally defined by solving an optimization problem for accuracy given a certain computational budget. We address not only the choice of evaluation points but also of required simulation accuracy, both of values and gradients of the forward model. Numerical results show a significant reduction of the computational effort compared to just position-adaptive and static designs as well as a clear benefit of including gradient information into the surrogate training. Y1 - 2025 U6 - https://doi.org/10.1515/9783111376776-005 SP - 59 EP - 78 PB - De Gruyter ER - TY - CHAP A1 - Villani, Paolo A1 - Unger, Jörg F. A1 - Weiser, Martin T1 - Adaptive Gaussian Process Regression for Bayesian inverse problems T2 - Proceedings of the Conference Algoritmy 2024 N2 - We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on optimizing both the positioning and simulation accuracy of training data in order to reduce the computational cost of simulating training data without compromising the fidelity of the posterior distributions of parameters. The method interleaves a goal-oriented active learning algorithm selecting evaluation points and tolerances based on the expected impact on the Kullback-Leibler divergence of surrogated and true posterior with a Markov Chain Monte Carlo sampling of the posterior. The performance benefit of the adaptive approach is demonstrated for two simple test problems. Y1 - 2024 SP - 214 EP - 224 ER - TY - CHAP A1 - Andrés Arcones, Daniel A1 - Weiser, Martin A1 - Koutsourelakis, Faidon-Stelios A1 - Unger, Jörg F. T1 - Evaluation of Model Bias Identification Approaches Based on Bayesian Inference and Applications to Digital Twins T2 - 5th ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering N2 - In recent years, the use of simulation-based digital twins for monitoring and assessment of complex mechanical systems has greatly expanded. Their potential to increase the information obtained from limited data makes them an invaluable tool for a broad range of real-world applications. Nonetheless, there usually exists a discrepancy between the predicted response and the measurements of the system once built. One of the main contributors to this difference in addition to miscalibrated model parameters is the model error. Quantifying this socalled model bias (as well as proper values for the model parameters) is critical for the reliable performance of digital twins. Model bias identification is ultimately an inverse problem where information from measurements is used to update the original model. Bayesian formulations can tackle this task. Including the model bias as a parameter to be inferred enables the use of a Bayesian framework to obtain a probability distribution that represents the uncertainty between the measurements and the model. Simultaneously, this procedure can be combined with a classic parameter updating scheme to account for the trainable parameters in the original model. This study evaluates the effectiveness of different model bias identification approaches based on Bayesian inference methods. This includes more classical approaches such as direct parameter estimation using MCMC in a Bayesian setup, as well as more recent proposals such as stat-FEM or orthogonal Gaussian Processes. Their potential use in digital twins, generalization capabilities, and computational cost is extensively analyzed. Y1 - 2023 UR - https://2023.uncecomp.org/proceedings/pdf/19795.pdf SP - 1 EP - 15 ER - TY - CHAP A1 - Mukherjee, Deshabrato A1 - Burger, Sven A1 - Siefke, Thomas A1 - Gour, Jeetendra A1 - Bodermann, Bernd A1 - Petrik, Peter T1 - Modeling of dimensions and sensing properties of gold gratings by spectroscopic ellipsometry and finite element method T2 - EPJ Web of Conferences Y1 - 2024 U6 - https://doi.org/10.1051/epjconf/202430902016 VL - 309 SP - 02016 ER - TY - CHAP A1 - Binkowski, Felix A1 - Betz, Fridtjof A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Poles and Zeros in Resonant Nano-Photonic Systems T2 - 2024 Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR) Y1 - 2024 U6 - https://doi.org/10.1109/CLEO-PR60912.2024.10676837 ER - TY - CHAP A1 - Jäger, Klaus A1 - Burger, Sven A1 - Aeberhard, Urs A1 - Llado, Esther Alarcon A1 - Bläsi, Benedikt A1 - Ehrler, Bruno A1 - Favre, Wilfried A1 - Fejfar, Antonín A1 - Gageot, Tristan A1 - Gordon, Ivan A1 - Helmers, Henning A1 - Höhn, Oliver A1 - Isabella, Olindo A1 - Jošt, Marko A1 - Ledinský, Martin A1 - Mandal, Jyotirmoy A1 - Manley, Phillip A1 - Munoz, Delfina A1 - Lizcano, Juan Camilo Ortiz A1 - Paetzold, Ulrich W. A1 - Raman, Aaswath P. A1 - Sai, Hitoshi A1 - Saive, Rebecca A1 - Schmid, Martina A1 - Yablonovitch, Eli A1 - Becker, Christiane T1 - A Roadmap on Optics for Terawatt Scale Photovoltaics T2 - Advanced Photonics Congress 2024 Y1 - 2024 U6 - https://doi.org/10.1364/SELED.2024.STu2G.5 SP - STu2G.5 PB - Optica Publishing Group ER - TY - CHAP A1 - Winkler, Ludwig A1 - Richter, Lorenz A1 - Opper, Manfred T1 - Bridging discrete and continuous state spaces: Exploring the Ehrenfest process in time-continuous diffusion models T2 - Proceedings of the 41st International Conference on Machine Learning N2 - Generative modeling via stochastic processes has led to remarkable empirical results as well as to recent advances in their theoretical understanding. In principle, both space and time of the processes can be discrete or continuous. In this work, we study time-continuous Markov jump processes on discrete state spaces and investigate their correspondence to state-continuous diffusion processes given by SDEs. In particular, we revisit the Ehrenfest process, which converges to an Ornstein-Uhlenbeck process in the infinite state space limit. Likewise, we can show that the time-reversal of the Ehrenfest process converges to the time-reversed Ornstein-Uhlenbeck process. This observation bridges discrete and continuous state spaces and allows to carry over methods from one to the respective other setting. Additionally, we suggest an algorithm for training the time-reversal of Markov jump processes which relies on conditional expectations and can thus be directly related to denoising score matching. We demonstrate our methods in multiple convincing numerical experiments. Y1 - 2024 UR - https://raw.githubusercontent.com/mlresearch/v235/main/assets/winkler24a/winkler24a.pdf VL - 235 SP - 53017 EP - 53038 ER - TY - CHAP A1 - Ribera Borrell, Enric A1 - Richter, Lorenz A1 - Schütte, Christof T1 - Reinforcement Learning with Random Time Horizons T2 - Proceedings of the 42nd International Conference on Machine Learning Y1 - 2025 UR - https://raw.githubusercontent.com/mlresearch/v267/main/assets/borrell25a/borrell25a.pdf VL - 267 SP - 5101 EP - 5123 ER - TY - CHAP A1 - Schaible, Jonas A1 - Winarto, Hanifah A1 - Skorjanc, Victor A1 - Yoo, Danbi A1 - Zimmermann, Lea A1 - Wessels, Andreas A1 - Jäger, Klaus A1 - Sekulic, Ivan A1 - Schneider, Philipp-Immanuel A1 - Bläsi, Benedikt A1 - Burger, Sven A1 - Becker, Christiane T1 - Optimization strategies for colorful thin film solar cells T2 - Proc. SPIE Y1 - 2025 U6 - https://doi.org/10.1117/12.3041408 VL - PC13361 SP - PC133610E ER - TY - CHAP A1 - Kuen, Lilli A1 - Betz, Fridtjof A1 - Binkowski, Felix A1 - Schneider, Philipp-Immanuel A1 - Hammerschmidt, Martin A1 - Heermeier, Niels A1 - Rodt, Sven A1 - Reitzenstein, Stephan A1 - Burger, Sven T1 - Applying a Riesz-projection-based contour integral eigenvalue solver to compute resonance modes of a VCSEL T2 - Proc. SPIE Y1 - 2023 U6 - https://doi.org/10.1117/12.2665490 VL - 12575 SP - 125750J ER - TY - CHAP A1 - Zink, Christof A1 - Ekterai, Michael A1 - Martin, Dominik A1 - Clemens, William A1 - Maennel, Angela A1 - Mundinger, Konrad A1 - Richter, Lorenz A1 - Crump, Paul A1 - Knigge, Andrea T1 - Deep-learning-based visual inspection of facets and p-sides for efficient quality control of diode lasers T2 - High-Power Diode Laser Technology XXI N2 - The optical inspection of the surfaces of diode lasers, especially the p-sides and facets, is an essential part of the quality control in the laser fabrication procedure. With reliable, fast, and flexible optical inspection processes, it is possible to identify and eliminate defects, accelerate device selection, reduce production costs, and shorten the cycle time for product development. Due to a vast range of rapidly changing designs, structures, and coatings, however, it is impossible to realize a practical inspection with conventional software. In this work, we therefore suggest a deep learning based defect detection algorithm that builds on a Faster Regional Convolutional Neural Network (Faster R-CNN) as a core component. While for related, more general object detection problems, the application of such models is straightforward, it turns out that our task exhibits some additional challenges. On the one hand, a sophisticated pre- and postprocessing of the data has to be deployed to make the application of the deep learning model feasible. On the other hand, we find that creating labeled training data is not a trivial task in our scenario, and one has to be extra careful with model evaluation. We can demonstrate in multiple empirical assessments that our algorithm can detect defects in diode lasers accurately and reliably in most cases. We analyze the results of our production-ready pipeline in detail, discuss its limitations and provide some proposals for further improvements. Y1 - 2023 U6 - https://doi.org/10.1117/12.2648691 VL - 12403 SP - 94 EP - 112 PB - SPIE ER - TY - CHAP A1 - Richter, Lorenz A1 - Berner, Julius T1 - Improved sampling via learned diffusions T2 - International Conference on Learning Representations 2024 N2 - Recently, a series of papers proposed deep learning-based approaches to sample from unnormalized target densities using controlled diffusion processes. In this work, we identify these approaches as special cases of the Schrödinger bridge problem, seeking the most likely stochastic evolution between a given prior distribution and the specified target. We further generalize this framework by introducing a variational formulation based on divergences between path space measures of time-reversed diffusion processes. This abstract perspective leads to practical losses that can be optimized by gradient-based algorithms and includes previous objectives as special cases. At the same time, it allows us to consider divergences other than the reverse Kullback-Leibler divergence that is known to suffer from mode collapse. In particular, we propose the so-called log-variance loss, which exhibits favorable numerical properties and leads to significantly improved performance across all considered approaches. Y1 - 2024 UR - https://openreview.net/pdf?id=h4pNROsO06 ER - TY - CHAP A1 - Chaukair, Mustafa A1 - Schütte, Christof A1 - Sunkara, Vikram T1 - On the Activation Space of ReLU Equipped Deep Neural Networks T2 - Procedia Computer Science N2 - Modern Deep Neural Networks are getting wider and deeper in their architecture design. However, with an increasing number of parameters the decision mechanisms becomes more opaque. Therefore, there is a need for understanding the structures arising in the hidden layers of deep neural networks. In this work, we present a new mathematical framework for describing the canonical polyhedral decomposition in the input space, and in addition, we introduce the notions of collapsing- and preserving patches, pertinent to understanding the forward map and the activation space they induce. The activation space can be seen as the output of a layer and, in the particular case of ReLU activations, we prove that this output has the structure of a polyhedral complex. Y1 - 2023 U6 - https://doi.org/10.1016/j.procs.2023.08.200 VL - 222 SP - 624 EP - 635 ER - TY - CHAP A1 - Yousefian, Maryam A1 - Donati, Luca A1 - Sikorski, Alexander A1 - Weber, Marcus A1 - Röblitz, Susanna T1 - Exploring Metastable Dynamics of Gene Regulatory Networks with ISOKANN T2 - Computational Methods in Systems Biology. CMSB 2025 N2 - Stochastic dynamical systems like gene regulatory networks (GRNs) often exhibit behavior characterized by metastable sets (representing cellular phenotypes), in which trajectories remain for long times, whereas switches between these sets in the phase space are rare events. One way to capture these rare events is to infer the system’s long-term behavior from the spectral characteristics (eigenvalues and eigenvectors) of its Koopman operator. For GRNs, the Koopman operator is based on the chemical master equation (CME), which provides a precise mathematical modeling framework for stochastic GRNs. Since the CME is typically analytically intractable, methods based on discretizing the CME operator have been developed. However, determining the number and location of metastable sets in the phase space as well as the transition rates between them remains computationally challenging, especially for large GRNs with many genes and interactions. A promising alternative method, called ISOKANN (invariant subspaces of Koopman operators with artificial neural networks) has been developed in the context of molecular dynamics. ISOKANN uses a combination of the power iteration and neural networks to learn the basis functions of an invariant subspace of the Koopman operator. In this paper, we extend the application of ISOKANN to the CME operator and apply it to two small GRNs: a genetic toggle switch model and a model for macrophage polarization. Our work opens a new field of application for the ISOKANN algorithm and demonstrates the potential of this algorithm for studying large GRNs. Y1 - 2026 U6 - https://doi.org/10.1007/978-3-032-01436-8_8 VL - 15959 SP - 126 EP - 149 ER - TY - CHAP A1 - Sekulic, Ivan A1 - Schneider, Philipp-Immanuel A1 - Hammerschmidt, Martin A1 - Schaible, Jonas A1 - Burger, Sven T1 - Physics informed Bayesian optimization for inverse design of diffractive optical elements T2 - Proc. SPIE Y1 - 2025 U6 - https://doi.org/10.1117/12.3064372 VL - PC13573 SP - PC135730R ER - TY - CHAP A1 - Hammerschmidt, Martin A1 - Plock, Matthias A1 - Burger, Sven A1 - Truong, Vinh A1 - Soltwisch, Victor A1 - Schneider, Philipp-Immanuel T1 - Machine learning approach for full Bayesian parameter reconstruction T2 - Proc. SPIE Y1 - 2025 U6 - https://doi.org/10.1117/12.3062268 VL - 13568 SP - 1356806 ER - TY - CHAP A1 - Blessing, Denis A1 - Berner, Julius A1 - Richter, Lorenz A1 - Neumann, Gerhard T1 - Underdamped Diffusion Bridges with Applications to Sampling T2 - 13th International Conference on Learning Representations (ICLR 2025) N2 - We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices, where the noise only acts in certain dimensions. Extending previous findings, our framework allows to rigorously show that score matching in the underdamped case is indeed equivalent to maximizing a lower bound on the likelihood. Motivated by superior convergence properties and compatibility with sophisticated numerical integration schemes of underdamped stochastic processes, we propose \emph{underdamped diffusion bridges}, where a general density evolution is learned rather than prescribed by a fixed noising process. We apply our method to the challenging task of sampling from unnormalized densities without access to samples from the target distribution. Across a diverse range of sampling problems, our approach demonstrates state-of-the-art performance, notably outperforming alternative methods, while requiring significantly fewer discretization steps and no hyperparameter tuning. Y1 - 2025 UR - https://openreview.net/attachment?id=Q1QTxFm0Is&name=pdf ER - TY - CHAP A1 - Chen, Junhua A1 - Richter, Lorenz A1 - Berner, Julius A1 - Blessing, Denis A1 - Neumann, Gerhard A1 - Anandkumar, Anima T1 - Sequential Controlled Langevin Diffusions T2 - 13th International Conference on Learning Representations (ICLR 2025) N2 - An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where the transport is performed through successive annealed densities via prescribed Markov chains and resampling steps, and (2) recently developed diffusion-based sampling methods, where a learned dynamical transport is used. Despite the common goal, both approaches have different, often complementary, advantages and drawbacks. The resampling steps in SMC allow focusing on promising regions of the space, often leading to robust performance. While the algorithm enjoys asymptotic guarantees, the lack of flexible, learnable transitions can lead to slow convergence. On the other hand, diffusion-based samplers are learned and can potentially better adapt themselves to the target at hand, yet often suffer from training instabilities. In this work, we present a principled framework for combining SMC with diffusion-based samplers by viewing both methods in continuous time and considering measures on path space. This culminates in the new Sequential Controlled Langevin Diffusion (SCLD) sampling method, which is able to utilize the benefits of both methods and reaches improved performance on multiple benchmark problems, in many cases using only 10% of the training budget of previous diffusion-based samplers. Y1 - 2025 UR - https://openreview.net/pdf?id=dImD2sgy86 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - CHAP A1 - Richter, Lorenz A1 - Berner, Julius T1 - Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning T2 - Proceedings of the 39th International Conference on Machine Learning, PMLR N2 - The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations based on associated stochastic differential equations (SDEs), which allow the minimization of corresponding losses using gradient-based optimization methods. In respective numerical implementations it is therefore crucial to rely on adequate gradient estimators that exhibit low variance in order to reach convergence accurately and swiftly. In this article, we rigorously investigate corresponding numerical aspects that appear in the context of linear Kolmogorov PDEs. In particular, we systematically compare existing deep learning approaches and provide theoretical explanations for their performances. Subsequently, we suggest novel methods that can be shown to be more robust both theoretically and numerically, leading to substantial performance improvements. Y1 - 2022 VL - 162 SP - 18649 EP - 18666 ER - TY - CHAP A1 - Schneider, Philipp-Immanuel A1 - Zschiedrich, Lin A1 - Hammerschmidt, Martin A1 - Kuen, Lilli A1 - Sekulic, Ivan A1 - Kluge, Julien A1 - Leykauf, Bastian A1 - Krutzik, Markus A1 - Burger, Sven T1 - Boosting quantum optics experiments with Bayesian optimization T2 - Proc. SPIE Y1 - 2022 U6 - https://doi.org/10.1117/12.2632419 VL - 12227 SP - 122270F ER - TY - CHAP A1 - Krüger, Jan A1 - Manley, Phillip A1 - Zschiedrich, Lin A1 - Hammerschmidt, Martin A1 - Schneider, Philipp-Immanuel A1 - Köning, Rainer A1 - Bodermann, Bernd T1 - Untersuchung des Schwingungseinflusses auf gemessene Punktspreizfunktionen in der optischen Mikroskopie T2 - Proc. DGaO Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0287-2022-P005-6 SP - P5 ER - TY - CHAP A1 - Manley, Phillip A1 - Krüger, Jan A1 - Zschiedrich, Lin A1 - Hammerschmidt, Martin A1 - Bodermann, Bernd A1 - Köning, Rainer A1 - Schneider, Philipp-Immanuel T1 - Elementary, my dear Zernike: model order reduction for accelerating optical dimensional microscopy T2 - EPJ Web Conf. Y1 - 2022 U6 - https://doi.org/10.1051/epjconf/202226610010 VL - 266 SP - 10010 ER - TY - CHAP A1 - Sikorski, Alexander A1 - Rabben, Robert Julian A1 - Chewle, Surahit A1 - Weber, Marcus ED - Fackeldey, K. T1 - Capturing the Macroscopic Behaviour of Molecular Dynamics with Membership Functions T2 - Mathematical Optimization for Machine Learning: Proceedings of the MATH+ Thematic Einstein Semester 2023 N2 - Markov processes serve as foundational models in many scientific disciplines, such as molecular dynamics, and their simulation forms a common basis for analysis. While simulations produce useful trajectories, obtaining macroscopic information directly from microstate data presents significant challenges. This paper addresses this gap by introducing the concept of membership functions being the macrostates themselves. We derive equations for the holding times of these macrostates and demonstrate their consistency with the classical definition. Furthermore, we discuss the application of the ISOKANN method for learning these quantities from simulation data. In addition, we present a novel method for extracting transition paths based on the ISOKANN results and demonstrate its efficacy by applying it to simulations of the 𝜇-opioid receptor. With this approach we provide a new perspective on analyzing the macroscopic behaviour of Markov systems. Y1 - 2024 U6 - https://doi.org/10.1515/9783111376776-004 SP - 41 EP - 58 PB - De Gruyter ER - TY - CHAP A1 - Steyer, Joshua A1 - Chegini, Fatemeh A1 - Potse, Mark A1 - Loewe, Axel A1 - Weiser, Martin T1 - Continuity of Microscopic Cardiac Conduction in a Computational Cell-by-Cell Model T2 - 2023 Computing in Cardiology Conference (CinC) N2 - Conduction velocity in cardiac tissue is a crucial electrophysiological parameter for arrhythmia vulnerability. Pathologically reduced conduction velocity facilitates arrhythmogenesis because such conduction velocities decrease the wavelength with which re-entry may occur. Computational studies on CV and how it changes regionally in models at spatial scales multiple times larger than actual cardiac cells exist. However, microscopic conduction within cells and between them have been studied less in simulations. In this work, we study the relation of microscopic conduction patterns and clinically observable macroscopic conduction using an extracellular-membrane-intracellular model which represents cardiac tissue with these subdomains at subcellular resolution. By considering cell arrangement and non-uniform gap junction distribution, it yields anisotropic excitation propagation. This novel kind of model can for example be used to understand how discontinuous conduction on the microscopic level affects fractionation of electrograms in healthy and fibrotic tissue. Along the membrane of a cell, we observed a continuously propagating activation wavefront. When transitioning from one cell to the neighbouring one, jumps in local activation times occurred, which led to lower global conduction velocities than locally within each cell. Y1 - 2023 U6 - https://doi.org/10.22489/CinC.2023.385 SN - 2325-887X VL - 50 PB - Computing in Cardiology ER - TY - CHAP A1 - Chegini, Fatemeh A1 - Froehly, Algiane A1 - Huynh, Ngoc Mai Monica A1 - Pavarino, Luca A1 - Potse, Mark A1 - Scacchi, Simone A1 - Weiser, Martin T1 - Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution T2 - 10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023 N2 - The cardiac extracellular-membrane-intracellular (EMI) model enables the precise geometrical representation and resolution of aggregates of individual myocytes. As a result, it not only yields more accurate simulations of cardiac excitation compared to homogenized models but also presents the challenge of solving much larger problems. In this paper, we introduce recent advancements in three key areas: (i) the creation of artificial, yet realistic grids, (ii) efficient higher-order time stepping achieved by combining low-overhead spatial adaptivity on the algebraic level with progressive spectral deferred correction methods, and (iii) substructuring domain decomposition preconditioners tailored to address the complexities of heterogeneous problem structures. The efficiency gains of these proposed methods are demonstrated through numerical results on cardiac meshes of different sizes. Y1 - 2023 UR - https://www.scipedia.com/public/2023f U6 - https://doi.org/10.23967/c.coupled.2023.004 ER - TY - CHAP A1 - Steyer, Joshua A1 - Chegini, Fatemeh A1 - Starý, Tomas A1 - Potse, Mark A1 - Weiser, Martin A1 - Loewe, Axel T1 - Electrograms in a Cardiac Cell-by-Cell Model T2 - Workshop Biosignals 2024 N2 - Cardiac electrograms are an important tool to study the spread of excitation waves inside the heart, which in turn underlie muscle contraction. Electrograms can be used to analyse the dynamics of these waves, e.g. in fibrotic tissue. In computational models, these analyses can be done with greater detail than during minimally invasive in vivo procedures. Whilst homogenised models have been used to study electrogram genesis, such analyses have not yet been done in cellularly resolved models. Such high resolution may be required to develop a thorough understanding of the mechanisms behind abnormal excitation patterns leading to arrhythmias. In this study, we derived electrograms from an excitation propagation simulation in the Extracellular, Membrane, Intracellular (EMI) model, which represents these three domains explicitly in the mesh. We studied the effects of the microstructural excitation dynamics on electrogram genesis and morphology. We found that electrograms are sensitive to the myocyte alignment and connectivity, which translates into micro-fractionations in the electrograms. Y1 - 2024 U6 - https://doi.org/10.47952/gro-publ-194 ER - TY - CHAP A1 - Weiser, Martin A1 - Chegini, Fatemeh T1 - Adaptive multirate integration of cardiac electrophysiology with spectral deferred correction methods T2 - CMBE22 - 7th International Conference on Computational & Mathematical Biomedical Engineering N2 - The highly localized dynamics of cardiac electrophysiology models call for adaptive simulation methods. Unfortunately, the overhead incurred by classical mesh adaptivity turns out to outweigh the performance improvements achieved by reducing the problem size. Here, we explore a different approach to adaptivity based on algebraic degree of freedom subset selection during spectral deferred correction sweeps, which realizes a kind of multirate higher order integration. Numerical experience indicates a significant performance increase compared to uniform simulations. Y1 - 2022 SP - 528 EP - 531 ER - TY - CHAP A1 - Kostre, Margarita A1 - Sunkara, Vikram A1 - Djurdjevac Conrad, Natasa T1 - Inference of historical influence networks T2 - International Conference on Complex Networks & Their Applications Proceedings N2 - We study the romanization process of northern Africa from 50 BC till 300 AD. Our goal is to infer the communication strength between different subregions, based on the evolution of the status of cities. Herefore, we use the general inverse infection model, that infers the weights of a known underlying network, given observations of the spreading on this network. As infection process we choose the SI metapopulation model, where I stands for a city with a Roman status. To solve the minimization problem we use the particle swarm optimization algorithm with a specific choice of parameters. Y1 - 2021 U6 - https://doi.org/10.12752/8558 SP - 110 EP - 113 ET - International Conference on Complex Networks & Their Applications ER -