Bibliothek

Beschreibung: The Fairness-Oriented Crew Rostering Problem (FCRP) considers the joint optimization of attractiveness and fairness in cyclic crew rostering. Like many problems in scheduling and logistics, the combinatorial complexity of cyclic rostering causes exact methods to fail for large-scale practical instances. In case of the FCRP, this is accentuated by the additionally imposed fairness requirements. Hence, heuristic methods are necessary. We present a three-phase heuristic for the FCRP combining column generation techniques with variable-depth neighborhood search. The heuristic exploits different mathematical formulations to find feasible solutions and to search for improvements. We apply our methodology to practical instances from Netherlands Railways (NS), the main passenger railway operator in the Netherlands Our results show the three-phase heuristic finds good solutions for most instances and outperforms a state-of-the-art commercial solver.

Beschreibung: Docking is a fundamental problem in computational biology and drug discovery that seeks to predict a ligand’s binding mode and affinity to a target protein. However, the large search space size and the complexity of the underlying physical interactions make docking a challenging task. Here, we review a docking method, based on the ant colony optimization algorithm, that ranks a set of candidate ligands by solving a minimization problem for each ligand individually. In addition, we propose an augmented version that takes into account all energy functions collectively, allowing only one minimization problem to be solved. The results show that our modification outperforms in accuracy and efficiency.

Beschreibung: This publication comprises the Software Management Plan (SMP) developed in the HPO-Navi project. The project was funded in the Literature and Information System (LIS) track of the DFG with the aim of increasing the maturity level of scientific software under development, developing improved measures for the quality assurance of this software and for long-term availability. The Ubiquity Generator Framework (UG) software developed in the project provides a software infrastructure to make existing sequential implementations HPC-capable. The UG framework is of interest to developers of specialized optimization algorithms and can be used directly to solve specific problem classes in the field of scientific computing. Due to the naturally high software technology hurdles on HPC systems, UG was initially a highly specialized tool and could only be used to a limited extent without the involvement of the main developer. The central challenge of the project was to create a mechanism for the sustainable development and permanent provision and archiving of the research software. The aim was for UG to achieve the status of a "software product" with implementation of the following project content: - Documentation of the software: a description of the API and the simple connection of further basic solvers, installation instructions for various target platforms and a description of the structure and documentation of the source code as a basis for the distributed sustainable development of UG. - Development of missing user functions of UG: increased platform independence for shared memory parallelization and better logging function for the analysis and verification of results. - Development of a sample data management plan for future research projects that want to use UG and document their research results according to DFG standards for good scientific practice. - Quality assurance: by defining code guidelines, uniform concepts and criteria for the qualitative evaluation of new functions and implementing standards for code review and processes for continuous integration. A complementary goal was to improve the provision, accessibility and long-term reusability of the research software. - Use of an open Git server as a distributed development platform, provision of a download server for releases and sustainable storage of the software code and the associated meta-information. - Improved presentation and visibility through publication in publicly accessible repositories. This includes the prototypical extension of the OPUS 4 repository software widely used in Germany as a means of publishing software with a landing page that can be resolved via a DOI, and improved linking and presentation of UG in swMATH. - Digital long-term archiving: experimental inclusion of software code in an OAIS-compliant digital archiving system and evaluation of the approach in the areas of digital archiving and research data management.

Beschreibung: Molecular dynamics simulations are one of the methods in scientific computing that benefit from GPU acceleration. For those devices, SYCL is a promising API for writing portable codes. In this paper, we present the case study of HAL’s MD package that has been successfully migrated from CUDA to SYCL. We describe the different strategies that we followed in the process of porting the code. Following these strategies, we achieved code portability across major GPU vendors. Depending on the actual kernels, both significant performance improvements and regressions are observed. As a side effect of the migration process, we obtained impressing speedups also for execution on CPUs.

Beschreibung: The use of stand-alone, network-coupled Field Programmable Gate Array (FPGA) accelerators is intended to significantly increase the energy efficiency of HPC applications and thus also of HPC data centers. A loose coupling between the nodes of the HPC data center and the FPGAs is established through the high-speed network of the data center. This allows greater flexibility in combining different nodes and accelerators. Both the resulting energy savings and the increased flexibility through the network connection, enable the economical use of FPGAs. This work presents a communication stack to integrate the so-called Network-attached Accelerator (NAA) into the HPC data center. A low-level Remote Direct Memory Access (RDMA) Application Programming Interface (API) and a high-level Remote Procedure Call (RPC) API is designed on top of the RDMA over Converged Ethernet v2 (RoCEv2) communication stack. The experimental results over 100 Gbps RoCEv2 show that our design and implementation deliver performance close to the theoretical maximum.

Beschreibung: Für die Energiesystemforschung sind Software-Modelle ein Kernelement zur Analyse von Szenarien. Das Forschungsprojekt UNSEEN hatte das Ziel eine bisher unerreichte Anzahl an modellbasierten Energieszenarien zu berechnen, um Unsicherheiten – vor allem unter Nutzung linear optimierender Energiesystem-Modelle - besser bewerten zu können. Hierfür wurden umfangreiche Parametervariationen auf Energieszenarien angewendet und das wesentliche methodische Hindernis in diesem Zusammenhang adressiert: die rechnerische Beherrschbarkeit der zu lösenden mathematischen Optimierungsprobleme. Im Vorläuferprojekt BEAM-ME wurde mit der Entwicklung und Anwendung des Open-Source-Lösers PIPS-IPM++ die Grundlage für den Einsatz von High-Performance-Computing (HPC) zur Lösung dieser Modelle gelegt. In UNSEEN war dieser Löser die zentrale Komponente eines Workflows, welcher zur Generierung, Lösung und multi-kriteriellen Bewertung von Energieszenarien auf dem Hochleistungscomputer JUWELS am Forschungszentrum Jülich implementiert wurde. Zur effizienten Generierung und Kommunikation von Modellinstanzen für Methoden der mathematischen Optimierung auf HPC wurde eine weitere Workflow-Komponente von der GAMS Software GmbH entwickelt: der Szenariogenerator. Bei der Weiterentwicklung von Lösungsalgorithmen für linear optimierende Energie-Systemmodelle standen gemischt-ganzzahlige Optimierungsprobleme im Fokus, welche für die Modellierung konkreter Infrastrukturen und Maßnahmen zur Umsetzung der Energiewende gelöst werden müssen. Die in diesem Zusammenhang stehenden Arbeiten zur Entwicklung von Algorithmen wurden von der Technischen Universität Berlin verantwortet. Bei Design und Implementierung dieser Methoden wurde sie vom Zuse Instituts Berlin unterstützt.

Beschreibung: From August 2014 to September 2016, the ESA operated the Rosetta spacecraft mission alongside with comet 67P/Churyumov-Gerasimenko (67P). The mission provided valuable long-term data on the comet’s nucleus, including its volume, mass, tensor of inertia, spatial position of the orbital trajectory, and rotational state.

Beschreibung: Regolith is formed through weathering of the local rock by meteorite bombardment, space weathering (Pieters & Noble, 2016) and thermal erosion (Delbo et al., 2014). In the case of the Moon, the space weathering effects and diurnal temperature variations are reduced towards the poles. The aim of this study is to investigate whether the lunar regolith properties derived from the comparison of regolith temperatures measured by the Diviner radiometer (Paige et al., 2010) on board the Lunar Reconnaissance Orbiter (LRO) with simulated temperatures derived from a microphysical thermal model show a latitudinal dependence. The developed microphysical thermal model expands upon previous models by more directly simulating regolith properties, such as grain radius and volume filling factor.

Beschreibung: Die Metadatenqualität bestimmt wesentlich den Nutzen und Wert von Kulturerbedaten. ‚Gute‘ Metadaten erhöhen die Auffindbarkeit, Interoperabilität und Nutzbarkeit von Daten signifikant. Mit Blick auf Retrieval bzw. Discovery, Vernetzung im Kontext von Linked Open Data und wissenschaftliches Data Mining hängt die Qualität dabei wesentlich von der Verwendung von maschinenlesbaren kontrollierten Vokabularen ab. Diese wird in der vorliegenden Arbeit quantitativ untersucht. Als Datengrundlage dienen die in der Deutschen Digitalen Bibliothek aggregierten Metadaten aus Berliner Museen (ca. 1,2 Millionen Metadatenobjekte im LIDO-Format)

Beschreibung: We study a functional autoregressive model for high-frequency time series. We approach the estimation of the proposed model using a Mixed Integer Optimisation method. The proposed model captures serial dependence in the functional time series by including high-dimensional curves. We illustrate our methodology on large-scale natural gas network data. Our model provides more accurate day-ahead hourly out-of-sample forecast of the gas in and out-flows compared to alternative prediction models.

Beschreibung: The present study investigates the stability of a tangential-velocity discontinuity in porous media during the withdrawing and injecting processes of natural gases from and into an underground gas storage. The focus is placed on analyzing the impact of inertia forces on the interface stability using the Forchheimer equations. Other publications have relied primarily on Darcy's law to describe flow stability in porous media. However, Darcy's law only adequately describes flows in which viscous forces dominate over inertia forces. As the flow rate increases, the significance of inertia forces becomes more pronounced, and Darcy's law becomes insufficient for considering such flows. Our findings indicate that even a slight consideration of the inertia effect leads to permanent destabilization of the discontinuity interface, regardless of the fluid viscosity or the Mach number. In contrast, when the inertia effect is neglected, the interface is stabilized across the entire Mach number range if the fluid viscosity is strong enough.

Beschreibung: With the emergence of ”Big Data” the analysis of large data sets of high-dimensional energy time series in network structures have become feasible. However, building large-scale data-driven and computationally efficient models to accurately capture the underlying spatial and temporal dynamics and forecast the multivariate time series data remains a great challenge. Additional constraints make the problem more challenging to solve with conventional methods. For example, to ensure the security of supply, energy networks require the demand and supply to be balanced. This paper introduces a novel large-scale Hierarchical Network Regression model with Relaxed Balance constraint (HNR-RB) to investigate the network dynamics and predict multistep-ahead flows in the natural gas transmission network, where the total in- and out-flows of the network have to be balanced over a period of time. We concurrently address three main challenges: high dimensionality of networks with more than 100 nodes, unknown network dynamics, and constraint of balanced supply and demand in the network. The effectiveness of the proposed model is demonstrated through a real-world case study of forecasting demand and supply in a large-scale natural gas transmission network. The results demonstrate that HNR-RB outperforms alternative models for short- and mid-term horizons.

Beschreibung: Tai256c is the largest unsolved quadratic assignment problem (QAP) instance in QAPLIB. It is known that QAP tai256c can be converted into a 256 dimensional binary quadratic optimization problem (BQOP) with a single cardinality constraint which requires the sum of the binary variables to be 92. As the BQOP is much simpler than the original QAP, the conversion increases the possibility to solve the QAP. Solving exactly the BQOP, however, is still very difficult. Indeed, a 1.48% gap remains between the best known upper bound (UB) and lower bound (LB) of the unknown optimal value. This paper shows that the BQOP admits a nontrivial symmetry, a property that makes the BQOP very hard to solve. The symmetry induces equivalent subproblems in branch and bound (BB) methods. To effectively improve the LB, we propose an efficient BB method that incorporates a doubly nonnegative relaxation, the standard orbit branching and a technique to prune equivalent subproblems. With this BB method, a new LB with 1.25% gap is successfully obtained, and computing an LB with 1.0% gap is shown to be still quite difficult.

Beschreibung: Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method.

Beschreibung: Existing planning approaches for onshore wind farm siting and network integration often do not meet minimum cost solutions or social and environmental considerations. In this paper, we develop an approach for the multi-objective optimization of turbine locations and their network connection using a Quota Steiner tree problem. Applying a novel transformation on a known directed cut formulation, reduction techniques, and heuristics, we design an exact solver that makes large problem instances solvable and outperforms generic MIP solvers. Although our case studies in selected regions of Germany show large trade-offs between the objective criteria of cost and landscape impact, small burdens on one criterion can significantly improve the other criteria. In addition, we demonstrate that contrary to many approaches for exclusive turbine siting, network integration must be simultaneously optimized in order to avoid excessive costs or landscape impacts in the course of a wind farm project. Our novel problem formulation and the developed solver can assist planners in decision making and help optimize wind farms in large regions in the future.

Beschreibung: Virtual Screening Dataset for the paper "Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists" by Secker et al. (https://doi.org/10.1186/s13321-023-00746-4)

Beschreibung: Humans have a unique capacity to innovate, transmit and rely on complex, cumulative culture for survival. While an important body of work has attempted to explore the role of changes in the size and interconnectedness of populations in determining the persistence, diversity and complexity of material culture, results have achieved limited success in explaining the emergence and spatial distribution of cumulative culture over our evolutionary trajectory. Here, we develop a spatio-temporally explicit agent-based model to explore the role of environmentally driven changes in the population dynamics of hunter–gatherer communities in allowing the development, transmission and accumulation of complex culture. By modelling separately demography- and mobility-driven changes in interaction networks, we can assess the extent to which cultural change is driven by different types of population dynamics. We create and validate our model using empirical data from Central Africa spanning 120 000 years. We find that populations would have been able to maintain diverse and elaborate cultural repertoires despite abrupt environmental changes and demographic collapses by preventing isolation through mobility. However, we also reveal that the function of cultural features was also an essential determinant of the effects of environmental or demographic changes on their dynamics. Our work can therefore offer important insights into the role of a foraging lifestyle on the evolution of cumulative culture.

Beschreibung: In this repository are all files necessary to run the agent-based model of the paper "Insights into drivers of mobility and cultural dynamics of African hunter–gatherers over the past 120 000 years", Royal Society Open Science, 10(11), 2023.

Beschreibung: 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.

Beschreibung: MaRDMO, a plugin for the Research Data Management Organiser, was developed in the Mathematical Research Data Initiative to document interdisciplinary workflows using a standardised scheme. Interdisciplinary workflows recorded this way are published directly on the MaRDI portal. In addition, central information is integrated into the MaRDI knowledge graph. Next to the documentation, MaRDMO offers the possibility to retrieve existing interdisciplinary workflows from the MaRDI Knowledge Graph to allow the reproduction of the initial work and to provide scientists with new researchimpulses. Thus, MaRDMO creates a community-driven knowledge loop that could help to overcome the replication crisis.

Beschreibung: Research data are crucial in mathematics and all scientific disciplines, as they form the foundation for empirical evidence, by enabling the validation and reproducibility of scientific findings. Mathematical research data (MathRD) have become vast and complex, and their interdisciplinary potential and abstract nature make them ubiquitous in various scientific fields. The volume of data and the velocity of its creation are rapidly increasing due to advancements in data science and computing power. This complexity extends to other disciplines, resulting in diverse research data and computational models. Thus, proper handling of research data is crucial both within mathematics and for its manifold connections and exchange with other disciplines. The National Research Data Infrastructure (NFDI), funded by the federal and state governments of Germany, consists of discipline-oriented consortia, including the Mathematical Research Data Initiative (MaRDI). MaRDI has been established to develop services, guidelines and outreach measures for all aspects of MathRD, and thus support the mathematical research community. Research data management (RDM) should be an integral component of every scientific project, and is becoming a mandatory component of grants with funding bodies such as the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation). At the core of RDM are the FAIR (Findable, Accessible, Interoperable, and Reusable) principles. This document aims to guide mathematicians and researchers from related disciplines who create RDM plans. It highlights the benefits and opportunities of RDM in mathematics and interdisciplinary studies, showcases examples of diverse MathRD, and suggests technical solutions that meet the requirements of funding agencies with specific examples. The document is regularly updated to reflect the latest developments within the mathematical community represented by MaRDI.

Beschreibung: Ontologies and knowledge graphs for mathematical algorithms and models are presented, that have been developed by the Mathematical Research Data Initiative. This enables FAIR data handling in mathematics and the applied disciplines. Moreover, challenges of harmonization during the ontology development are discussed.

Beschreibung: The security of lattice-based cryptography relies on the hardness of solving lattice problems. Lattice basis reduction is a strong tool for solving lattice problems, and the block Korkine–Zolotarev (BKZ) reduction algorithm is the de facto standard in cryptanalysis. We propose a parallel algorithm of BKZ-type reduction based on randomization. Randomized copies of an input lattice basis are independently reduced in parallel, while several basis vectors are shared asynchronously among all processes. There is a trade-off between randomization and information sharing; if a substantial amount of information is shared, all processes might work on the same problem, which diminishes the benefit of parallelization. To monitor the balance between randomness and sharing, we propose a new metric to quantify the variety of lattice bases, and we empirically find an optimal parameter of sharing for high-dimensional lattices. We also demonstrate the effectiveness of our parallel algorithm and metric through experiments from multiple perspectives.

Beschreibung: Aims: Interpretation of continuous EEG is a demanding task that requires the expertise of trained neurologists. However, these experts are not always available in many medical centers. As part of the 2023 George B. Moody PhysioNet Challenge, we developed a deep learning based method for analyzing EEG data of comatose patients and predicting prognosis following cardiac arrest. Methods: Our approach is a two-step pipeline that consists of a prediction model and a decision-making strategy. The prediction model is a residual neural network (ResNet-18) that extracts features and makes a prediction based on a short 5-minute EEG recording. In the second step, a majority vote over multiple predictions made for several EEG recordings of a patient determines the final prognosis. Results: Based on 10-fold cross-validation on the training set, we achieved a true positive rate (TPR) of 0.41 for predicting poor outcome while keeping the false positive rate below 0.05 at 72 hours after recovery of spontaneous circulation. On the official challenge leaderboard, our team ZIB_Visual scored 0.426 TPR. Conclusion: Our approach, while simple to implement and execute, faced overfitting challenges during the official competition phase. In this paper, we discuss our implementation and potential improvements to address these issues.

Beschreibung: How many mutually non-attacking queens can be placed on a d-dimensional chessboard of size n? The n-queens problem in higher dimensions is a generalization of the well-known n-queens problem. We provide a comprehensive overview of theoretical results, bounds, solution methods, and the interconnectivity of the problem within topics of discrete optimization and combinatorics. We present an integer programming formulation of the n-queens problem in higher dimensions and several strengthenings through additional valid inequalities. Compared to recent benchmarks, we achieve a speedup in computational time between 15-70x over all instances of the integer programs. Our computational results prove optimality of certificates for several large instances. Breaking additional, previously unsolved instances with the proposed methods is likely possible. On the primal side, we further discuss heuristic approaches to constructing solutions that turn out to be optimal when compared to the IP. We conclude with preliminary results on the number and density of the solutions.

Beschreibung: We previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. The design process of NFEPP was based on mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands, recognizing that GPCRs function differently under pathological versus healthy conditions. We now present an additional and novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels and their dependence on parameters of inflamed and healthy tissue (pH, radicals). The model is validated against in vitro experimental data for the ligands NFEPP and fentanyl at different pH values and radical concentrations. We observe markedly reduced binding affinity and calcium channel inhibition for NFEPP at normal pH compared to lower pH, in contrast to the effect of fentanyl. For increasing radical concentrations, we find enhanced constitutive G-protein activation but reduced ligand binding affinity. Assessing the different effects, the results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.

Beschreibung: The chemical diffusion master equation (CDME) describes the probabilistic dynamics of reaction--diffusion systems at the molecular level [del Razo et al., Lett. Math. Phys. 112:49, 2022]; it can be considered the master equation for reaction--diffusion processes. The CDME consists of an infinite ordered family of Fokker--Planck equations, where each level of the ordered family corresponds to a certain number of particles and each particle represents a molecule. The equations at each level describe the spatial diffusion of the corresponding set of particles, and they are coupled to each other via reaction operators --linear operators representing chemical reactions. These operators change the number of particles in the system, and thus transport probability between different levels in the family. In this work, we present three approaches to formulate the CDME and show the relations between them. We further deduce the non-trivial combinatorial factors contained in the reaction operators, and we elucidate the relation to the original formulation of the CDME, which is based on creation and annihilation operators acting on many-particle probability density functions. Finally we discuss applications to multiscale simulations of biochemical systems among other future prospects.

Beschreibung: Opioids are essential pharmaceuticals due to their analgesic properties, however, lethal side effects, addiction, and opioid tolerance are extremely challenging. The development of novel molecules targeting the μ-opioid receptor (MOR) in inflamed, but not in healthy tissue, could significantly reduce these unwanted effects. Finding such novel molecules can be achieved by maximizing the binding affinity to the MOR at acidic pH while minimizing it at neutral pH, thus combining two conflicting objectives. Here, this multi-objective optimal affinity approach is presented, together with a virtual drug discovery pipeline for its practical implementation. When applied to finding pH-specific drug candidates, it combines protonation state-dependent structure and ligand preparation with high-throughput virtual screening. We employ this pipeline to characterize a set of MOR agonists identifying a morphine-like opioid derivative with higher predicted binding affinities to the MOR at low pH compared to neutral pH. Our results also confirm existing experimental evidence that NFEPP, a previously described fentanyl derivative with reduced side effects, and recently reported β-fluorofentanyls and -morphines show an increased specificity for the MOR at acidic pH when compared to fentanyl and morphine. We further applied our approach to screen a 〉50K ligand library identifying novel molecules with pH-specific predicted binding affinities to the MOR. The presented differential docking pipeline can be applied to perform multi-objective affinity optimization to identify safer and more specific drug candidates at large scale.

Beschreibung: Measurable levels of immunoglobulin G antibodies develop after infections with and vaccinations against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). These antibody levels are dynamic: due to waning, antibody levels will drop over time. During the COVID-19 pandemic, multiple models predicting infection dynamics were used by policymakers to support the planning of public health policies. Explicitly integrating antibody and waning effects into the models is crucial for reliable calculations of individual infection risk. However, only few approaches have been suggested that explicitly treat these effects. This paper presents a methodology that explicitly models antibody levels and the resulting protection against infection for individuals within an agent-based model. The model was developed in response to the complexity of different immunization sequences and types and is based on neutralization titer studies. This approach allows complex population studies with explicit antibody and waning effects. We demonstrate the usefulness of our model in two use cases.

Beschreibung: In this letter we present a stochastic dynamic model which can explain economic cycles. We show that the macroscopic description yields a complex dynamical landscape consisting of multiple stable fixed points, each corresponding to a split of the population into a large low and a small high income group. The stochastic fluctuations induce switching between the resulting metastable states, and excitation oscillations just below a deterministic bifurcation. The shocks are caused by the decisions of a few agents who have a disproportionate influence over the macroscopic state of the economy due to the unequal distribution of wealth among the population. The fluctuations have a long-term effect on the growth of economic output and lead to business cycle oscillations exhibiting coherence resonance, where the correlation time is controlled by the population size which is inversely proportional to the noise intensity.

Beschreibung: 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.

Beschreibung: In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model y with a surrogate model y(s) that can be evaluated quickly leads to a significant speedup. The approximation quality of the surrogate model depends strongly on the number, position, and accuracy of the sample points. With an additional finite computational budget, this leads to a problem of (computer) experimental design. In contrast to the selection of sample points, the trade-off between accuracy and effort has hardly been studied systematically. We therefore propose an adaptive algorithm to find an optimal design in terms of position and accuracy. Pursuing a sequential design by incrementally appending the computational budget leads to a convex and constrained optimization problem. As a surrogate, we construct a Gaussian process regression model. We measure the global approximation error in terms of its impact on the accuracy of the identified parameter and aim for a uniform absolute tolerance, assuming that y(s) is computed by finite element calculations. A priori error estimates and a coarse estimate of computational effort relate the expected improvement of the surrogate model error to computational effort, resulting in the most efficient combination of sample point and evaluation tolerance. We also allow for improving the accuracy of already existing sample points by continuing previously truncated finite element solution procedures.