@inproceedings{CheginiFroehlyHuynhetal., author = {Chegini, Fatemeh and Froehly, Algiane and Huynh, Ngoc Mai Monica and Pavarino, Luca and Potse, Mark and Scacchi, Simone and Weiser, Martin}, title = {Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution}, series = {10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023}, booktitle = {10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023}, doi = {10.23967/c.coupled.2023.004}, abstract = {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.}, language = {en} } @inproceedings{SteyerCheginiStaryetal., author = {Steyer, Joshua and Chegini, Fatemeh and Star{\´y}, Tomas and Potse, Mark and Weiser, Martin and Loewe, Axel}, title = {Electrograms in a Cardiac Cell-by-Cell Model}, abstract = {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.}, language = {en} } @article{BartelsFisikopoulosWeiser, author = {Bartels, Tinko and Fisikopoulos, Vissarion and Weiser, Martin}, title = {Fast Floating-Point Filters for Robust Predicates}, series = {BIT Numerical Mathematics}, volume = {63}, journal = {BIT Numerical Mathematics}, doi = {10.1007/s10543-023-00975-x}, abstract = {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.}, language = {en} } @incollection{DeuflhardWeiser1997, author = {Deuflhard, Peter and Weiser, Martin}, title = {Local inexact Newton multilevel FEM for nonlinear elliptic problems}, series = {Computational science for the 21st century}, booktitle = {Computational science for the 21st century}, editor = {et al. Bristeau, M.-O.}, publisher = {Chichester: John Wiley \& Sons.}, pages = {129 -- 138}, year = {1997}, language = {en} } @article{NiemannUramWolfetal., author = {Niemann, Jan-Hendrik and Uram, Samuel and Wolf, Sarah and Conrad, Natasa Djurdjevac and Weiser, Martin}, title = {Multilevel Optimization for Policy Design with Agent-Based Epidemic Models}, series = {Computational Science}, volume = {77}, journal = {Computational Science}, doi = {10.1016/j.jocs.2024.102242}, pages = {102242}, abstract = {Epidemiological models can not only be used to forecast the course of a pandemic like COVID-19, but also to propose and design non-pharmaceutical interventions such as school and work closing. In general, the design of optimal policies leads to nonlinear optimization problems that can be solved by numerical algorithms. Epidemiological models come in different complexities, ranging from systems of simple ordinary differential equations (ODEs) to complex agent-based models (ABMs). The former allow a fast and straightforward optimization, but are limited in accuracy, detail, and parameterization, while the latter can resolve spreading processes in detail, but are extremely expensive to optimize. We consider policy optimization in a prototypical situation modeled as both ODE and ABM, review numerical optimization approaches, and propose a heterogeneous multilevel approach based on combining a fine-resolution ABM and a coarse ODE model. Numerical experiments, in particular with respect to convergence speed, are given for illustrative examples.}, language = {en} } @inproceedings{SemlerWeiser, author = {Semler, Phillip and Weiser, Martin}, title = {Adaptive Gradient Enhanced Gaussian Process Surrogates for Inverse Problems}, series = {Proceedings of the MATH+ Thematic Einstein Semester on Mathematical Optimization for Machine Learning}, booktitle = {Proceedings of the MATH+ Thematic Einstein Semester on Mathematical Optimization for Machine Learning}, abstract = {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.}, language = {en} } @inproceedings{SteyerCheginiPotseetal., author = {Steyer, Joshua and Chegini, Fatemeh and Potse, Mark and Loewe, Axel and Weiser, Martin}, title = {Continuity of Microscopic Cardiac Conduction in a Computational Cell-by-Cell Model}, series = {2023 Computing in Cardiology Conference (CinC)}, volume = {50}, booktitle = {2023 Computing in Cardiology Conference (CinC)}, publisher = {Computing in Cardiology}, issn = {2325-887X}, doi = {10.22489/CinC.2023.385}, abstract = {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.}, language = {en} } @article{SemlerWeiser, author = {Semler, Phillip and Weiser, Martin}, title = {Adaptive Gaussian Process Regression for Efficient Building of Surrogate Models in Inverse Problems}, series = {Inverse Problems}, volume = {39}, journal = {Inverse Problems}, number = {12}, doi = {10.1088/1361-6420/ad0028}, pages = {125003}, abstract = {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.}, language = {en} } @inproceedings{CheginiSteinkeWeiser, author = {Chegini, Fatemeh and Steinke, Thomas and Weiser, Martin}, title = {Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods}, abstract = {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.}, language = {en} } @inproceedings{AndresArconesWeiserKoutsourelakisetal., author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Faidon-Stelios and Unger, J{\"o}rg F.}, title = {Evaluation of Model Bias Identification Approaches Based on Bayesian Inference and Applications to Digital Twins}, series = {5th ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering}, booktitle = {5th ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering}, pages = {1 -- 15}, abstract = {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.}, language = {en} }