Rolf Krause

• Prof. Dr. rer. nat - Chair for Advanced Scientific
• Managing Director at Università della Svizzera italiana

We introduce a simple, low-latency model for the simulation and analysis of energy transition pathways in Switzerland. It is designed as the calculation and data storage layer of the "Ensured Energy" game (Figure 1), developed as part of the SFOE SWEET-SURE project.

Parallel training methods are increasingly relevant in machine learning (ML) due to the continuing growth in model and dataset sizes. We propose a variant of the Additively Preconditioned Trust-Region Strategy (APTS) for training deep neural networks (DNNs). The proposed APTS method utilizes a data-parallel approach to construct a nonlinear precond...

Precision cardiology based on cardiac digital twins requires accurate simulations of cardiac arrhythmias. However, detailed models, such as the monodomain model, are computationally costly and have limited applicability in practice. Thus, it desirable to have fast models that can still represent the main physiological features presented during card...

We introduce a two-level trust-region method (TLTR) for solving unconstrained nonlinear optimization problems. Our method uses a composite iteration step, which is based on two distinct search directions. The first search direction is obtained through minimization in the full/high-resolution space, ensuring global convergence to a critical point. T...

Geological applications of phase-field methods for fracture are notably scarce. This work conducts a numerical examination of the applicability of standard phase-field models in reproducing jointing within sedimentary layers. We explore how the volumetric-deviatoric split alongside the AT1 and AT2 phase-field formulations have several advantages in...

Simulation of the monodomain equation, crucial for modeling the heart's electrical activity, faces scalability limits when traditional numerical methods only parallelize in space. To optimize the use of large multi-processor computers by distributing the computational load more effectively, time parallelization is essential. We introduce a high-ord...

Fully explicit stabilized multirate (mRKC) methods are well-suited for the numerical solution of large multiscale systems of stiff ordinary differential equations thanks to their improved stability properties. To demonstrate their efficiency for the numerical solution of stiff, multiscale, nonlinear parabolic PDE's, we apply mRKC methods to the mon...

We consider a Lipschitz domain Ω C Rd, d = 23 and a triangulation T on Ω.

Context. Approximated forms of the R II and R III redistribution matrices are frequently applied to simplify the numerical solution of the radiative transfer problem for polarized radiation, taking partial frequency redistribution (PRD) effects into account. A widely used approximation for R III is to consider its expression under the assumption of...

The efficient construction of an anatomical model is one of the major challenges of patient-specific in-silico models of the human heart. Current methods frequently rely on linear statistical models, allowing no advanced topological changes, or requiring medical image segmentation followed by a meshing pipeline, which strongly depends on image reso...

We propose to enhance the training of physics-informed neural networks (PINNs). To this aim, we introduce nonlinear additive and multiplicative preconditioning strategies for the widely used L-BFGS optimizer. The nonlinear preconditioners are constructed by utilizing the Schwarz domain-decomposition framework, where the parameters of the network ar...

Gap junction arrangement is a major determinant of cardiac conduction velocity. Importantly, structural remodeling of the myocardium may lead to pathological CV and a pro-arrhythmic substrate. In this work we aim at quantifying the side-to-side conduction velocity in a sub-micrometer model of the myocardium that accounts for gap junctions. We consi...

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,...

Context. Approximated forms of the R II and R III redistribution matrices are frequently applied to simplify the numerical solution of the radiative transfer problem for polarized radiation, taking partial frequency redistribution (PRD) effects into account, A widely used approximation for R III is to consider its expression under the assumption of...

The numerical solution of partial differential equations (PDEs) is often carried out using discretization techniques, such as the finite element method (FEM), and typically requires the solution of a nonlinear system of equations. These nonlinear systems are often solved using some variant of the Newton method, which utilizes a sequence of iterates...

Multigrid (MG) methods are among the most successful strategies for solving linear systems arising from discretized elliptic equations. The main idea is to combine different levels of approximation in a multilevel hierarchy to compute the solution: it is possible to show that this algorithm is effective on the entire spectrum, thus leading to an op...

Multilevel methods are known to be optimal solution strategies for systems arising from the discretization of, usually elliptic, PDEs, as their convergence rate is often independent of the problem size and the number of required arithmetic operations grows proportionally with the number of unknowns. These methods were originally designed for uncons...

Reliable cardiac excitation predictions depend not only on accurate geometric and physiological models, usually formulated as PDEs, and our ability to solve those faithfully, but also on the model’s correct parameterization.

We propose a boundary element method for the accurate solution of the cell-by-cell bidomain model of electrophysiology. The cell-by-cell model, also called Extracellular-Membrane-Intracellular (EMI) model, is a system of reaction-diffusion equations describing the evolution of the electric potential within each domain: intra- and extra-cellular spa...

We examine the dual formulation of the frictionless Signorini problem for a deformable body in contact with a rigid obstacle. We discretize the problem by means of the finite element method. Since the dual formulation solves directly for the stress variable and is not affected by locking, it is very attractive for many engineering applications. How...

Cell migration is a pivotal biological process, whose dysregulation is found in many diseases including inflammation and cancer. Advances in microscopy technologies allow now to study cell migration in vitro, within engineered microenvironments that resemble in vivo conditions. However, to capture an entire 3D migration chamber for extended periods...

One of the state-of-the-art strategies for predicting crack propagation, nucleation, and interaction is the phase-field approach. Despite its reliability and robustness, the phase-field approach suffers from burdensome computational cost, caused by the non-convexity of the underlying energy functional and a large number of unknowns required to reso...

Live-cell imaging allows the study of apoptosis at cellular level, highlighting morphological hallmarks such as nuclear shrinkage, membrane blebbing, and cell disruption. Identifying the exact location and timing of this process is essential to foster the understanding of its spatial-temporal regulation. However, the analysis of live-cell imaging d...

We propose a nonlinear additive Schwarz method for solving nonlinear optimization problems with bound constraints. Our method is used as a "right-preconditioner" for solving the first-order optimality system arising within the sequential quadratic programming (SQP) framework using Newton's method. The algorithmic scalability of this preconditioner...

Images conveniently capture the result of physical processes, representing rich source of information for data driven medicine, engineering, and science. The modeling of an image as a graph allows the application of graph-based algorithms for content analysis. Amongst these, one of the most used is the Dijkstra Single Source Shortest Path algorithm...

Background Cardiac resynchronization therapy (CRT) is clinically proven in patients with heart failure (HF) and left bundle branch block (LBBB). However, approximately 30% of CRT individuals are non responsive to the therapy while factors affecting electromechanical coupling remain not fully understood. Objective To determine the optimal combinati...

It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As consequence of this, and due to the conservative nature of the problem, we adopt a finite volume elements discretization approach over a generic non-uniform mesh. We focus on grids mapped by a smooth...

Aims Electromechanical coupling in patients receiving cardiac resynchronization therapy (CRT) is not fully understood. Our aim was to determine the best combination of electrical and mechanical substrates associated with effective CRT. Methods and results Sixty-two patients were prospectively enrolled from two centres. Patients underwent 12-lead e...

We present an efficient and massively parallel solution strategy for the transfer problem of polarized radiation. We consider a 3D medium out of local thermodynamic equilibrium, accounting for partial frequency redistribution effects in scattering processes. Such a setting results in one of the most challenging problems in radiative transfer modell...

Context. The polarization signals produced by the scattering of anistropic radiation in strong resonance lines encode important information about the elusive magnetic fields in the outer layers of the solar atmosphere. An accurate modeling of these signals is a very challenging problem from the computational point of view, in particular when partia...

Phase-field models have been proven to be reliable methods for the simulation of complex crack patterns and crack propagation. In this contribution we investigate the phase-field model in linear and finite elasticity and summarize the influences of model specific parameters. Furthermore, externally driven fracture processes, in particular in the co...

Complex geometries as common in industrial applications consist of multiple patches, if spline based parametrizations are used. The requirements for the generation of analysis-suitable models are increasing dramatically since isogeometric analysis is directly based on the spline parametrization and nowadays used for the calculation of higher-order...

One of the state-of-the-art strategies for predicting crack propagation, nucleation, and interaction is the phase-field approach. Despite its reliability and robustness, the phase-field approach suffers from burdensome computational cost, caused by the non-convexity of the underlying energy functional and a large number of unknowns required to reso...

Internal interfaces in a domain could exist as a material defect or they can appear due to propagations of cracks. Discretization of such geometries and solution of the contact problem on the internal interfaces can be computationally challenging. We employ an unfitted Finite Element (FE) framework for the discretization of the domains and develop...

In this article, we focus on a two‐dimensional conservative steady‐state Riesz fractional diffusion problem. As is typical for problems in conservative form, we adopt a finite volume (FV)‐based discretization approach. Precisely, we use both classical FVs and the so‐called finite volume elements (FVEs). While FVEs have already been applied in the c...

Computational models of atrial fibrillation have successfully been used to predict optimal ablation sites. A critical step to assess the effect of an ablation pattern is to pace the model from different, potentially random, locations to determine whether arrhythmias can be induced in the atria. In this work, we propose to use multi-fidelity Gaussia...

Two-photon intravital microscopy (2P-IVM) has become a widely used technique to study cell-to-cell interactions in living organisms. Four-dimensional imaging data obtained via 2P-IVM are classically analyzed by performing automated cell tracking, a procedure that computes the trajectories followed by each cell. However, technical artifacts, such as...

Cell migration is a pivotal biological process, whose dysregulation is found in many diseases including inflammation and cancer. Advances in microscopy technologies allow now to study cell migration in vitro , within microenvironments that resemble in vivo conditions. However, when cells are observed within large 3D migration chambers at low magnif...

The migration of immune cells plays a key role in inflammation. This is evident in the fact that inflammatory stimuli elicit a broad range of migration patterns in immune cells. Since these patterns are pivotal for initiating the immune response, their dysregulation is associated with life-threatening conditions including organ failure, chronic inf...

The stress-based formulation of elastic contact with Coulomb friction in the form of a quasi-variational inequality is investigated. Weakly symmetric stress approximations are constructed using a finite element combination on the basis of Raviart–Thomas spaces of next-to-lowest order. An error estimator is derived based on a displacement reconstruc...

Computational models of atrial fibrillation have successfully been used to predict optimal ablation sites. A critical step to assess the effect of an ablation pattern is to pace the model from different, potentially random, locations to determine whether arrhythmias can be induced in the atria. In this work, we propose to use multi-fidelity Gaussia...

We focus on a time-dependent one-dimensional space-fractional diffusion equation with constant diffusion coefficients. An all-at-once rephrasing of the discretized problem, obtained by considering the time as an additional dimension, yields a large block linear system and paves the way for parallelization. In particular, in case of uniform space-ti...

Context. Numerical solutions to transfer problems of polarized radiation in solar and stellar atmospheres commonly rely on stationary iterative methods, which often perform poorly when applied to large problems. In recent times, stationary iterative methods have been replaced by state-of-the-art preconditioned Krylov iterative methods for many appl...

We consider the space-time discretization of the diffusion equation, using an iso-geometric analysis (IgA) approximation in space and a discontinuous Galerkin (DG) approximation in time. Drawing inspiration from a former spectral analysis, we propose for the resulting space-time linear system a multigrid preconditioned GMRES method, which combines...

The dual formulation for linear elasticity, in contrast to the primal formulation, is not affected by locking, as it is based on the stresses as main unknowns. Thus it is quite attractive for nearly incompressible and incompressible materials. Discretization with mixed finite elements will lead to—possibly large—linear saddle point systems. Whereas...

In this paper, we investigate the combination of multigrid methods and neural networks, starting from a Finite Element discretization of an elliptic PDE. Multigrid methods use interpolation operators to transfer information between different levels of approximation. These operators are crucial for fast convergence of multigrid, but they are general...

Context. Numerical solutions to transfer problems of polarized radiation in solar and stellar atmospheres commonly rely on stationary iterative methods, which often perform poorly when applied to large problems. In recent times, stationary iterative methods have been replaced by state-of-the-art preconditioned Krylov iterative methods for many appl...

Context. The numerical modeling of the generation and transfer of polarized radiation is a key task in solar and stellar physics research and has led to a relevant class of discrete problems that can be reframed as linear systems. In order to solve such problems, it is common to rely on efficient stationary iterative methods. However, the convergen...

In electrocardiography, the “classic” inverse problem is the reconstruction of electric potentials at a surface enclosing the heart from remote recordings at the body surface and an accurate description of the anatomy. The latter being affected by noise and obtained with limited resolution due to clinical constraints, a possibly large uncertainty m...

We train deep residual networks with a stochastic variant of the nonlinear multigrid method MG/OPT. To build the multilevel hierarchy, we use the dynamical systems viewpoint specific to residual networks. We report significant speed-ups and additional robustness for training MNIST on deep residual networks. Our numerical experiments also indicate t...

We present a tailored multigrid method for linear problems stemming from a Nitsche-based extended finite element method (XFEM). Our multigrid method is robust with respect to highly varying coefficients and the number of interfaces in a domain. It shows level independent convergence rates when applied to different variants of Nitsche's method. Gene...

Multigrid methods for two-body contact problems are mostly based on special mortar discretizations, nonlinear Gauss-Seidel solvers, and solution-adapted coarse grid spaces. Their high computational efficiency comes at the cost of a complex implementation and a nonsymmetric master-slave discretization of the nonpenetration condition. Here we investi...

We present a new multilevel minimization framework for the training of deep residual networks (ResNets), which has the potential to significantly reduce training time and effort. Our framework is based on the dynamical system’s viewpoint, which formulates a ResNet as the discretization of an initial value problem. The training process is then formu...

We consider two parallel-in-time approaches applied to a (reaction) diffusion problem, possibly non-linear. In particular, we consider PFASST (Parallel Full Approximation Scheme in Space and Time) and space-time multigrid strategies. For both approaches, we start from an integral formulation of the continuous time dependent problem. Then, a colloca...

We propose a globally convergent multilevel training method for deep residual networks (ResNets). The devised method can be seen as a novel variant of the recursive multilevel trust-region (RMTR) method, which operates in hybrid (stochastic-deterministic) settings by adaptively adjusting mini-batch sizes during the training. The multilevel hierarch...

Internal interfaces in a domain could exist as a material defect or they can appear due to propagations of cracks. Discretization of such geometries and solution of the contact problem on the internal interfaces can be computationally challenging. We employ an unfitted Finite Element (FE) framework for the discretization of the domains and develop...

Non-linear phase field models are increasingly used for the simulation of fracture propagation problems. The numerical simulation of fracture networks of realistic size requires the efficient parallel solution of large coupled non-linear systems. Although in principle efficient iterative multi-level methods for these types of problems are available...

The dual formulation for linear elasticity, in contrast to the primal formulation, is not affected by locking, as it is based on the stresses as main unknowns. Thus it is quite attractive for nearly incompressible and incompressible materials. Discretization with mixed finite elements will lead to -- possibly large -- linear saddle point systems wi...

Electroanatomical maps are a key tool in the diagnosis and treatment of atrial fibrillation. Current approaches focus on the activation times recorded. However, more information can be extracted from the available data. The fibers in cardiac tissue conduct the electrical wave faster, and their direction could be inferred from activation times. In t...

The identification of the initial ventricular activation sequence is a critical step for the correct personalization of patient‐specific cardiac models. In healthy conditions, the Purkinje network is the main source of the electrical activation, but under pathological conditions the so‐called earliest activation sites (EASs) are possibly sparser an...

We present a novel approach which aims at high-performance uncertainty quantification for cardiac electrophysiology simulations. Employing the monodomain equation to model the transmembrane potential inside the cardiac cells, we evaluate the effect of spatially correlated perturbations of the heart fibers on the statistics of the resulting quantiti...

Context: We consider a relevant class of linear problems arising from the modeling of the transfer of polarized radiation in solar and stellar atmospheres. In order to solve such problems, it is common to rely on efficient stationary iterative methods. However, the convergence properties of these methods are problem-dependent and a rigorous investi...

Context: Numerical solutions to transfer problems of polarized radiation in solar and stellar atmospheres commonly rely on stationary iterative methods, which often perform poorly when applied to large problems. In recent times, stationary iterative methods have been replaced by state-of-the-art Krylov iterative methods for many applications. Howev...

The parallel solution of large scale non-linear programming problems, which arise for example from the discretization of non-linear partial differential equations, is a highly demanding task. Here, a novel solution strategy is presented, which is inherently parallel and globally convergent. Each global non-linear iteration step consists of asynchro...

We introduce a novel variant of the recursive multilevel trust-region (RMTR) method, called MASTR. The method is designed for solving non-convex bound-constrained minimization problems, which arise from the finite element discretization of partial differential equations. MASTR utilizes an active-set strategy based on the truncated basis approach in...

In this work, we propose a multigrid preconditioner for Jacobian-free Newton-Krylov (JFNK) methods. Our multigrid method does not require to store any representation of the Jacobian at any level of the multigrid hierarchy. As it is common in standard multigrid methods, the proposed method also relies on three building blocks: transfer operators, sm...

Aims Electric conduction in the atria is direction-dependent, being faster in fibre direction, and possibly heterogeneous due to structural remodelling. Intracardiac recordings of atrial activation may convey such information, but only with high-quality data. The aim of this study was to apply a patient-specific approach to enable such assessment e...

Aims Recent clinical studies showed that antiarrhythmic drug (AAD) treatment and pulmonary vein isolation (PVI) synergistically reduce atrial fibrillation (AF) recurrences after initially successful ablation. Among newly developed atrial-selective AADs, inhibitors of the G-protein-gated acetylcholine-activated inward rectifier current (IKACh) were...

Aims This work aims at presenting a fully coupled approach for the numerical solution of contact problems between multiple elastic structures immersed in a fluid flow. The key features of the computational model are (i) a fully coupled fluid–structure interaction with contact, (ii) the use of a fibre-reinforced material for the leaflets, (iii) a st...

Aims Detection and quantification of myocardial scars are helpful for diagnosis of heart diseases and for personalized simulation models. Scar tissue is generally characterized by a different conduction of excitation. We aim at estimating conductivity-related parameters from endocardial mapping data. Solving this inverse problem requires computatio...

Electroanatomical maps are a key tool in the diagnosis and treatment of atrial fibrillation. Current approaches focus on the activation times recorded. However, more information can be extracted from the available data. The fibers in cardiac tissue conduct the electrical wave faster, and their direction could be inferred from activation times. In t...

The personalization of cardiac models is the cornerstone of patient-specific modeling. Ideally, non-invasive or minimally-invasive clinical data, such as the standard ECG or intracardiac contact recordings, could provide an insight on model parameters. Parameter selection of such models is however a challenging and potentially time-consuming task....

In this work, we consider the modeling of inclusions in the material using an unfitted finite element method. In the unfitted methods, structured background meshes are used and only the underlying finite element space is modified to incorporate the discontinuities, such as inclusions. Hence, the unfitted methods provide a more flexible framework fo...

We present a novel approach aimed at high-performance uncertainty quantification for time-dependent problems governed by partial differential equations. In particular, we consider input uncertainties described by a Karhunen-Loève expansion and compute statistics of high-dimensional quantities-of-interest, such as the cardiac activation potential. O...

Electroanatomical mapping, a keystone diagnostic tool in cardiac electrophysiology studies, can provide high-density maps of the local electric properties of the tissue. It is therefore tempting to use such data to better individualize current patient-specific models of the heart through a data assimilation procedure and to extract potentially insi...

In this work, we consider the modeling of inclusions in the material using an unfitted finite element method. In the unfitted methods, structured background meshes are used and only the underlying finite element space is modified to incorporate the discontinuities, such as inclusions. Hence, the unfitted methods provide a more flexible framework fo...

Gas turbines are used in aviation and energy production. As efficiency of gas turbines increases with firing temperatures, the hot gas components of a gas turbine are subject to extreme termo-mechanical load.

The reliability of atomistic simulations depends on the quality of the underlying energy models providing the source of physical information, for instance for the calculation of migration barriers in atomistic Kinetic Monte Carlo simulations. Accurate (high-fidelity) methods are often available, but since they are usually computationally expensive,...

Aims. Non-invasive imaging of electrical activation requires high-density body surface potential mapping. The 9 electrodes of the 12-lead ECG are insufficient for a reliable reconstruction with standard inverse methods. Patient-specific modeling may offer an alternative route to physiologically constraint the reconstruction. The aim of the study wa...

In electrocardiography, the "classic" inverse problem consists of finding electric potentials on a surface enclosing the heart from remote recordings on the body surface and an accurate description of the anatomy. The latter being affected by noise and obtained with limited resolution due to clinical constraints, a possibly large uncertainty may be...