74 citations · 525 across the 47 of their papers we have counts for
55 papers
Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies
Alena Kopaničáková, Hardik Kothari, George Em Karniadakis +1
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 w…
Boundary Integral Formulation of the Cell-by-Cell Model of Cardiac Electrophysiology
Giacomo Rosilho de Souza, Rolf Krause, Simone Pezzuto
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-I…
Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints
Hardik Kothari, Alena Kopaničáková, Rolf Krause
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 fi…
AnyDijkstra, an algorithm to compute shortest paths on images with anytime properties
Diego Ulisse Pizzagalli, Rolf Krause
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 a…
Multigrid for two-sided fractional differential equations discretized by finite volume elements on graded meshes
Marco Donatelli, Rolf Krause, Mariarosa Mazza +1
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 t…
Nonlinear Field-split Preconditioners for Solving Monolithic Phase-field Models of Brittle Fracture
Alena Kopaničáková, Hardik Kothari, Rolf Krause
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-…
Construction of Grid Operators for Multilevel Solvers: a Neural Network Approach
Claudio Tomasi, Rolf Krause
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 inte…
Training of deep residual networks with stochastic MG/OPT
Cyrill von Planta, Alena Kopanicakova, Rolf Krause
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 specif…
Globally Convergent Multilevel Training of Deep Residual Networks
Alena Kopaničáková, Rolf Krause
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 trus…
A Generalized Multigrid Method for Solving Contact Problems in Lagrange Multiplier based Unfitted Finite Element Method
Hardik Kothari, Rolf Krause
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 pro…
Patch-Smoother and Multigrid for the Dual Formulation for Linear Elasticity
Gabriele Rovi, Rolf Krause
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 att…
Space-time multilevel quadrature methods and their application for cardiac electrophysiology
Seif Ben Bader, Helmut Harbrecht, Rolf Krause +3
We present a novel approach which aims at high-performance uncertainty quantification for cardiac electrophysiology simulations. Employing the monodomain equation to model the tran…
On the Globalization of ASPIN Employing Trust-Region Control Strategies -- Convergence Analysis and Numerical Examples
Christian Gross, Rolf Krause
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 dema…
Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization
Alena Kopaničáková, Rolf Krause
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 prob…
A Multigrid Preconditioner for Jacobian-free Newton-Krylov Methods
Hardik Kothari, Alena Kopaničáková, Rolf Krause
In this work, we propose a multigrid preconditioner for Jacobian-free Newton-Krylov (JFNK) methods. Our multigrid method does not require knowledge of the Jacobian at any level of…
Multigrid and saddle-point preconditioners for unfitted finite element modelling of inclusions
Hardik Kothari, Rolf Krause
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 onl…
Learning atrial fiber orientations and conductivity tensors from intracardiac maps using physics-informed neural networks
Thomas Grandits, Simone Pezzuto, Francisco Sahli Costabal +4
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 ca…
GEASI: Geodesic-based Earliest Activation Sites Identification in cardiac models
Thomas Grandits, Alexander Effland, Thomas Pock +3
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…
Space-time shape uncertainties in the forward and inverse problem of electrocardiography
Lia Gander, Rolf Krause, Michael Multerer +1
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 a…
PIEMAP: Personalized Inverse Eikonal Model from cardiac Electro-Anatomical Maps
Thomas Grandits, Simone Pezzuto, Jolijn M. Lubrecht +3
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 ther…
Large scale simulation of pressure induced phase-field fracture propagation using Utopia
Patrick Zulian, Alena Kopaničáková, Maria Giuseppina Chiara Nestola +4
Non-linear phase field models are increasingly used for the simulation of fracture propagation models. The numerical simulation of fracture networks of realistic size requires the…
A Multilevel Approach to Training
Vanessa Braglia, Alena Kopaničáková, Rolf Krause
We propose a novel training method based on nonlinear multilevel minimization techniques, commonly used for solving discretized large scale partial differential equations. Our mult…
An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem
Pietro Benedusi, Michael Minion, Rolf Krause
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…
Frontiers in Mortar Methods for Isogeometric Analysis
Christian Hesch, Ustim Khristenko, Rolf Krause +4
Complex geometries as common in industrial applications consist of multiple patches, if spline based parametrizations are used. The requirements for the generation of analysis-suit…