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Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the…
In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a…
A phase field model of a crystalline material at the mesoscale is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase field free energy…
We present a new approach to model the gravitational dynamics of large-scale structures. Instead of solving the equations of motion up to a finite perturbative order or building phenomenological models, we follow the evolution of the…
Non-intrusive methods have been used since two decades to derive reduced-order models for geometrically nonlinear structures, with a particular emphasis on the so-called STiffness Evaluation Procedure (STEP), relying on the static…
Continuum models of dislocation plasticity require constitutive closure assumptions, e.g., by relating details of the dislocation microstructure to energy densities. Currently, there is no systematic way for deriving or extracting such…
We consider the simulation of barotropic flow of gas in long pipes and pipe networks. Based on a Hamiltonian reformulation of the governing system, a fully discrete approximation scheme is proposed using mixed finite elements in space and…
We present a model-based derivative-free method for optimization subject to general convex constraints, which we assume are unrelaxable and accessed only through a projection operator that is cheap to evaluate. We prove global convergence…
We present a new line-based discontinuous Galerkin (DG) discretization scheme for first- and second-order systems of partial differential equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements,…
We present two new methods for linear elasticity with simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p. This is achieved within the recently developed…
Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to…
We derive a dimension-reduction limit for a three-dimensional rod with material voids by means of $\Gamma$-convergence. Hereby, we generalize the results of the purely elastic setting [57] to a framework of free discontinuity problems. The…
Solving large-scale optimization problems is a bottleneck and is very important for machine learning and multiple kinds of scientific problems. Subspace-based methods using the local approximation strategy are one of the most important…
Methods for reconstructing the topology of complex networks from time-resolved observations of node dynamics are gaining relevance across scientific disciplines. Of biggest practical interest are methods that make no assumptions about…
We investigate the collective dynamics of self-propelled droplets, confined in a one dimensional micro-fluidic channel. On one hand, neighboring droplets align and form large trains of droplets moving in the same direction. On the other…
The paper presents a novel learning-based sampling strategy that guarantees rejection-free sampling of the free space under both biased and approximately uniform conditions, leveraging multivariate kernel densities. Historical data from a…
The nonlinear decay of oscillations of a liquid column in a U-shaped tube is investigated within the theoretical framework of the projection method formalized by Bongarzone et al. (2021) [1]. Starting from the full hydrodynamic system…
Monocular 3D tracking aims to capture the long-term motion of pixels in 3D space from a single monocular video and has witnessed rapid progress in recent years. However, we argue that the existing monocular 3D tracking methods still fall…
Deformation gradient tensor fields are reconstructed in three dimensions (mapping all 9 tensor components) using synthetic Dark-Field X-ray Microscopy data. Owing to the unique properties of the microscope, our results imply that the…