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In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...
The ability to reason, plan and solve highly abstract problems is a hallmark of human intelligence. Recent advancements in artificial intelligence, propelled by deep neural networks, have revolutionized disciplines like computer vision and natural language ...
In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...
vanishing viscosity, networks. This work has received funding from the Alexander von Humboldt-Professorship program, the Transregio 154 Project "Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks" of the DFG, the grant PI ...
We present a numerical model for the approximation of multiphase flows with free surfaces and strong interfacial effects. The model relies on the multiphase incompressible Navier-Stokes equations, and includes surface tension effects on the interfaces betw ...
Gruber et al. (2022) offered a framework how to explain "Physical time within human time", solving the 'two times problem: Here, I am asking whether such a problem exists at all. To question the question, I will appeal to neurobiological, evolutionary, and ...
Graph machine learning offers a powerful framework with natural applications in scientific fields such as chemistry, biology and material sciences. By representing data as a graph, we encode the prior knowledge that the data is composed of a set of entitie ...
We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...
When can a unimodular random planar graph be drawn in the Euclidean or the hyperbolic plane in a way that the distribution of the random drawing is isometry-invariant? This question was answered for one-ended unimodular graphs in Benjamini and Timar, using ...
We investigate the stability of the steady vertical path and the emerging trajectories of a buoyancy -driven annular disk as the diameter of its central hole is varied. The steady and axisymmetric wake associated with the steady vertical path of the disk, ...
