Author

A. Uschmajew

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Preprint Sep 2026

A stable rank-adaptive step-and-truncate finite volume method for Vlasov transport on domains with piecewise linear boundaries

We consider the numerical solution of the linear Vlasov transport equation on bounded spatial domains with inflow boundary conditions based on low-rank approximation. We combine a finite volume discretization with a rank-adaptive step-and-truncate scheme for the resulting matrix ODE. The spatial and velocity meshes may...

A. Uschmajew, A. Zeiser · 0 citations

Preprint Sep 2026

Stochastic Optimization of Tree Tensor Networks

Tensor networks, originally developed for quantum many-body physics, are promising models for machine learning. We derive stochastic Riemannian optimizers for tree tensor networks (TTNs) on both their parameter and quotient manifolds, including adaptive and learning-rate-free schemes suitable for minibatch training. Us...

Marius Willner, Maximilian Karl Scharf, A. Uschmajew et al. · 0 citations