[HTML][HTML] Cross interpolation for solving high-dimensional dynamical systems on low-rank Tucker and tensor train manifolds
We present a novel tensor interpolation algorithm for the time integration of nonlinear tensor
differential equations (TDEs) on the tensor train and Tucker tensor low-rank manifolds …
differential equations (TDEs) on the tensor train and Tucker tensor low-rank manifolds …
Cur for implicit time integration of random partial differential equations on low-rank matrix manifolds
Dynamical low-rank approximation allows for solving large-scale matrix differential
equations (MDEs) with significantly fewer degrees of freedom and has been applied to a …
equations (MDEs) with significantly fewer degrees of freedom and has been applied to a …
A parallel Basis Update and Galerkin Integrator for Tree Tensor Networks
Computing the numerical solution to high-dimensional tensor differential equations can lead
to prohibitive computational costs and memory requirements. To reduce the memory and …
to prohibitive computational costs and memory requirements. To reduce the memory and …
A stable multiplicative dynamical low-rank discretization for the linear Boltzmann-BGK equation
The numerical method of dynamical low-rank approximation (DLRA) has recently been
applied to various kinetic equations showing a significant reduction of the computational …
applied to various kinetic equations showing a significant reduction of the computational …
Robust and conservative dynamical low-rank methods for the Vlasov equation via a novel macro-micro decomposition
Dynamical low-rank (DLR) approximation has gained interest in recent years as a viable
solution to the curse of dimensionality in the numerical solution of kinetic equations …
solution to the curse of dimensionality in the numerical solution of kinetic equations …