5 papers · 1 filter
Rank Bounds for Approximating Gaussian Densities in the Tensor-Train Format
Paul B. Rohrbach, Sergey Dolgov, Lars Grasedyck +1
Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up lar…
Solving differential Riccati equations: A nonlinear space-time method using tensor trains
Tobias Breiten, Sergey Dolgov, Martin Stoll
Differential algebraic Riccati equations are at the heart of many applications in control theory. They are time-depent, matrix-valued, and in particular nonlinear equations that re…
Guaranteed a posteriori error bounds for low rank tensor approximate solutions
Sergey Dolgov, Tomáš Vejchodský
We propose a guaranteed and fully computable upper bound on the energy norm of the error in low-rank Tensor Train (TT) approximate solutions of (possibly) high dimensional reaction…
Approximation and sampling of multivariate probability distributions in the tensor train decomposition
Sergey Dolgov, Karim Anaya-Izquierdo, Colin Fox +1
General multivariate distributions are notoriously expensive to sample from, particularly the high-dimensional posterior distributions in PDE-constrained inverse problems. This pap…
Greedy low-rank algorithm for spatial connectome regression
Patrick Kürschner, Sergey Dolgov, Kameron Decker Harris +1
Recovering brain connectivity from tract tracing data is an important computational problem in the neurosciences. Mesoscopic connectome reconstruction was previously formulated as…