257 citations · 1.1k across the 33 of their papers we have counts for
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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…
Parallel time-dependent variational principle algorithm for matrix product states
Paul Secular, Nikita Gourianov, Michael Lubasch +3
Combining the time-dependent variational principle (TDVP) algorithm with the parallelization scheme introduced by Stoudenmire and White for the density matrix renormalization group…
Tensor Decomposition Methods for High-dimensional Hamilton-Jacobi-Bellman Equations
Sergey Dolgov, Dante Kalise, Karl Kunisch
A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton-Jacobi-Bellman equations arising in optimal feedback control of nonlinear dynamics is…
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…
Kriging in Tensor Train data format
Sergey Dolgov, Alexander Litvinenko, Dishi Liu
Combination of low-tensor rank techniques and the Fast Fourier transform (FFT) based methods had turned out to be prominent in accelerating various statistical operations such as K…
Parallel cross interpolation for high-precision calculation of high-dimensional integrals
Sergey Dolgov, Dmitry Savostyanov
We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics. In contrast to…