257 citations · 1.1k across the 33 of their papers we have counts for
37 papers
Numerical solution of the incompressible Navier-Stokes equations for chemical mixers via quantum-inspired Tensor Train Finite Element Method
Egor Kornev, Sergey Dolgov, Karan Pinto +3
The solution of computational fluid dynamics problems is one of the most computationally hard tasks, especially in the case of complex geometries and turbulent flow regimes. We pro…
Self-reinforced polynomial approximation methods for concentrated probability densities
Tiangang Cui, Sergey Dolgov, Olivier Zahm
Transport map methods offer a powerful statistical learning tool that can couple a target high-dimensional random variable with some reference random variable using invertible tran…
A weighted subspace exponential kernel for support tensor machines
Kirandeep Kour, Sergey Dolgov, Peter Benner +2
High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernel…
Smoothed Moreau-Yosida Tensor Train Approximation of State-constrained Optimization Problems under Uncertainty
Harbir Antil, Sergey Dolgov, Akwum Onwunta
We propose an algorithm to solve optimization problems constrained by partial (ordinary) differential equations under uncertainty, with almost sure constraints on the state variabl…
Deep importance sampling using tensor trains with application to a priori and a posteriori rare event estimation
Tiangang Cui, Sergey Dolgov, Robert Scheichl
We propose a deep importance sampling method that is suitable for estimating rare event probabilities in high-dimensional problems. We approximate the optimal importance distributi…
Tensor product approach to modelling epidemics on networks
Sergey V. Dolgov, Dmitry V. Savostyanov
To improve mathematical models of epidemics it is essential to move beyond the traditional assumption of homogeneous well--mixed population and involve more precise information on…