30 citations · 41 across the 11 of their papers we have counts for
12 papers
Global Optimization of Atomic Clusters via Physically-Constrained Tensor Train Decomposition
Konstantin Sozykin, Nikita Rybin, Andrei Chertkov +5
The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with sy…
High-dimensional Optimization with Low Rank Tensor Sampling and Local Search
Konstantin Sozykin, Andrei Chertkov, Anh-Huy Phan +2
We present a novel method called TESALOCS (TEnsor SAmpling and LOCal Search) for multidimensional optimization, combining the strengths of gradient-free discrete methods and gradie…
Black-Box Approximation and Optimization with Hierarchical Tucker Decomposition
Gleb Ryzhakov, Andrei Chertkov, Artem Basharin +1
We develop a new method HTBB for the multidimensional black-box approximation and gradient-free optimization, which is based on the low-rank hierarchical Tucker decomposition with…
Explicit Flow Matching: On The Theory of Flow Matching Algorithms with Applications
Gleb Ryzhakov, Svetlana Pavlova, Egor Sevriugov +1
This paper proposes a novel method, Explicit Flow Matching (ExFM), for training and analyzing flow-based generative models. ExFM leverages a theoretically grounded loss function, E…
PROTES: Probabilistic Optimization with Tensor Sampling
Anastasia Batsheva, Andrei Chertkov, Gleb Ryzhakov +1
We developed a new method PROTES for black-box optimization, which is based on the probabilistic sampling from a probability density function given in the low-parametric tensor tra…
Optimization of Functions Given in the Tensor Train Format
Andrei Chertkov, Gleb Ryzhakov, Georgii Novikov +1
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of appli…
Black box approximation in the tensor train format initialized by ANOVA decomposition
Andrei Chertkov, Gleb Ryzhakov, Ivan Oseledets
Surrogate models can reduce computational costs for multivariable functions with an unknown internal structure (black boxes). In a discrete formulation, surrogate modeling is equiv…
Constructive TT-representation of the tensors given as index interaction functions with applications
Gleb Ryzhakov, Ivan Oseledets
This paper presents a method to build explicit tensor-train (TT) representations. We show that a wide class of tensors can be explicitly represented with sparse TT-cores, obtaining…
Optimal soil sampling design based on the maxvol algorithm
Anna Petrovskaia, Gleb Ryzhakov, Ivan Oseledets
Spatial soil sampling is an integral part of a soil survey aimed at creating a soil map. We propose considering the soil sampling procedure as a task of optimal design. In practica…
Two-phase approaches to optimal model-based design of experiments: how many experiments and which ones?
Charlie Vanaret, Philipp Seufert, Jan Schwientek +5
Model-based experimental design is attracting increasing attention in chemical process engineering. Typically, an iterative procedure is pursued: an approximate model is devised, p…
Gradient Descent-based D-optimal Design for the Least-Squares Polynomial Approximation
V. P. Zankin, G. V. Ryzhakov, I. V. Oseledets
In this work, we propose a novel sampling method for Design of Experiments. This method allows to sample such input values of the parameters of a computational model for which the…
Function approximation using gradient information with application to parametric and stochastic differential equations
Gleb Ryzhakov, Ivan Oseledets
In the paper we consider the problem of multivariate function approximation in polynomial basis. In order to solve this problem, we adjust the least squares method (LSM) by adding…