90 citations · 116 across the 16 of their papers we have counts for
16 papers
PERELMAN: Pipeline for scientific literature meta-analysis. Technical report
Daniil Sherki, Daniil Merkulov, Alexandra Savina +1
We present PERELMAN (PipEline foR sciEntific Literature Meta-ANalysis), an agentic framework designed to extract specific information from a large corpus of scientific articles to…
Spectral Analysis of the Weighted Frobenius Objective
Vladislav Trifonov, Ivan Oseledets, Ekaterina Muravleva
We analyze a weighted Frobenius loss for approximating symmetric positive definite matrices in the context of preconditioning iterative solvers. Unlike the standard Frobenius norm,…
Deep Learning for Subspace Regression
Vladimir Fanaskov, Vladislav Trifonov, Alexander Rudikov +2
It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appeali…
Geological Field Restoration through the Lens of Image Inpainting
Vladislav Trifonov, Ivan Oseledets, Ekaterina Muravleva
We study an ill-posed problem of geological field reconstruction under limited observations. Engineers often have to deal with the problem of reconstructing the subsurface geologic…
Locally Subspace-Informed Neural Operators for Efficient Multiscale PDE Solving
Alexander Rudikov, Vladimir Fanaskov, Sergei Stepanov +4
Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use th…
Bayesian Inverse Problems Meet Flow Matching: Efficient and Flexible Inference via Transformers
Daniil Sherki, Ivan Oseledets, Ekaterina Muravleva
The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel fram…
Message-Passing GNNs Fail to Approximate Sparse Triangular Factorizations
Vladislav Trifonov, Ekaterina Muravleva, Ivan Oseledets
Graph Neural Networks (GNNs) have been proposed as a tool for learning sparse matrix preconditioners, which are key components in accelerating linear solvers. We present theoretica…
ConDiff: A Challenging Dataset for Neural Solvers of Partial Differential Equations
Vladislav Trifonov, Alexander Rudikov, Oleg Iliev +3
We present ConDiff, a novel dataset for scientific machine learning. ConDiff focuses on the parametric diffusion equation with space dependent coefficients, a fundamental problem i…
Learning from Linear Algebra: A Graph Neural Network Approach to Preconditioner Design for Conjugate Gradient Solvers
Vladislav Trifonov, Alexander Rudikov, Oleg Iliev +3
Large linear systems are ubiquitous in modern computational science and engineering. The main recipe for solving them is the use of Krylov subspace iterative methods with well-desi…
Quantization of Large Language Models with an Overdetermined Basis
Daniil Merkulov, Daria Cherniuk, Alexander Rudikov +4
In this paper, we introduce an algorithm for data quantization based on the principles of Kashin representation. This approach hinges on decomposing any given vector, matrix, or te…
Neural operators meet conjugate gradients: The FCG-NO method for efficient PDE solving
Alexander Rudikov, Vladimir Fanaskov, Ekaterina Muravleva +2
Deep learning solvers for partial differential equations typically have limited accuracy. We propose to overcome this problem by using them as preconditioners. More specifically, w…
On the structure of the Schur complement matrix for the Stokes equation
Vladislav Pimanov, Ekaterina Muravleva, Ivan Oseledets +1
In this paper, we investigate the structure of the Schur complement matrix for the fully-staggered finite-difference discretization of the stationary Stokes equation. Specifically,…
On the efficient preconditioning of the Stokes equations in tight geometries
Vladislav Pimanov, Oleg Iliev, Ivan Oseledets +1
If the Stokes equations are properly discretized, it is known that the Schur complement matrix is spectrally equivalent to the identity matrix. Moreover, in the case of simple geom…
Microstructure synthesis using style-based generative adversarial network
Daria Fokina, Ekaterina Muravleva, George Ovchinnikov +1
Work considers the usage of StyleGAN architecture for the task of microstructure synthesis. The task is the following: given number of samples of structure we try to generate simil…
Application of machine learning to viscoplastic flow modeling
E. Muravleva, I. Oseledets, D. Koroteev
We present a method to construct reduced-order models for duct flows of Bingham media. Our method is based on proper orthogonal decomposition (POD) to find a low-dimensional approx…
Fast low-rank solution of the Poisson equation with application to the Stokes problem
E. A. Muravleva, I. V. Oseledets
We consider the problem of computing approximate solution of Poisson equation in the low-parametric tensor formats. We propose a new algorithm to compute the solution based on the…