90 citations · 116 across the 16 of their papers we have counts for
6 papers · 1 filter
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…
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…