6 papers
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…
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…
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,…
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…