7 citations · 17 across the 13 of their papers we have counts for
9 papers · 1 filter
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…
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…
Neural functional a posteriori error estimates
Vladimir Fanaskov, Alexander Rudikov, Ivan Oseledets
We propose a new loss function for supervised and physics-informed training of neural networks and operators that incorporates a posteriori error estimate. More specifically, durin…
Neural Multigrid Architectures
Vladimir Fanaskov
We propose a convenient matrix-free neural architecture for the multigrid method. The architecture is simple enough to be implemented in less than fifty lines of code, yet it encom…
Uncertainty calibration for probabilistic projection methods
Vladimir Fanaskov
Classical Krylov subspace projection methods for the solution of linear problem output an approximate solution . Recently, it has been recognized th…
General Covariance Data Augmentation for Neural PDE Solvers
Vladimir Fanaskov, Tianchi Yu, Alexander Rudikov +1
The growing body of research shows how to replace classical partial differential equation (PDE) integrators with neural networks. The popular strategy is to generate the input-outp…
Direct optimization of BPX preconditioners
Vladimir Fanaskov, Ivan Oseledets
We consider an automatic construction of locally optimal preconditioners for positive definite linear systems. To achieve this goal, we introduce a differentiable loss function tha…
Spectral Neural Operators
V. Fanaskov, I. Oseledets
A plentitude of applications in scientific computing requires the approximation of mappings between Banach spaces. Recently introduced Fourier Neural Operator (FNO) and Deep Operat…
Gaussian belief propagation solvers for nonsymmetric systems of linear equations
Vladimir Fanaskov
In this paper, we argue for the utility of deterministic inference in the classical problem of numerical linear algebra, that of solving a linear system. We show how the Gaussian b…