7 citations · 17 across the 13 of their papers we have counts for
6 papers · 1 filter
Associative memory and dead neurons
Vladimir Fanaskov, Ivan Oseledets
In "Large Associative Memory Problem in Neurobiology and Machine Learning," Dmitry Krotov and John Hopfield introduced a general technique for the systematic construction of neural…
Astral: training physics-informed neural networks with error majorants
Vladimir Fanaskov, Tianchi Yu, Alexander Rudikov +1
The primal approach to physics-informed learning is a residual minimization. We argue that residual is, at best, an indirect measure of the error of approximate solution and propos…
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…