5 papers
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…
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…
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…
Binding threshold units with artificial oscillatory neurons
Vladimir Fanaskov, Ivan Oseledets
Artificial Kuramoto oscillatory neurons were recently introduced as an alternative to threshold units. Empirical evidence suggests that oscillatory units outperform threshold units…
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…