From the 1 of 79 linked papers with an AI index.
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Spectral-Informed Neural Networks Outperform Spectral Methods in High-dimensional PDEs
Tianchi Yu, Ivan Oseledets
The paper introduces Modified Spectral-Informed Neural Networks (SINNs) that combine spectral methods with physics-informed neural networks, using coefficient decay scaling and bas…
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…
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,…