3 citations · 9 across the 6 of their papers we have counts for
6 papers
Spectral-Informed Neural Networks Outperform Spectral Methods in High-dimensional PDEs
Tianchi Yu, Ivan Oseledets
For low-dimensional problems (), spectral methods can achieve exceptionally high accuracy. For middle-dimensional problems (), spectral methods remain…
Quasi-Random Physics-informed Neural Networks
Tianchi Yu, Ivan Oseledets
Physics-informed neural networks have shown promise in solving partial differential equations (PDEs) by integrating physical constraints into neural network training, but their per…
Sinc Kolmogorov-Arnold network and its application for solving PDEs with singularities
Tianchi Yu, Jingwei Qiu, Jiang Yang +1
In this paper, we propose to use Sinc interpolation in the context of Kolmogorov-Arnold Networks, neural networks with learnable activation functions, which recently gained attenti…
Spectral Informed Neural Network: An Efficient and Low-Memory PINN
Tianchi Yu, Yiming Qi, Ivan Oseledets +1
With growing investigations into solving partial differential equations by physics-informed neural networks (PINNs), more accurate and efficient PINNs are required to meet the prac…
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…
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…