5 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…