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math.NA2026
TensorSpectra: Bridging the Spectral and Tensor Worlds for High-Dimensional PDEs
Bingcheng Hu, Tianchi Yu, Zhaoxiang Li +1
High-dimensional partial differential equations (PDEs) remain challenging for spectral methods due to the exponential growth of multidimensional coefficient spaces. We propose Tens…
math.NA2026
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…
math.NA2023★ 2 cited
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…