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For middle-dimensional problems ($4 \\leq d \\lesssim 10$), spectral methods remain feasible through specific techniques such as sparse grids or hyperbolic cross. However, for high-dimensional problems ($d\\gg 10$), spectral methods suffer frome the curse of dimensionality. Physics-informed neural networks (PINNs) have emerged as a promising approach to overcome this challenge, offering scalability to high dimensions, but often suffer from limited accuracy and efficiency. Recently proposed spectral-informed neural networks (SINNs) combine spectral methods with PINNs, operating directly in the spectral domain to avoid spatial derivative computations and to reduce memory consumption. In this work, we introduce Modified SINNs, which integrate coefficient decay scaling and basis embeddings motivated by harmonic analysis to enhance accuracy in hi","title":"Spectral-Informed Neural Networks Outperform Spectral Methods in High-dimensional PDEs","url":"https://arxiv.org/abs/2607.13566","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.13566v1 Announce Type: cross \nAbstract: For low-dimensional problems ($d\\leq3$), spectral methods can achieve exceptionally high accuracy. For middle-dimensional problems ($4 \\leq d \\lesssim 10$), spectral methods remain feasible through specific techniques such as sparse grids or hyperbolic cross. However, for high-dimensional problems ($d\\gg 10$), spectral methods suffer frome the curse of dimensionality. Physics-informed neural networks (PINNs) have emerged as a promising approach to overcome this challenge, offering scalability to high dimensions, but often suffer from limited accuracy and efficiency. 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