Low-Fidelity FDM Spectral Guidance for Neural Eigenvalue Solvers
A coarse finite-difference pass is used to steer the neural solver toward the right eigenvalues.
The paper uses approximate FDM eigenvalues as fixed shifts during neural training, so the model searches the relevant part of the spectrum instead of wandering. It also introduces SIPMNN, a stabilized inverse-power-method neural network for higher-dimensional cases. In five 10-dimensional test problems, the hybrid method is reported as more accurate overall than the tested fully neural baselines while needing eight to ten times fewer iterations. ArXiv · AI/CL/LG's note
The paper uses approximate FDM eigenvalues as fixed shifts during neural training, so the model searches the relevant part of the spectrum instead of wandering. It also introduces SIPMNN, a stabilized inverse-power-method neural network for higher-dimensional cases. In five 10-dimensional test problems, the hybrid method is reported as more accurate overall than the tested fully neural baselines while needing eight to ten times fewer iterations. ArXiv · AI/CL/LG's note
score 3