We propose a self-supervising learning framework for finding the dominant eigenfunction-eigenvalue pairs of linear and self-adjoint operators.We represent target eigenfunctions with coordinate-based neural networks an...We propose a self-supervising learning framework for finding the dominant eigenfunction-eigenvalue pairs of linear and self-adjoint operators.We represent target eigenfunctions with coordinate-based neural networks and employ the Fourier positional encodings to enable the approximation of high-frequency modes.We formulate a self-supervised training objective for spectral learning and propose a novel regularization mechanism to ensure that the network finds the exact eigenfunctions instead of a space spanned by the eigenfunctions.Furthermore,we investigate the effect of weight normalization as a mechanism to alleviate the risk of recovering linear dependent modes,allowing us to accurately recover a large number of eigenpairs.The effectiveness of our methods is demonstrated across a collection of representative benchmarks including both local and non-local diffusion operators,as well as high-dimensional time-series data from a video sequence.Our results indicate that the present algorithm can outperform competing approaches in terms of both approximation accuracy and computational cost.展开更多
基金Project supported by the U.S.Department of Energy under the Advanced Scientific Computing Research Program(No.DE-SC0019116)the U.S.Air Force Office of Scientific Research(No.AFOSR FA9550-20-1-0060)。
文摘We propose a self-supervising learning framework for finding the dominant eigenfunction-eigenvalue pairs of linear and self-adjoint operators.We represent target eigenfunctions with coordinate-based neural networks and employ the Fourier positional encodings to enable the approximation of high-frequency modes.We formulate a self-supervised training objective for spectral learning and propose a novel regularization mechanism to ensure that the network finds the exact eigenfunctions instead of a space spanned by the eigenfunctions.Furthermore,we investigate the effect of weight normalization as a mechanism to alleviate the risk of recovering linear dependent modes,allowing us to accurately recover a large number of eigenpairs.The effectiveness of our methods is demonstrated across a collection of representative benchmarks including both local and non-local diffusion operators,as well as high-dimensional time-series data from a video sequence.Our results indicate that the present algorithm can outperform competing approaches in terms of both approximation accuracy and computational cost.
