Solving the functional Eigen-Problem using Neural Networks
This work addresses the eigen-problem in image processing and other domains, offering a potentially more robust alternative to numeric methods, though it is incremental as it focuses on simple cases.
The authors tackled the problem of finding eigen-pairs for self-adjoint operators in ordinary differential equations using neural networks, achieving initial results on simple problems with known analytical solutions to explore the method's capabilities and limitations.
In this work, we explore the ability of NN (Neural Networks) to serve as a tool for finding eigen-pairs of ordinary differential equations. The question we aime to address is whether, given a self-adjoint operator, we can learn what are the eigenfunctions, and their matching eigenvalues. The topic of solving the eigen-problem is widely discussed in Image Processing, as many image processing algorithms can be thought of as such operators. We suggest an alternative to numeric methods of finding eigenpairs, which may potentially be more robust and have the ability to solve more complex problems. In this work, we focus on simple problems for which the analytical solution is known. This way, we are able to make initial steps in discovering the capabilities and shortcomings of DNN (Deep Neural Networks) in the given setting.