# Solving the functional Eigen-Problem using Neural Networks

arXiv: https://arxiv.org/abs/2007.10205 · HTML: https://mlsanity.com/paper/2007.10205/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2020.

## Built on by (most cited first, 4 of 4)

- [Neural Networks Based on Power Method and Inverse Power Method for Solving Linear Eigenvalue Problems](https://mlsanity.com/paper/2209.11134/) (2022)
- [BASiS: Batch Aligned Spectral Embedding Space](https://mlsanity.com/paper/2211.16960/) (2022)
- [STNet: Spectral Transformation Network for Solving Operator Eigenvalue Problem](https://mlsanity.com/paper/2510.23986/) (2025)
- [Learning-Guided Integration Contours Construction for Fast Large-Scale Generalized Eigensolvers](https://mlsanity.com/paper/2511.01927/) (2025)

## Abstract (arXiv)

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.