# Application of machine learning regression models to inverse eigenvalue problems

arXiv: https://arxiv.org/abs/2212.04279 · HTML: https://mlsanity.com/paper/2212.04279/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 62 references that are in the map.
- First posted on arXiv 8 Dec 2022.

## Builds on (most cited first, 7 of 7)

- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [Conditional physics informed neural networks](https://mlsanity.com/paper/2104.02741/) (2021)
- [Physics-Informed Neural Networks for Quantum Eigenvalue Problems](https://mlsanity.com/paper/2203.00451/) (2022)
- [Applications of Deep Neural Networks with Keras](https://mlsanity.com/paper/2009.05673/) (2020)

## Built on by (most cited first, 1 of 1)

- [Estimating properties of a homogeneous bounded soil using machine learning models](https://mlsanity.com/paper/2506.04256/) (2025)

## Abstract (arXiv)

In this work, we study the numerical solution of inverse eigenvalue problems from a machine learning perspective. Two different problems are considered: the inverse Strum-Liouville eigenvalue problem for symmetric potentials and the inverse transmission eigenvalue problem for spherically symmetric refractive indices. Firstly, we solve the corresponding direct problems to produce the required eigenvalues datasets in order to train the machine learning algorithms. Next, we consider several examples of inverse problems and compare the performance of each model to predict the unknown potentials and refractive indices respectively, from a given small set of the lowest eigenvalues. The supervised regression models we use are k-Nearest Neighbours, Random Forests and Multi-Layer Perceptron. Our experiments show that these machine learning methods, under appropriate tuning on their parameters, can numerically solve the examined inverse eigenvalue problems.