# Experimental observation on a low-rank tensor model for eigenvalue problems

arXiv: https://arxiv.org/abs/2302.00538 · HTML: https://mlsanity.com/paper/2302.00538/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 17 references that are in the map.
- First posted on arXiv 1 Feb 2023.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022)

## Built on by (most cited first, 2 of 2)

- [A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples](https://mlsanity.com/paper/2402.07156/) (2024)
- [Learning solution operators of PDEs defined on varying domains via MIONet](https://mlsanity.com/paper/2402.15097/) (2024)

## Abstract (arXiv)

Here we utilize a low-rank tensor model (LTM) as a function approximator, combined with the gradient descent method, to solve eigenvalue problems including the Laplacian operator and the harmonic oscillator. Experimental results show the superiority of the polynomial-based low-rank tensor model (PLTM) compared to the tensor neural network (TNN). We also test such low-rank architectures for the classification problem on the MNIST dataset.