# Unsupervised Neural Networks for Quantum Eigenvalue Problems

arXiv: https://arxiv.org/abs/2010.05075 · HTML: https://mlsanity.com/paper/2010.05075/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2020.

## Built on by (most cited first, 15 of 15)

- [Learning Size and Shape of Calabi-Yau Spaces](https://mlsanity.com/paper/2111.01436/) (2021)
- [Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems](https://mlsanity.com/paper/2112.03749/) (2021)
- [Physics-Informed Neural Networks for Quantum Eigenvalue Problems](https://mlsanity.com/paper/2203.00451/) (2022)
- [Operator SVD with Neural Networks via Nested Low-Rank Approximation](https://mlsanity.com/paper/2402.03655/) (2024)
- [Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows](https://mlsanity.com/paper/2211.00214/) (2022)
- [Unsupervised Reservoir Computing for Solving Ordinary Differential Equations](https://mlsanity.com/paper/2108.11417/) (2021)
- [Physics-informed neural network solves minimal surfaces in curved spacetime](https://mlsanity.com/paper/2509.10866/) (2025)
- [A Swarm Variant for the Schr"odinger Solver](https://mlsanity.com/paper/2104.04795/) (2021)
- [First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfaces](https://mlsanity.com/paper/2211.04607/) (2022)
- [On the uncertainty analysis of the data-enabled physics-informed neural network for solving neutron diffusion eigenvalue problem](https://mlsanity.com/paper/2303.08455/) (2023)
- [A New Artificial Neuron Proposal with Trainable Simultaneous Local and Global Activation Function](https://mlsanity.com/paper/2101.06100/) (2021)
- [Adversarial Sampling for Solving Differential Equations with Neural Networks](https://mlsanity.com/paper/2111.12024/) (2021)
- [A ZeNN architecture to avoid the Gaussian trap](https://mlsanity.com/paper/2505.20553/) (2025)
- [Physics-Informed Neural Solvers for Periodic Quantum Eigenproblems](https://mlsanity.com/paper/2512.21349/) (2025)
- [PIEFS: Physics-Informed Eigenfunction Features with Learnable Scaling](https://mlsanity.com/paper/2607.03692/) (2026)

## Abstract (arXiv)

Eigenvalue problems are critical to several fields of science and engineering. We present a novel unsupervised neural network for discovering eigenfunctions and eigenvalues for differential eigenvalue problems with solutions that identically satisfy the boundary conditions. A scanning mechanism is embedded allowing the method to find an arbitrary number of solutions. The network optimization is data-free and depends solely on the predictions. The unsupervised method is used to solve the quantum infinite well and quantum oscillator eigenvalue problems.