# A Swarm Variant for the Schr"odinger Solver

arXiv: https://arxiv.org/abs/2104.04795 · HTML: https://mlsanity.com/paper/2104.04795/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 10 Apr 2021.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data](https://mlsanity.com/paper/1908.03190/) (2019)
- [Solving Differential Equations Using Neural Network Solution Bundles](https://mlsanity.com/paper/2006.14372/) (2020)
- [Neural Networks Trained to Solve Differential Equations Learn General Representations](https://mlsanity.com/paper/1807.00042/) (2018)
- [Unsupervised Neural Networks for Quantum Eigenvalue Problems](https://mlsanity.com/paper/2010.05075/) (2020)
- [A Discussion on Solving Partial Differential Equations using Neural Networks](https://mlsanity.com/paper/1904.07200/) (2019)

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

- [Encoding Involutory Invariances in Neural Networks](https://mlsanity.com/paper/2106.12891/) (2021)
- [Hamiltonian Monte Carlo Particle Swarm Optimizer](https://mlsanity.com/paper/2206.14134/) (2022)

## Abstract (arXiv)

This paper introduces application of the Exponentially Averaged Momentum Particle Swarm Optimization (EM-PSO) as a derivative-free optimizer for Neural Networks. It adopts PSO's major advantages such as search space exploration and higher robustness to local minima compared to gradient-descent optimizers such as Adam. Neural network based solvers endowed with gradient optimization are now being used to approximate solutions to Differential Equations. Here, we demonstrate the novelty of EM-PSO in approximating gradients and leveraging the property in solving the Schr"odinger equation, for the Particle-in-a-Box problem. We also provide the optimal set of hyper-parameters supported by mathematical proofs, suited for our algorithm.