# PSO-PINN: Physics-Informed Neural Networks Trained with Particle Swarm Optimization

arXiv: https://arxiv.org/abs/2202.01943 · HTML: https://mlsanity.com/paper/2202.01943/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 42 references that are in the map.
- First posted on arXiv 4 Feb 2022.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [Parallel Physics-Informed Neural Networks via Domain Decomposition](https://mlsanity.com/paper/2104.10013/) (2021)

## Built on by (most cited first, 11 of 11)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [On the Role of Fixed Points of Dynamical Systems in Training Physics-Informed Neural Networks](https://mlsanity.com/paper/2203.13648/) (2022)
- [Physics-Informed Neural Networks with Adaptive Localized Artificial Viscosity](https://mlsanity.com/paper/2203.08802/) (2022)
- [On the Limitations of Physics-informed Deep Learning: Illustrations Using First Order Hyperbolic Conservation Law-based Traffic Flow Models](https://mlsanity.com/paper/2302.12337/) (2023)
- [Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities](https://mlsanity.com/paper/2501.06572/) (2025)
- [Achieving High Accuracy with PINNs via Energy Natural Gradients](https://mlsanity.com/paper/2302.13163/) (2023)
- [The AI Scientific Community: Agentic Virtual Lab Swarms](https://mlsanity.com/paper/2603.21344/) (2026)
- [Probing optimisation in physics-informed neural networks](https://mlsanity.com/paper/2303.15196/) (2023)
- [Gradient Based Hybridization of PSO](https://mlsanity.com/paper/2312.09703/) (2023)
- [B-PL-PINN: Stabilizing PINN Training with Bayesian Pseudo Labeling](https://mlsanity.com/paper/2507.01714/) (2025)
- [Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers](https://mlsanity.com/paper/2607.22004/) (2026)

## Abstract (arXiv)

Physics-informed neural networks (PINN) have recently emerged as a promising application of deep learning in a wide range of engineering and scientific problems based on partial differential equation (PDE) models. However, evidence shows that PINN training by gradient descent displays pathologies that often prevent convergence when solving PDEs with irregular solutions. In this paper, we propose the use of a particle swarm optimization (PSO) approach to train PINNs. The resulting PSO-PINN algorithm not only mitigates the undesired behaviors of PINNs trained with standard gradient descent but also presents an ensemble approach to PINN that affords the possibility of robust predictions with quantified uncertainty. We also propose PSO-BP-CD (PSO with Back-Propagation and Coefficient Decay), a hybrid PSO variant that combines swarm optimization with gradient descent, putting more weight on the latter as training progresses and the swarm zeros in on a good local optimum. Comprehensive experimental results show that PSO-PINN with the proposed PSO-BP-CD algorithm outperforms PINN ensembles trained with other PSO variants or with pure gradient descent.