# Enriched Physics-informed Neural Networks for Dynamic Poisson-Nernst-Planck Systems

arXiv: https://arxiv.org/abs/2402.01768 · HTML: https://mlsanity.com/paper/2402.01768/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 44 references that are in the map.
- First posted on arXiv 1 Feb 2024.

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

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)

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

- [Virtual boundary integral neural network for three-dimensional exterior acoustic problems](https://mlsanity.com/paper/2604.18636/) (2026)
- [Coupling-Robust Accuracy in Multiphysics Physics Informed Neural Networks via Kronecker-Preconditioned Optimization](https://mlsanity.com/paper/2605.23391/) (2026)

## Abstract (arXiv)

This paper proposes a meshless deep learning algorithm, enriched physics-informed neural networks (EPINNs), to solve dynamic Poisson-Nernst-Planck (PNP) equations with strong coupling and nonlinear characteristics. The EPINNs takes the traditional physics-informed neural networks as the foundation framework, and adds the adaptive loss weight to balance the loss functions, which automatically assigns the weights of losses by updating the parameters in each iteration based on the maximum likelihood estimate. The resampling strategy is employed in the EPINNs to accelerate the convergence of loss function. Meanwhile, the GPU parallel computing technique is adopted to accelerate the solving process. Four examples are provided to demonstrate the validity and effectiveness of the proposed method. Numerical results indicate that the new method has better applicability than traditional numerical methods in solving such coupled nonlinear systems. More importantly, the EPINNs is more accurate, stable, and fast than the traditional physics-informed neural networks. This work provides a simple and high-performance numerical tool for addressing PNPs with arbitrary boundary shapes and boundary conditions.